Near‐Field Nano‐Optical Imaging of van der Waals Materials

Abstract

2D van der Waals (vdW) materials are emerging as the next generation platform for optical and electronic devices with their wide coverage of the energy bandgaps. The strong light–matter interactions in 2D vdW layers allow for exploring novel optical and electronic phenomena such as 2D polaritons exhibiting ultrahigh field confinement, defects‐induced new quantum states, and strain‐modulated quantum confinement of 2D excitons. Far‐field optical imaging techniques are extensively used to characterize the 2D vdW materials so far, however, subdiffraction spatial resolution is required for comprehensive investigations of 2D vdW materials of which physical properties are greatly influenced by local defects and strain. This article aims to cover historical advances, fundamental principles, and distinct features of emerging near‐field optical imaging techniques: scattering‐type scanning near‐field optical microscopy, tip‐enhanced Raman spectroscopy, tip‐enhanced photoluminescence techniques, and photo‐induced force microscopy. The recent developments toward spectroscopic analysis of near‐field imaging and applications for unveiling unique properties of 2D polaritons, nanoscale defects, and mechanical strains in 2D vdW materials, are also discussed. This review article provides an understanding of emerging near‐field imaging techniques and suggests prospective applications for exploring 2D vdW materials.

Introduction

Since the discovery of graphene (single layer of bulk graphite) in 2004, the rapid growth in the research of atomically thin materials has led to a rampant interest in extending the 2D materials toward applications to enable the next generation of electronics technology beyond Moore's law. Nevertheless, the actualization of novel applications and future technologies based on 2D materials necessitate extensive understanding and characterization of the unique properties within this new class of materials. Atomic force microscopy (AFM) and scanning tunneling microscopy (STM) methods can image surface structures at the sub-nanometer resolution but are not capable of revealing optical responses (e.g., refractive index and quasiparticles) and not sensitive to resolving chemical heterogeneity (i.e., unable to image molecular vibrational spectra).^[1–6] The well-established scanning electron microscopy (SEM) provides energy dispersive X-ray analysis of elements but no molecular information.^[7] Moreover, transmission electron microscopy is suited for internal structural analysis and is not ideal for investigating surface and interfacial behaviors.^[8] Integrating spectroscopy with optical microscopy techniques, confocal optical microscopy leverages far-field optical imaging to measure optical responses such as Raman scattering, photoluminescence (PL), and optical absorption without stringent probing conditions (e.g., vacuum/low-temperature environment or sample preparation).^[9–11] The challenge with the confocal method based on far-field signal is low surface sensitivity and the diffraction limit producing a coarse spatial resolution of a few hundreds of nanometers (≈300 nm), which is insufficient for analyzing nanoparticles with dimensions below 100 nm and for distinguishing the characteristics of nanoscale defects such as edge defects.^[7,9] Recent advancements in far-field localization techniques report achieving a high lateral resolution of 20 nm but depend primarily on fluorescence and require sample preparation (i.e., dilution and labeling using dyes).^[12] The characterization of desirable phenomena such as nanoscale structural defects (e.g., grain boundaries, wrinkles, and spatial distribution of local charge carriers) in the subdiffraction length scales requires ultrahigh spatial resolution optical imaging and spectroscopy. Near-field optical imaging (and spectroscopy) represents a critical methodology to comprehensively investigate 2D materials and their unique properties.

2D materials exhibit exclusive and desirable properties compared to their bulk counterparts. The prominent monolayer graphene, a planar sheet of densely packed sp²-bonded carbon atoms in a honeycomb crystal lattice with single-atom thickness, showcases superior mechanical strength, carrier mobilities, and unique band structure. Previous works from the literature demonstrate intriguing electrical, thermal, mechanical, optical, and magnetic properties in graphene that are not present in graphite_.^[13–15] The isolation of a single graphene layer from bulk graphite using adhesive tape also reveals the weak interlayer van der Waals (vdW) forces in contrast to the strong intralayer covalent bonds holding the carbon sheet together. The interaction energy (10⁻²–10⁻¹ kJ mol⁻¹) of the vdW force is 2–3 orders of magnitude lower than that of ionic or covalent bonds (10²–10³ kJ mol⁻¹).^[16–18] The anisotropic bonding strength of 2D materials provides the foundation for the emergence of vdW material systems. Accordingly, the integration of similar or dissimilar 2D materials by stacking the individual layers to fabricate novel vdW heterostructures further extends the possibilities of 2D materials toward their implementation for potential applications that include electronics and optoelectronics. Despite the significant findings, shortcomings of the semimetallic graphene such as the zero bandgap deter its implementation as semiconductor, which leads to the recent rise in transition metal dichalcogenides (TMDs) and their integrations toward vdW heterostructures.^[19] High-quality heterostructures are typically synthesized using conventional chemical vapor deposition (CVD) methods, but they are limited to materials with similar chemical compositions and lattice structures (i.e., same elemental group).^[16,20] The compatibility limitations are overcome by the mechanical stacking (i.e., vertical, lateral, twisted, and mixed-dimensional integration) of 2D vdW layers as the interlayer vdW forces bind two disparate 2D materials. This provides a revolutionary platform to design and engineer the combination of many different 2D materials without detrimental effects caused by substantial interfacial strain or lattice (or chemical) disorder. The artificial integration through the vdW forces allows the intrinsic properties of the constituent materials to be retained while achieving novel heterostructure functions that combine the intrinsic advantages of the individual layers.

TMDs, in the form of MX₂, are a family of 2D materials based on a transition metal layer (M) intercalated between two chalcogen layers (X₂). Atomically thin TMDs exhibit direct electronic and optical bandgaps in the monolayer, unlike their bulk counterparts with an indirect bandgap. The weak interlayer bonding of the monolayer TMDs owing to the vdW force allows them to be mechanically or chemically exfoliated into mono or few layers.^[21] Without the crystal lattice matching constraint, the ability to stack different TMDs beyond graphene and other 2D materials such as nitrides (e.g., hexagonal boron nitride (hBN)), phosphorenes (e.g., black phosphorus), and MXenes (e.g., Ti₃C₂T_x) expands the synthesis of a wide variety of vdW heterostructures to enable unique properties not present in their respective isolated monolayer state. The versatile yet effective strain engineering (Figure 1a), such as lattice mismatch, elastic stretching, strain gradient, and compressive pressure, provides a structural approach to tailor the electronic band structures and the quantum states subsequent to the assembly of 2D layered materials.^[22,23] Since vdW heterostructures are sensitive to interfacial commensurability, modulation of the stacking characteristics, such as controlling the stacking sequence, twist angle, strain, or defects can generate moiré patterns due to incommensurate layer stacking. Recent studies have revealed that such novel moiré engineering demonstrates the potential to further tune the bandgap, interlayer excitons, and optical absorption.^[19,24–26] Moreover, the widespread attention of novel vdW heterostructures has extended to the investigation of implementing Janus materials (e.g., MoSSe and WSSe), which showcase distinctive properties due to their mirror asymmetric layer structures. The intrinsic intralayer polarization of Janus materials couples with the interlayer polarization to provide an additional degree of freedom to tune the physical and chemical properties of the heterostructure.^[27] Overall, the emerging class of vdW heterostructures augments the design and combination of different 2D layered materials to obtain tailored properties for a wide range of applications such as optoelectronic sensors, energy storage, medicine, catalysis, and thermal management.^[14,27–30] As superior candidates to replace conventional bulk materials, 2D vdW materials, and their heterostructures can provide revolutionary functionalities beyond their integration in current applications, such as optics and optoelectronics. Nevertheless, the advancement in research and development of vdW materials, which is still in the early stage, requires an extensive investigation of the layer-dependent properties and their hybrid derivatives to utilize different vdW heterostructures.

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Advances and Principles of Near-Field Optical Imaging Techniques

Near-field optical imaging surpasses far-field optical imaging in terms of spatial resolution and therefore represents an attractive approach to characterize nanoscale materials. Most of the near-field investigations were yet limited to spatial mappings at fixed wavelengths, and there has been growing interest for spectroscopic analyses to explore spectrally resolved dielectric functions and electronic band structures of vdW materials. With vdW materials being in the atomically thin length scale, near-field optical imaging with subdiffraction spatial resolution enables comprehensive investigations of the physical properties of low-dimensional systems. For instance, tensile/compressive strain, doping, defects, stacking, electric field, and chemical modification represent critical properties to fully understand the intra, interlayer, and interfacial effects of vdW heterostructures.^[35] In particular, the behaviors of the straddling type-I, staggered type-II, and broken-gap type-III energy band alignments of different vdW heterostructures necessitate the investigation of the heterojunction.^[34,36] Furthermore, the quality as determined by the edges, grain boundaries, local strain, chemical bonding, molecular orientation, and presence of nanoscale defects in the constituent monolayers greatly influence their properties. 2D materials are susceptible to localized defects originated from vacancies, disorder, dopants, and edge interface (Figure 1b), which considerably impact their chemical, electrical, and optical responses or introduce intriguing functionalities (e.g., color centers).^[24,36,37] As PL signal becomes significant and distinctive with the reduction of materials from bulk to monolayer states, defects can also shift and change the PL spectra. The elimination of folding, wrinkles, tearing, and contamination or impurities during the synthesis and assembly of the vdW heterostructures remains a challenge to realize large-scale fabrication, especially for defect-free large-area material synthesis. Nevertheless, the imminent setback is the ability to comprehensively study the location and density of defects and distinguish the defects based on their intrinsic, material synthesis, or postprocessing origin.^[38] In addition to the material quality, the exploration of polaritonic modes such as plasmon polaritons (PPs), exciton polaritons (EPs), and phonon polaritons (PhPs) to enable the study of quantum phenomena and electrical tunability of vdW heterostructures has recently attracted immense research interest but requires advanced optical imaging methods to investigate the physics and interactions of intralayer polaritonic waves and their modulation owing to interlayer couplings.^[39–41] Furthermore, the engineering of strain and defect enables polariton formation which also alters the light–matter interaction (Figure 1c). As designs of nanoscale material structures become more complex, the emergence of near-field optical imaging techniques in recent decades exemplifies the passage to unravel the aforementioned challenges to propel vdW material systems beyond the rudimentary stage after their discovery.

The first near-field optical imaging technique is scanning near-field optical microscopy (SNOM) demonstrated independently by Pohl et al.^[42] and Lewis and co-workers^[43] in 1984. SNOM combined optical microscopy and scanning probe microscopy (e.g., STM and AFM) that was developed around the same time (AFM was introduced in 1986 by Binnig et al.^[44]) for surface structural study at the nanoscale resolution. SNOM implements a tapered optical fiber probe tip that is metal-coated except at the tip with a nanoaperture of diameter of ≈50–100 nm, in which the aperture size corresponds to the practical spatial resolution (Figure 2a).^[45,46] This subwavelength resolution in the probing of near-field signals on sample surfaces breaks the constraint determined by the optical diffraction limit, where the achievable resolution with optical light is ≈200 nm.^[47] The SNOM modes of operation are divided into three different imaging approaches. First, the transmission mode involves light propagating through the sample and the tip can be used for illumination or detection, but this mode is restricted to probing transparent samples. Meanwhile, the reflection mode is designated for opaque samples but suffers from strong background signals. Also applicable for opaque samples, the illumination-collection mode uses the tip for both light emission and collection but is prone to weak signal intensity because of the small aperture size leading to low light collection efficiency.^[38] Aperture-based SNOM is beneficial for fluorescence labeling and imaging in biomedical applications because the highly localized irradiation mitigates far-field background signal to suppress photobleaching of the sample region near the tip.^[10,12,48] Despite the groundbreaking development in near-field microscopy up until then, SNOM is less suitable and insufficient for a wide range of nanoscale applications involving 2D materials, namely, vdW materials and their heterostructures. SNOM suffers from low surface sensitivity owing to the very low light transmissivity of the probe, which is inversely proportional to the fourth power of the aperture size, as the evanescent wave intensity decays exponentially toward the aperture.^[49] The optical throughput is low owing to the light being absorbed or reflected internally within the probe.^[50,51] Furthermore, the fiber-based probes restrict the input power intensity due to the thermal damage threshold of the metal coating on the probe tip. In addition to the poor signal-to-noise ratio of SNOM, other issues with optical fibers (e.g., optical loss, polarization change, and dispersion) greatly limit the applications of SNOM.^[52–54] For instance, pulse-broadening due to the optical nonlinear and dispersion effects of the fiber-based probe complicates dynamic studies as it alters the ultrafast (e.g., femtosecond) optical pulses, where the periodic thermal expansion/contraction of fiber probe exacerbates time-resolved SNOM applications by generating artifacts in the near-field signal.^[50,55–57]

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Subsequently, the introduction of scattering-type scanning near-field optical microscopy (s-SNOM) and then the realization of the technique by Wickramasinghe and co-workers^[58] in 1995^[52] enabled optical imaging beyond the diffraction limit at the atomic resolution by accessing evanescent waves. While SNOM is limited to specific wavelength regions considering the transmission coefficient, the apertureless approach of s-SNOM widens the application range from visible to infrared light.^[59] Using broadband illumination, hyperspectral nanoimaging was enabled by recording a nano Fourier transform infrared (FTIR) spectrum at each pixel of 2D map.^[60,61] Stemmed from the tip-based scanning probe microscopy, a metallic or metal-coated AFM probe tip (mechanical cantilever) is implemented where the incident light beam is nano-focused and then scattered at the apertureless tip apex owing to the tip–sample polarization (Figure 2b). The scattered evanescent wave is subsequently converted into a propagating wave that is detected at the far-field by a photodetector, and the detected signal contains the collected nanoscopic information beneath the tip that is not limited by the wavelength of the incident light. The achievable spatial resolution of s-SNOM (<10 nm) is limited by the tip apex radius, which is correlated with the available fabrication technique.^[62,63] The primary modes of operation include the interferometric (for refractive index measurement), and non-interferometric mode (for inelastic-scattering measurement, suitable for Raman/PL) configurations working in transmission or reflection mode, which are further differentiated by the detection schemes (e.g., homodyne, heterodyne, and pseudo-heterodyne).

In tapping or dynamic noncontact AFM mode s-SNOM, background signal demodulation through interferometer is necessary to extract genuine near-field scattering signal consisted of their spectral amplitude and phase. Adjusting the optical path length, the phase of the reference field can be changed, implementing homo or heterodyne amplification of near-field signal.^[46] In homodyne amplification, both the amplitude and phase of the scattered near field are determined by measuring the magnitude of the s-SNOM with the same frequency of reference wave and tip oscillation, however, heterodyne implements different frequency between them. Alternatively, the advanced technique, pseudo-heterodyne provides improved multiplicative background suppression by modulating the reference phase.^[64] According to the calculation, higher demodulation order of tip oscillation harmonics achieves the background contribution reaching to zero more quickly than the near-field signal over the entire spectral range.^[65]

Reported independently by Stöckle et al.,^[66] Hayazawa et al.,^[67] Anderson,^[68] and Pettinger et al.^[69] in 2000, tip-enhanced spectroscopy improves upon s-SNOM by integrating a plasmonic probe tip, typically coated with Au or Ag (Figure 2c). Tip-enhanced techniques encompass a wide range of optical characterization to probe elastic scattering, inelastic scattering (e.g., Raman scattering), and other nonlinear optical responses. The incorporation of a plasmonic probe in the tip-enhanced approach benefits from plasmonic field enhancement, in which the nonlinear dependence of signal on the local field strength leads to an amplified near-field signal to suppress the weaker background contribution.^[70] Accordingly, the near-field signal at the hot spot, or the nanogap between the excited molecules and the tip apex, is significantly boosted owing to the irradiation of the incident light confined at the tip–sample junction. Previously, the introduction of surface-enhanced Raman spectroscopy (SERS) was demonstrated as a powerful nanoscale optical imaging and spectroscopy technique due to its high surface sensitivity. However, SERS shows compromises in achieving high spatial resolution because the field enhancement appears at a distribution of hot spots and ultimately produces averaged signals.^[71] Meanwhile, tip-enhanced Raman spectroscopy (TERS), similar to the operating principles of SERS, overcomes this limitation as the enhancement effect concentrates on the localized hot spot at the tip apex. The near-field signal enhancement ensures consistent intensity and repeatable measurements at each sample position without influences from the surrounding region due to the averaging effect of the detected signals. In practice, demodulation of TERS signals with tip engaged and retracted is necessary owing to intricate factors contributing to the field enhancement.^[72,73] The field enhancement in SERS and TERS is attributed to the primary electromagnetic mechanism (i.e., surface plasmon resonance effect) and the chemical mechanism (i.e., charge transfer). The induced surface plasmon resonance primarily contributes to amplifying the local field enhancement at the tip apex (acting as an optical nanoantenna) to increase the sensitivity and subsequently the near-field signal for detection. The modulation of the tip apex geometry (e.g., radius, angle, and morphology) can further optimize the field enhancement, but its complexity is determined by the fabrication capabilities. Nevertheless, strong intrinsic local field enhancement is necessary to obtain high signal-to-noise ratios.

Compared to far-field techniques, the polarization-dependent field effect strongly influences the phonon modes and excitonic states. Notably, the polarization of the light irradiation originates from the localized surface plasmon resonance and the lightning rod effect at the tip apex. The predominant field enhancement maximizes at p-polarization (i.e., parallel to the tip axis) and continuously decreases when changing to s-polarization (i.e., perpendicular to the tip axis). Correspondingly, a significant field enhancement in TERS enables the probing of IR-active modes and higher-order (e.g., overtone and combinational) modes. The weak near-field (Raman scattering) signal with conventional Raman spectroscopy techniques can be largely enhanced by several orders of magnitude in TERS.^[17,74,75] The adoption of metallic substrates induces stronger tip–sample coupling to generate substantial field enhancement compared to the enhancement from a standalone plasmonic tip.^[76,77] Correspondingly, the field gradient effect owing to further field enhancement from the plasmonic substrate alters the selection rules. As in any scattering setup, mapping of the full phonon dispersion is often limited by selection rules. The selection rules prohibit the observation of certain phonon modes (e.g., odd parity phonon), and this is due to the presence of symmetries because of momentum conservation.^[76–78] TERS imaging is compatible with rough surface morphology, in which rough surfaces lead to largely localized field enhancement in TERS to dominate the far-field background signal to prove higher signal-to-noise ratio compared to SNOM/s-SNOM, where the nearby scattered light complicates signal detection.^[75,79,80] The enhanced signal consequently widens the applications for studying soft and biological samples.^[52,81] TERS can also accommodate various probing environments such as ambient air, ultrahigh vacuum, or liquid solutions.^[74,82] Overall, TERS enables spectroscopic characterization and identification of vibration modes from in-plane or out-of plane strain, defects, and interlayer coupling in vdW heterostructures with high surface sensitivity and resolution (<10 nm).^[83,84] Similar principles have been applied to enable tip-enhanced photoluminescence (TEPL) to provide optoelectronic properties of samples of interest.^[85] The field enhancement factor of TEPL is correlated with the excitation rate and the photoexcited spontaneous emission rate. The resultant PL intensity and peak position demonstrates excitonic emission as TMDs are optically pumped, where the PL signal enhances for monolayers but quenches for multiple layers due to the transition from indirect to direct bandgap.^[34,86–88]

Despite the progress of tip-enhanced spectroscopy techniques, inefficiency owing to the inherent far-field background signal in the detection scheme restrains optical and chemical imaging of 2D materials at the atomically thin limit at high spectral resolution, especially for the characterization of nanoscale structural defects.^[87] The showcase of photo-induced force microscopy (PiFM) by Rajapaksa et al.^[89] in 2010 circumvents the challenges associated with s-SNOM and its successors. The PiFM technique exploits tip–sample force interactions induced by the highly enhanced field that is then detected via noncontact or tapping-mode AFM to enable nondestructive and label-free imaging (Figure 2d). The operating principle of PiFM compared against SNOM, s-SNOM, and TERS/TEPL is shown schematically in Table 1. PiFM uses a precise and tunable laser source to provide higher thermal stability and improved signal strength. The distinctive force gradient detection of PiFM provides a high signal-to-noise ratio by eliminating background scattering as in other optical spectroscopic techniques that rely on optical feedback. The photo-induced force can be attributed to several factors as detailed in previous studies.^[90–93] PiFM leverages near-field extraction of the attractive photo-induced force (typically at pN or less) confined at the tip–sample junction rather than collecting scattered signal at the far-field that contains a contribution from the propagating background interference.^[90,94] The optomechanical response detection of PiFM enables spatial resolution below 10 nm without the high harmonic demodulation process. Consequently, PiFM provides simultaneous imaging of topographic and spectroscopic information in vdW materials and their heterostructures.^[95–97] Also, due to competing optical effects in the visible spectrum, the visible PiFM spectroscopy is more complicated than mapping the PiFM signal at a fixed wavelength.

Table 1 Comparison of the operating principles for the different nano-optical imaging techniques

	SNOM	s-SNOM	TERS/TEPL	PiFM
Spatial resolution	≈50–100 nm	<10 nm	<10 nm	<10 nm
Aperture
Detection	Light	Elastically scattered light	Inelastically scattered light	Force gradient

In contrast to AFM-based infrared spectroscopy (AFM-IR) techniques relying on thermal expansion from the photoabsorption in the sample that reduces surface sensitivity and spatial resolution, PiFM represents an advantageous approach since it instead measures the electromagnetic force generated from the external optical field to mitigate issues such as thermal drift or heat diffusion effects.^[92] Furthermore, AFM-IR is restricted to operating in contact or tapping modes, where the probe tip engages in direct contact with the sample during raster scanning, and depends on repulsive contact force interactions. By contrast, PiFM operates in noncontact or tapping mode and avoids tip–sample damage (i.e., tip contamination and sample deformation due to dragging tip) and instability in the contact resonance and quality factor.^[98] Correspondingly, PiFM can perform nanoscale chemical imaging as well as optical phonon polariton imaging and accommodate organic and inorganic samples.^[91,94]

PiFM is sensitive to the electromagnetic forces generated from the local polarization of the sample, where there exists the optical tweezer force (exerted on the tip in free space), dipole–dipole interaction force (between the tip and small polarizable sample particle), and image dipole force (between the tip and semi-infinite substrate). Depending on the tip–sample distance, the attractive gradient force dominates at only a few nm and reveals optical properties of the sample while the repulsive scattering force dominates at larger distances. Accordingly, the measurement of the force gradient through heterodyne detection suppresses the contributions owing to the scattering force and the photothermal effect on the cantilever, where the laser excitation impacts the cantilever dynamics.^[99–103] The PiFM signal also involves photothermal force originating from the sample expansion after optical absorption that is mediated by the noncontact vdW force, which is termed the thermally modulated vdW force. In addition, there is the thermally induced photoacoustic force due to acoustic wave propagation (in a nonvacuum medium) and the optomechanical damping caused by the vibrating cantilever. Nevertheless, full understanding of the complex mechanisms contributing to the PiFM signal remains unclear and thus necessitates further investigation to enable quantitative assessment and establish PiFM as the epitome of nano-optical imaging of vdW materials.

In the following section, we summarize recent works on the light–matter investigation of 2D vdW materials and their heterostructures using s-SNOM, TERS/TEPL, and PiFM. First, we discuss the unique properties of quasiparticles revealed by near-field imaging techniques. Next, we present the characterization of nanoscale defects. In addition, we further discuss the nanoscale strain characterization enabled by near-field imaging. Finally, we provide a brief outlook on the existing challenges and future development prospects of various emerging near-field nano-optical imaging techniques.

Near-Field Interrogations of vdW Materials and Heterostructures

Unveiling Unique Light–Matter Interaction via Near-Field Optical Microscopy

In nano-optics, light trapping and manipulation at nanoscale below the optical wavelength have been intensively explored to enhance the electric field, which results in stronger light–matter interaction.^{[40,104–106]} Under light illumination, electric dipoles in materials can be excited generating electromagnetic quasiparticles, termed polaritons,^[104,105] which appear as electromagnetic modes at the interface between a positive and a negative permittivity material.^[40,106] Polaritons associated with oscillations of conduction electrons, electron–hole pairs, and vibrations of polar insulators are PPs, EPs, and PhPs, respectively.^[104,107]

Atomically thin layers of 2D materials offer a promising platform for strong light–matter interactions, such as enhancing optical absorption, manipulating the light propagation velocities, guiding light generation and propagation, and metasurface engineering for hyperlenses or superlenses.^{[105,106,108]} Unique properties of 2D polaritons have been widely explored by optical far-field, optical near-field (e.g., s-SNOM, TERS/TEPL, and PiFM) and electron spectroscopy (e.g., electron energy loss spectroscopy) methods to overcome the momentum mismatch.^[105,107] To detect 2D polaritons, far-field spectroscopy can cover a broad spectral range but spatial resolution is limited by Abbe diffraction. Electronic spectroscopy can realize higher spatial resolution than optical methods due to the short de Broglie wavelength; however, the detection of low-energy polaritons is still a challenge.^[105] In this section, we begin by discussing near-field imaging and spectroscopy techniques for detecting 2D polaritons.

s-SNOM Imaging of 2D Optical Response

s-SNOM facilitates imaging of propagating polaritons in real space with an ultrahigh spatial resolution of less than several tens of nanometers.^[104,105] A sharp AFM tip, of which the radius determines the spatial resolution of the imaging is used as an optical antenna, to generate local electric field concentration of polariton wave. The near-field s-SNOM amplitude, s(ω) represents real-space variations in the local electric field underneath the tip.^[109,110]

Fei et al. reported 2D plasmon excitations of Dirac fermions in graphene/SiO₂/Si by monitoring s-SNOM amplitude (s(ω)) and phase (ϕ(ω)) spectra for graphene/SiO₂ and SiO₂ substrates in mid-IR region from 883 to 1270 cm⁻¹.^[109] By modeling the apex of the tip as a point dipole and calculating the reflection coefficient at P-polarized light excitation, experimental s(ω) and ϕ(ω) spectra were revealed to show resonance due to the Dirac plasmon in graphene. The strongly enhanced s(ω) in 1110 to 1250 cm⁻¹ spectral region and its gate voltage dependence at 1150 cm⁻¹ only in graphene/SiO₂ originated from the high density of mobile carriers in graphene with the increased group velocity. A steep increase of ϕ(ω) below 970 cm⁻¹ in graphene/SiO₂ is attributed to the direct near-field coupling to the Dirac plasmon in graphene due to the relatively weak coupling strength of plasmon–phonon at graphene/SiO₂ interface at low frequency.

The first observation of PPs in graphene was exhibited by s-SNOM imaging in real space.^[110,111] The metal-coated AFM tip scatters incident free-space light into PPs in graphene and further produces momentum to overcome the momentum mismatch between free-space light and confined PPs. When PPs with complex wavevector, q, propagate toward the edge of the graphene and reflect toward the tip, s-SNOM can detect the out-scattered light due to the interference between the reflected and incident PPs. The spacing between the scanned fringes represents a half wavelength of PPs, π/Re[q], and the fringes decay exponentially as (−Im[q]x).^[110–112] To probe the graphene plasmons, the light with a frequency of ω = 892 cm⁻¹ corresponding to wavelength 11.2 µm was used, to prevent the strong coupling of plasmon–phonon supported in graphene/SiO₂ interface. By applying back gate voltage in graphene/SiO₂/Si structure, tuning plasmon momentum with carrier density in graphene could be monitored by measuring the wavelength of PPs in s-SNOM, due to the Dirac-like dispersion of Fermi energy in graphene.^[110,111] The wavelength of PPs and damping rates captured at s(ω) images along with plasmon interferometry quantified the complex optical conductivity of graphene. In addition to observing the PPs’ signature in graphene, s-SNOM techniques were used to investigate the ultrafast dynamics of surface plasmon excitations. Wagner et al. examined near-IR pump and mid-IR probe spectroscopy in graphene/SiO₂/Si based on s-SNOM by combining spatial, spectral, as well as 200 fs temporal resolution.^[113] The near-IR light-induced changes of s(ω) and spectral features were explicitly compared with electrical gating-induced changes, which modulate the effective electron temperature associated with graphene plasmonic resonance. Ultrafast plasmonic tuning in graphene was realized even at 1200 cm⁻¹ pump pulses near the SiO₂ surface phonon modes (1125 cm⁻¹), which give rise to substantial plasmon–phonon coupling.

At the edge of the graphene on SiO₂ substrate, s-SNOM and AFM-IR imaging showed qualitative correspondence with the oscillation fringe spacings (Figure 3a).^[114] While s-SNOM detects surface plasmon polariton (SPP) interference patterns with complex values of near-field which is proportional to the local SPP field, AFM-IR mechanically detects the thermal expansion following light absorption and SPP decay, giving rise to a measured amplitude is proportional to local SPP electric field intensity. In particular, the AFM-IR signal (Figure 3a, bottom) showed a higher SPP fringe contrast across the graphene edge than s-SNOM imaginary signal (Figure 3a, center), which was attributed to the fundamental differences of two techniques. In s-SNOM, the tip acts as a local scattering center providing momentum for SPP propagation, and also detects the signal in an interferometric manner. Therefore, observed standing wave is the superposition of resonant local SPP and reflected SPP field.^[44,45] By contrast, AFM-IR measures collected averaged signals from photothermal expansion regardless of the polarization direction, capturing all nonorientation-sensitive sample information, contributing higher SPP fringe contrast than s-SNOM.^[115] Such comparison of s-SNOM and AFM-IR intensity maps at the same frequency suggested a new way of imaging SPP interference at specific energy and SPP decay via ohmic losses within graphene or evanescent coupling of SPP field to heavily damped SiO₂ substrate phonon modes.

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The role of the s-SNOM tip on both surface plasmon resonance and SPPs was examined further in the following research on graphene nanoribbons.^[117] Hu et al. compared the s-SNOM images of graphene nanoribbons that are aligned parallel and perpendicular to the in-plane component electric field and observed symmetric and asymmetric plasmonic interference fringes, respectively. They concluded that asymmetric fringes are from the superposition of localized surface plasmon resonance excited by graphene nanoribbons and propagating SPPs launched by the s-SNOM tip, different from symmetric fringes from only tip-launched SPP modes. The localized plasmon modes along the graphene nanoribbons were strongly dependent on the size of the graphene pattern, the aligned angles, the wavelength of IR excitation, and the edge structure of graphene (i.e., zigzag or armchair).^[117,118]

Recently, s-SNOM measurements in monolayer and few-layer graphene heterostructures were utilized to reconstruct the complex optical conductivity resonance and their plasmonic dispersion behaviors under gate-tuning.^[119–121] In a dual-gating structure consisting of monolayer graphene as the top gate as well as plasmon wavelength magnifier, and bilayer graphene with Au back gate, s-SNOM field patterns were imaged under a fixed top voltage and variable back gate voltage.^[119] To explain dispersion behaviors change under back gate voltage modulation, plasmon wavelength was extracted from the Fourier transform of the field patterns in s-SNOM image and the band structure of bilayer graphene was calculated from the tight-binding approximation. The calculations revealed that the Fermi energy and bandgap can be tuned independently in the bilayer graphene with an asymmetric band structure. Moreover, local IR phonon characteristics of few-layer graphene were explained by the fact that IR phonon intensity extracted from s-SNOM intensity decreased with increasing the laser power, which stems from the strong coupling between phonons and nonequilibrium hot electrons.^[121] These research results on graphene PPs and PhPs enabled the establishment of ground principles for exploring polaritons in 2D materials and manipulating electron–phonon interactions.

EPs are half-light and half-matter quasiparticles resulting from strong coupling of the electromagnetic dipolar oscillations of excitons and photons in the microcavity. EPs’ long-distance propagation and the splitting of polaritonic branches into lower and upper modes in the strong coupling regime are believed to affect energy and information transfer in future photonic and quantum technologies.^[122–125] Large exciton binding energies in TMDs enable stable polariton formation even at room temperature through the strongly coupled cavity EPs.^[122–125] For monolayer TMDs, they should be placed in an optical cavity so that these excitons can couple with cavity photons and form an out-of-plane propagating EPs since real part of dielectric constant in TMDs is positive. In-plane propagating EP modes of monolayer TMDs were only predicted when TMDs are encapsulated with hBN and cooled to cryogenic temperature, attaining negative dielectric constant, however, it was not yet observed in experiments.^[126]

s-SNOM has also been used to examine EPs in multilayer TMDs, whose large refractive indices enable sustaining Fabry–Perot resonance modes without any external cavity.^[127] The nano-optical imaging of waveguide modes inside WSe₂ and MoSe₂ exhibited signatures of coupling between waveguide photons and excitons.^[122,125] From the s-SNOM signal map of a 120-nm-thick WSe₂ flake at 850 nm (1.46 eV) excitation (Figure 3b), interference fringe periodicity equal to the wavelength of the mode was determined by Fourier transform analysis of the real-space profile.^[125] Two peaks (TM₀ and TE₀) in FT analysis corresponded to the momenta (q = 2π/λ_p) of the in-plane modes with interference fringe periodicity (λ_p) above the far-field photon energy line (q = 1.46 k₀). Based on the extracted λ_p through fringe analyses, energy-momentum dispersion relation of the waveguide mode can be constructed, and the waveguide modes close to the exciton resonance are classified as EPs. As the excitation wavelength decreases (from 900 to 760 nm), the intensity of fringe profiles on WSe₂ significantly decreased, indicating the damping of EP modes becomes larger at shorter wavelength. The propagation length of the EPs was demonstrated with the interference between photons collected from different paths, including the mode from incident photons scattered directly by the s-SNOM tip and tip-launched in-plane propagative mode.^[122] Small wavelengths of EPs (down to 300 nm) and long propagation lengths (up to 12 µm) of multilayer TMDs under ambient conditions were uncovered through s-SNOM technique. Furthermore, the thickness and excitation photon energy dependence results of the EP modes in TMDs provided rigorous understanding to utilize TMDs as self-hybridized waveguides.

The hyperbolic materials with dielectric permittivity of opposite signs in different principal axes can confine long-wavelength electromagnetic fields to the nanoscale.^{[116,128–131]} Representative hyperbolic PhPs in hBN, having low loss in the upper Reststrahlen (RS) band (1370–1610 cm⁻¹) were also imaged employing s-SNOM techniques. Standing waves produced in hBN by the interference of tip-launched propagating PhPs and the reflections at their edge indicate that the lattice vibrations and PhPs were locally enhanced.^[116] The near-field interference patterns in s-SNOM are compared with photothermal microscopy where the light-driven local interaction between surface and tip was imaged via detecting the mechanical oscillation of cantilevers (Figure 3c).^[116] The corresponding periodicity in the two methods revealed that the enhanced lattice vibrations were induced by the enhanced radiative heat transfer mediated by PhPs. Although it has been observed that the spatial pattern of polaritonic fringes in AFM-IR was comparable to that in s-SNOM with equal resolution, the signal-generating mechanism in AFM-IR was different from s-SNOM. AFM-IR detects the photothermal expansion when the polaritonic waves launched by the metallic tip constructively interfere with those reflected from the edges. The consistency between s-SNOM and AFM-IR fringes stems from the fact that stronger polaritonic waves cause more energy absorption and dissipation after the decay of PPs and PhPs.^[114,129]

In situ measurements in probing features of EPs and PhPs, various methods of s-SNOM were implemented such as time-resolved techniques, cryogenic measurements, and changing the surrounding materials for further exploration. In particular, the transient dynamics with ultrafast pump-probe techniques contributed to direct visualizations of the formation and propagation of PPs in graphene,^[132] EPs in TMDs,^[123] and PhPs in hBN.^[124] The high spatial resolution and temporal resolution with this method have shown real space information of the polaritons, such as EPs formation process, propagation length, field distribution, and exciton coupling.^{[114,126,127,134]} For imaging ultrafast polariton behaviors with s-SNOM, the setup similar to FTIR with ultrafast probing laser and reference beam or pump-probe setup combining a pump light with wavelength shorter than the probe light focused onto the tip have been carried out in the IR to THz range. The probe beam arriving at various time delays after pumping detects the photoexcited electrons and their recovery to thermal equilibrium.^[133] Near-field pump-probe setup revealed time-resolved changes of spectrally integrated near-field amplitude in different layers of graphene showing the relaxation process from the interaction of Dirac plasmons in graphene and surface phonons of the SiO₂ substrate.^[113] Also, ultrafast EPs in WSe₂ flake captured by near-field signal with different time delay realized the modification of the dielectric function by intense laser around the exciton resonance, called renormalization, slowing the group velocity of EPs.^{[ 61,126,135]}

In addition, cryogenic s-SNOM and the normal-incidence transflection mode s-SNOM in liquid were realized to observe the long-lived and ultraconfined PhPs in hBN, respectively.^[130,131] Propagation lengths of more than 8 µm and lifetimes of more than 5 ps have been identified close to liquid-nitrogen temperatures due to lower losses for hyperbolic PhPs in isotropic hBN.^[130] The dispersion of hBN PhPs in liquid environment providing increased permittivity shifted to higher momentum due to field confinement near the hBN surface, resulting in compressed wavelength of PhPs.^[131] Recently, atomically flat and low-loss monocrystalline gold flakes substrates were introduced for near-field probing of image polaritons, eventually allowing the complex propagation constant of hyperbolic PhPs in hBN to be measured.^[134] PhPs launched in hBN capping layers exhibited reflection at domain wall and enabled visualizing the moiré structure in bilayer graphene sandwiched with hBN, which suggested in situ method to manipulate the local conductivity of vdW heterostructures using PhPs.^[135]

Under broadband near-field light excitation, s-SNOM can detect wavelength-dependent near-field amplitude and phase spectrum simultaneously, providing access to the complex dielectric function. The real and imaginary value of dielectric constant can be represented as spectral amplitude and phase. Hyperspectral s-SNOM in MoSe₂/WSe₂ heterobilayers was reported in the visible/near IR range introducing the pseudo-heterodyne interferometry to determine the genuine near-field scattering amplitude and phase in high harmonic data.^[61] In the mid-IR range, the second or third harmonics in pseudo-heterodyne interferometeric detection sufficiently provided nearly background free data,^[64,65] however, the shorter wavelength of visible light gives rise to an artificial background resulting from more scattering in AFM tip and phase change by optical path length drift. As a result, higher demodulation order of 5 was used to ensure the background-free signals in visible-range s-SNOM. Zhang et al. revealed the strong exciton responses of each monolayer TMDs and redshift of the exciton resonance energies in MoSe₂/WSe₂ due to dielectric screening with 20 nm resolution, which was corresponding to spatial resolution.^[61] The s-SNOM spectra and images allowed extracting the Lorentzian form of dielectric function based on the point dipole model and screening length of exciton resonance from spatial evolution of the exciton lines across the interfaces.^[90]

TERS/TEPL Imaging of 2D Optical Response

2D TMDs exhibit high exciton binding energies, providing opportunities to control spin-valley coupling even at room temperature when excitons are coupled with the light, forming stable EPs. The strong Coulomb interaction in TMDs results from weak dielectric screening from surrounding environments, accordingly the interaction between charge carriers is very sensitive to the local dielectric environment.^[136] The formation of exciton, trion, and biexciton and their modulation by surrounding materials in TMDs should be examined in depth to utilize their optical and optoelectronic properties. Micro-Raman spectroscopy, which relies on Raman scattering induced by far-field light interaction with molecular vibrations, phonon, etc., can characterize intra and interlayer information of 2D materials, such as strain, doping concentration, defects, stacking, and the number of layers.^[137] In particular, graphene vibration modes corresponding to 2D and G bands are sensitive to the strain and doping, and the ratio of the D to the G band is used for identifying defect states. Compared to the conventional micro-Raman scattering or micro-PL measurements, TERS and TEPL can achieve spatial resolution below the optical diffraction limit via localized surface plasmon excited by lightning rod effect in metal tip.^[107] Diverse characteristics which can be examined by TERS and TEPL such as lattice vibration, doping effect, and exciton characteristics in nanoscale are expected to realize more specific visualization of polaritonic modes.^[138]

To observe properties of EPs in monolayer TMDs, they should be placed in an optical cavity such as dielectric^[139,140] or metallic mirror^[141,142] structure so that excitons can strongly couple with cavity photons and form propagating EPs.^[126] For quantum dot excitons and cavity plasmon, TEPL spectra in strong coupling regime only showed two clear PL peaks due to large PL enhancement and Rabi splitting.^[143] Even though investigation of EPs in monolayer TMDs through TEPL has not been reported due to their positive dielectric function, tip–sample optical cavity allowed studying exciton characteristics by increased coupling between tip plasmon and exciton.^[9,144] Further, TMD sandwiched between the metal tip and metallic bowtie antenna cavity enabled inducing localized excitons of WS₂ monolayer and probing them with TEPL.^[145] Since tip-induced plasmon enhancement in TEPL generates excess carriers in TMDs and hence causes the doping effect, the exciton species including biexcitons and trions can be stronger than far-field PL.^[9,144] 20 nm spatial resolution which was not achievable in aperture-type SNOM was realized with TEPL for probing excitons and trions in monolayer MoS₂ and WSe₂.^[144,146] When different metal (e.g., Au or Ag) tips were compared in TERS and TEPL measurements, it was discovered that the work function difference between the metal tip and TMDs, followed by hole or electron doping in TMDs, should be considered to improve near-field signals.^[144] Compared with the far-field PL dominated by neutral A excitons, TEPL facilitated observing enhanced B excitons and trions emission intensities. Also, the dependence of distance from metal tip and substrates was investigated to understand the TEPL intensities.^[147] In the coupling regime (≈1 nm), PL responses for neutral excitons and trions were dominating, however, in the direct tunneling regime (≈0.3 nm), tunneling of electrons from metal tip to TMDs facilitated conversion of neutral excitons to trions.^[147,148]

The near-field imaging of lateral and vertical 2D heterostructures has been carried out to understand the localized optical and electronic responses at the interface.^[137,138] TEPL imaging can capture the spatial and spectral changes of PL emission caused by the charge/exciton transfer and exchanges at the heterointerfaces depending on the type of the energy band alignments (e.g., straddling, staggered, or broken gap).^[9,137] Tang et al. demonstrated charge transport and hot electron injection in the depletion region at the interface of lateral WSe₂/MoSe₂ on Si/SiO₂ using near-field TEPL signals and their dependence on the tip–sample distance.^[148] In the classical regime (i.e., 0.36 nm < tip–sample distance < 20 nm), the photo-induced charge transfer and accumulation of injected hot electrons in MoSe₂ led to the gradual decrease of WSe₂ PL signal along with the increase of MoSe₂ PL signal. However, in the quantum regime (<0.36 nm), tunneling-assisted hot electron injection from the plasmonic tip to MoSe₂/WSe₂ resulted in a larger recombination rate than near-field quenching process resulting in an abruptly enhanced MoSe₂ PL signal (Figure 4a).^[148] Shao et al. demonstrated atomic diffusion phenomena at lateral bilayer WS₂/MoS₂ heterojunctions using multimodal nanoscopic study with complementary measurements of TERS/TEPL and Kelvin probe force microscopy (KPFM).^[138] The charge accumulation and atomic diffusion from alloying effects were investigated at the vicinity of the junction considering the excitonic energies of the two materials (Figure 4b). Assuming that the tip apex is not optically responsive to the focused incident 785 nm laser (1.58 eV), the incident photon energy of 1.58 eV is smaller than the indirect bandgap of each material is not expected to change the contact potential difference in KPFM. However, the light-induced surface photovoltage effect was clearly shown, which was attributed to release of the charges from the shallow midgap states. The concentration of W in MoS₂ across the heterojunctions was shown by the redshift of the A exciton at the interface in TEPL spectra and the decreased Raman peak intensity in the region next to the pure WS₂ in TERS spectra.

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Regarding TEPL imaging of vertical TMD/TMD heterostructures, only a few papers were reported due to the low TEPL intensity from charge separation toward each layer.^[72,149] Due to nonradiative charge transfer at type-II band alignment, WSe₂/MoSe₂ heterobilayers have relatively low interlayer emission intensities (1.36 eV) than monolayer WSe₂ (1.63 eV) and MoSe₂ (1.56 eV).^[149] May et al. introduced nano-optical cavity methods to understand the interplay between excitation rate, radiative and non-radiative relaxation of intra and interlayer excitons. Since the distance between the Au plasmonic probe tip and substrate serves as an optical nanocavity in TEPL, the relative rate of the radiative and nonradiative pathways can be controlled by tuning the distance. Using interlayer charge transfer lifetime (44 fs) as a reference clock allowed extracting the long interlayer exciton radiative lifetime (94 ns) from the nonradiative lifetime (0.6 ps) in a rate-equation model.^[113] Rodriguez et al. investigated different combinations of heterobilayers composed MoS₂, MoSe₂, WS₂, and WSe₂ with TEPL characterizations.^[72] Different from MoS₂/WS₂ and MoSe₂/WSe₂, the TEPL spectra of WSe₂/MoS₂ did not show the clear sign of interlayer exciton (e. g., ≈1.55 eV for K–L transition) due to larger lattice mismatch and the offset of energy levels, even in the heterobilayers exhibiting a moiré pattern. They focused on the TEPL energy peak shift caused by different topographic features such as nanobubbles and blisters from transfer-induced contamination and concluded that interlayer exciton PL peak in WSe₂/MoS₂ (≈1.1 eV for K–K transition) can only be seen in optically flat areas with substantial interaction between the layers.

PiFM Imaging of 2D Optical Response

PiFM works by mechanically detecting the photo-induced electromagnetic force between tip and sample, therefore it is much more insensitive to the far-field scattering contributions compared to s-SNOM and TERS/TEPL.^[46,47] Electromagnetic gradient force and thermally induced expansion force are dominantly detected in the sub-nanometer distance between the tip and sample.^[90] In principle, the light-mediated charge oscillations in the tip produce an induced polarization at the optical driving frequency, approximated as an oscillating dipole. The dipole experiences a time-averaged electromagnetic force which is proportional to the gradient of the driving field in the vicinity of the tip and the real or imaginary part of the tip polarizability.^[90] Since PiFM measures the z component of the gradient field, which has the same distribution of the local charge density in Gauss's law, PiFM signal contrast is observed when the tip is placed near the strong local fields supported by polariton modes.^[47,48] PiFM can assist in probing 2D polaritons by acquiring hyperspectral images and capturing the resonant modes in the structure.^[105] It has been used for detecting hBN PhPs and graphene PPs complementary to s-SNOM imaging so far. Even though continuing discussions exist on the origin of the PiFM signals, PiFM has been and is expected to image polaritons (i.e., PhPs, PPs, EPs) in both visible and IR light wavelength ranges.

Tamagnone et al. reported strong light–matter interaction in hBN PhPs with hyperbolic dispersion by comparing s-SNOM and PiFM images and spectra.^[150] In hBN nanodisk, PiFM allowed imaging modes in RS bands and resonant optical modes, which could not be obtained by s-SNOM.^[49] Hyperspectral PiFM images enabled the capture of all the resonant modes in the structure with a single scan, which agreed well with analytical and numerical predictions. Ambrosio et al. experimentally imaged hBN flakes on Au substrates and demonstrated hBN dispersion in the first (730 to 830 cm⁻¹, where out-of-plane permittivity is negative) and second (1370 to 1610 cm⁻¹, where in-plane hBN permittivity is negative) RS bands by both s-SNOM and PiFM.^[151] Through hyperspectral imaging with 2 cm⁻¹ spectral resolution of the modes with PiFM in mid-IR ranges, they experimentally revealed the first RS band as well as the highly confined modes in the second RS band due to the mirror symmetry introduced by Au substrates. The respective PiFM, s-SNOM maps, and line profiles (Figure 5a) show the fringes with single (1240 nm) and double periodicity (610 nm), corresponding to the direct and roundtrip components of the first polaritonic guided modes, respectively. The direct mode originated from the scattering at the sharp edges of hBN, exhibiting the same periodicity as the polariton mode. A roundtrip mode is attributed to polaritonic modes from AFM tip and their coupling into the flakes via reflection at the edge, which produces fringes in the optical image with a periodicity of half the phonon–polariton wavelength. Peaks in the same position of PiFM and s-SNOM fringes thereby indicate the similarity of the origins of two signals, the PhP resonance modes of hBN.

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Liu et al. reported near-field features of graphene plasmon suspended on YbF₃/Au trench under mid-IR illumination using PiFM techniques.^[152] Wave vector mismatch between the graphene plasmon and the light in free space could be compensated by periodic trench structures. Optical force measured in PiFM reflected the interaction between the electric field of graphene plasmons in the normal direction and dipoles in a metal tip, and hence, the magnitude of the optical force was proportional to the field intensity of the graphene plasmon.^[152,153] From the average PiFM spectra for the ridge, trench, and graphene-broken areas (Figure 5b), the interaction between the induced dipoles and tips was carefully compared. Especially, PiFM signal on the trenches with graphene (areas 2 and 4 in Figure 5b) was much stronger than that on the ridges at 1430 to 1520 cm⁻¹. The origins were explained by the graphene plasmons being distinctly concentrated on the trenches and experiencing interference, from which the wavelength and propagation length of graphene plasmons could be determined at specific wavenumbers. The PiFM technique itself and its complementary use with s-SNOM demonstrated possibilities in precise probing and engineering of polaritonic modes in vdW materials.

Nanoscale Defect Characterizations via Near-Field Optical Microscopy

The presence of defects alters material behavior in unexpected ways and is thus often desired to be reduced. Working with 2D materials involves sustaining a wide range of defects: 1) vacancies, adatoms, substitutions, interstitials, or antisites at the atomistic scale from processes like plasma treatment to etch backside graphene on copper foil, 2) grain boundaries and adlayers in various types of 2D materials introduced during CVD syntheses, and 3) micro- and nanoscale wrinkles, bubbles, tears, and other strained landscapes and irregularities easily introducible through conventional wet and dry transfer techniques in stacking of heterostructures.^[154–157] However, understanding the nature of defects and the effect of specific types of defects (e.g., vacancies or substitutions) can help bolster designing and exploiting materials. By intentionally introducing defects known to adjust the optoelectronic behavior of materials, a range of bandgaps may be tapped into, or other more favorable properties can be attained, which is the goal of defect engineering.^[158] For 2D materials, the study of defects is important because of the sensitivity of a 2D layer where even minor changes (e.g., nanoscale features such as nanobubbles or adlayers) result in significant functional alteration. One example of defect engineering is the intentional introduction of sulfur vacancies for the hydrogen evolution reaction present in water splitting.^[159] The introduction of sulfur vacancies, into TMDs such as MoS₂ or WS₂ monolayers, adjusts the bandgap, becoming more appropriate for the reaction. This controlled introduction provides additional bonding sites for hydrogen and has enhanced stability leading to longer-lasting reactions. However, the introduction of an excess of vacancy defects prevents the reaction from occurring at all, so the defects must be carefully controlled.

Electron microscopy techniques utilizing high-energy electrons induce defects such as vacancies in the sample, while near-field techniques have access to the low-energy landscape, enabling nondestructive optical measurements. For example, the exciton diffusion of MoS₂ grown on Si/SiO₂ substrate through CVD sulfurization of MoO₃ was estimated to be approximately $$L\ = \ 2\ \sqrt {{D}_{{\rm{exc}}}\tau } = \ 24\ {\rm{nm}}$$ with exciton lifetime τ = 40 ps and exciton diffusivity D_exc = 0.04 cm² s⁻¹.^[160] For measuring such a predicted excitonic diffusion length of <100 nm, the spatial resolution of near-field microscopy techniques would be tremendously useful in mapping excitonic phenomena. Nanoscale imaging and spectroscopy allow for different types of defects to be studied and classified, and atomistic theoretical posits (e.g., related to grain boundaries or zigzag and armchair step edges) may be presented through TERS/TEPL characteristics. Adlayer defects, for example, which are widespread on the surface of CVD-grown TMDs can modify the averaged PL response acquired by far-field PL, but each of the defects can be recognized using near-field optical microscopy techniques with enhanced spatial resolutions.

s-SNOM Imaging of Nanoscale Defects

s-SNOM has been used to quantify the presence of adlayer defects on CVD-grown monolayer TMDs.^[161] In CVD synthesis of TMD monolayers, sometimes there appears secondary growth of an upper layer on top of the monolayer in the form of nanoscale islands called adlayer defects. In far-field PL mappings, these adlayer defects are not visible yet significantly reduce overall PL intensities. In TEPL mappings, these defects are differentiated, and their optical response and orientation are quantifiable. Lee et al. identified that the adlayer defects had triangular shapes oriented at 0° and 60° in equal proportions consistent with interlayer coupling growth^[162] on monolayer TMDs related to their atomic configuration^[125] (Figure 6a, left).^[163]

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Grain boundaries, another defect type, may exist at surface during CVD growth of monolayer TMDs. Previously, van der Zande et al. hypothesized that a mirror boundary led to a reduction in the PL intensity while a tilt boundary led to an increase in the PL intensity based on far-field PL mappings.^[160] Although they postulated that n-doping in molybdenum-rich mirror boundary and p-doping in sulfur-rich tilt boundary would decrease and increase the PL intensity respectively, the far-field PL mapping results were not completely explained by this theory. Lee et al.^[161] used s-SNOM-based PL to study a similar mirror boundary that did not exhibit a similar decrease in PL intensity (Figure 6a right). In regions where grain boundaries should have been present, no change in PL intensity was visible despite significantly better spatial resolution (110 nm) of s-SNOM that was capable of resolving. Similar to van der Zande et al., Lee et al. also used far-field PL to examine their samples with an approximate spatial resolution of 440 nm which produced a 4% contrast that is insufficient to be noticed in a mapping. On the other hand, s-SNOM was able to distinguish line features of 20 nm width with an approximate spatial resolution of 110 nm. These line features are hypothesized to be cracks during growth, as opposed to line defects, the latter of which are significantly smaller in length. As a result, the crack regions result in lower PL intensities from reduced scattering response. However, far-field PL only vaguely captures the outlines of these nanoscale features even at optimal device conditions, leading to a lower resolution for an averaged effect, while s-SNOM-based PL significantly and clearly captured these features that were later confirmed by SEM. A similar attempt at modifying SNOM to conduct PL mapping was utilized by Huang et al., who replaced the standard metal-coated tip with a pyramidal silicon tip.^[164] Huang et al. suggested that there was interference present with the standard metal-coated tip in traditional SNOM setup capturing the combined near-field and far-field signals, which were hypothesized to cause non-negligible PL quenching, electron transfer, and Rabi splitting that could be reduced by incorporating the novel pyramidal design. Using a combination of AFM topography and SNOM-based PL, Huang et al. identified flat, multilayer, wrinkled, and bubble-type regions based on defining characteristics such as the height profile and PL response (Figure 6b). Their defect presence was associated with the transfer process of the TMD monolayer, which resulted in unwanted wrinkles and bubble-type heaves. Careful control of wrinkle structures can also be an example of strain manipulation.^[166]

The intentional introduction of defects has also been used as a designing mechanism for 2D materials for those particularly sensitive to changes in charge density, using the method of an electron beam to dope vdW materials to create p–n junctions and modify carrier concentration^[127] (Figure 6c).^[165] The high spatial resolution of s-SNOM in mapping led to s-SNOM being used to examine the fabrication method, observing consecutive decreasing thickness line features ≈1 µm thick (Figure 6c, top) and a letter “B” of 200 nm width (Figure 6c, bottom). The reported approximate spatial resolution of electron-beam-induced doping was 200 nm, which allows for the distinguishing of the “B” based on the contrast in the near-field mapping.

TERS/TEPL Imaging of Nanoscale Defects

The advantages of using TERS are the enhanced ability to capture characteristic peaks such as in-plane and out-of-plane vibration modes (E¹_2g, A_1g) and defect peaks (D, D′) in TMDs such as WS₂ (Figure 7a)^[167] or sp² hybridization of structures (G) and disorder peaks (D, D′, 2D) in graphene. Defect peaks provide extensive information about defect type and prevalence in a sample. The ratio of D and D′ peaks for graphene corresponding to ≈13, ≈7, and ≈3.5 are known to be associated with sp³, vacancy, and boundary-type defects, respectively.^[168] Su et al. used the ratio between the D and G peaks to quantify defects present in graphene oxide through hyperspectral TERS and TEPL.^[169] They saw the topography limited by the tip radius ≈100 nm, whereas TERS could resolve features just a few nanometers wide. They posited that regions with lower PL intensity could be attributed to vacancies related to defect densities with increasing defect presence A < B < C (Figure 7b) based on the D/G peak intensities.

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In TMDs, Lee et al. investigated two defect peaks present in defective monolayer WS₂.^[167] By scanning WSe₂ on a gold substrate with a gold-coated tip at an excitation laser wavelength of 633 nm, they identified a shoulder secondary peak next to the A_1g peak called the D peak (Figure 7a). The use of a gold substrate and gold-coated tip combination was hypothesized to enhance Raman signals through a gap-mode in the gap between the tip and the sample. At ≈432 cm⁻¹, they identified a secondary defect-associated peak, D′. To disprove that this D′ peak was from mechanical strain, Lee et al. used far-field Raman spectroscopy to test against already-known strain-induced blueshift of the E¹_2g peak. From the unchanged E¹_2g peak position, they concluded that D′ peak was due to the presence of defects rather than strain. The mappings of far-field Raman were also used for checking local strain-induced blueshift. Other TMDs such as MoSe₂ and WSe₂ also share similar D and D' defect peaks shown in WS₂.^[172–174] The TERS mapping with 45 nm spatial resolution exhibits ripples, cracks, wrinkles, and folds with the Raman intensities.

The D and D′ defect peaks in TMDs have also been used to classify defect density and type. Kato et al. carried out TERS and TEPL mapping of WS₂ where they estimated that the scanned area had 5.2% sulfur vacancies attributed to the D peak^[170] (bright blue in Figure 7c) compared with literature reports of 1–3%^[175,176] that attempted to use only far-field PL to quantify the defect presence.^[177] They also identified 0.2% attributed to the D′ peak. Their methodology and type of mapping addressed the issue of long scanning times for TERS by modifying the procedure with a controller. One of the challenges associated with TERS is the need to scan a sample for a long period of time. Over time, the tip may drift or lose focus caused by out-of-plane drift. Kato et al. added a feedback loop to track the tip and focus drifts, enabling long scanning times of several hours, and thus large-area scans. They postulated that the 0.2% of D′ peak highlighted in a relatively large mapping area of 4 µm² for TERS mappings would otherwise have been missed using conventional TERS mapping. They also used TEPL to identify foreign metallic grain (contaminants) only a few nanometers wide deposited during the fabrication process originating from the metallic substrate. Oxidized particles of WS₂, which were likely to reduce the PL intensity were ruled out due to the strong PL intensity at these points. The increased PL intensity identified by TEPL was hypothesized to be either the result of localized strain caused by the metallic grains that modified the TMD bandgap closer to the excitation laser wavelength, or the metallic grains causing localized and strong light confinement referred to as the lightning rod effect that would result in significant field enhancement. Interestingly, narrower monolayer regions had weaker PL intensity than wider monolayer regions, both surrounded by thicker and substrate regions, reflecting the partial intake of far-field PL contributions to TEPL signals. The feedback loop to accelerate the time taken to scan each pixel at 0.54 s per pixel, reduces drift and offset challenges from long-term scanning.^[178] In addition, the humidity, temperature, and air purity of the enclosure where the TERS measurements were taking place were controlled to prevent degradation of the silver tip. This approach was used because tips had been reported to degrade over several hours of scanning.^[179] Such a stable scanning system would help alleviate reproducibility issues in TERS, such as sample drift experienced by an early TERS work such as graphene grown on copper foil.

In multilayer systems, step-edge defects may occur at the edge of a step between layers of different thicknesses. For example, additional atoms stacked at the edge cause a jump in the PL intensity between these layers. Kato et al. identified step-edge defects in their TEPL mapping through the PL response, as the signal would briefly but consistently increase before decreasing, marking the transition from a monolayer to bilayer based on its line scan. The line scans capture zigzag and armchair step-edge defects, which agree with the findings of Huang et al. for MoS₂ zigzag and armchair step-edge defects using TERS. (Figure 7d).^[171] Huang et al. found that the zigzag and armchair edges were metallic and semiconducting, respectively, and further, they were able to characterize the spectral behavior of zigzag and armchair edges, such as identifying 220 and 396 cm⁻¹ Raman shift peaks. 220 cm⁻¹ peak, associated with the longitudinal acoustic phonon mode, only appeared in samples with dangling bonds. 396 cm⁻¹ peak only occurred in multilayer defects including two-layer and one-to-two layer transitions that excluded monolayer regions. They also found that zigzag and armchair edges redshifted and blueshifted the A_1g peak, respectively. Their measured zigzag and armchair TERS line-traces matched with line-traces from Kato et al. Furthermore, Huang et al. also carried out corroborating density functional theory predictions for the shift in the A_1g peak and atomistic reconstructions of zigzag and armchair edges, from which they were able to determine different edge structures associated with 60° and 90° angled TMDs viewed under an optical microscope image. Their reported spatial resolution was ≈7 nm, which is among the highest. However, due to the various methods to approximate the spatial resolution, caution should be taken to directly compare the reported spatial resolutions with the actual ability to distinguish. Regardless, the nanometer-scale zigzag and armchair edge defects were successfully captured.

PiFM Imaging of Nanoscale Defects

The mechanical feedback and absorbance spectroscopy capabilities of PiFM have not yet been widely adopted for vdW materials. Novak et al. used IR PiFM to study block copolymer-oriented elastomers on SiO₂ (Figure 8a),^[94] identifying a foreign contaminant based on low intensity in PiFM signals at large height of the particle shown in AFM topography (Figure 8a, left and center). Further, an unexcited material defect ≈7 nm in diameter was captured in hyperspectral methods (Figure 8a, right). Accordingly, they claimed that inconsistencies between the topography and the PiFM mappings indicated the presence of foreign contaminants. Their spatial resolution was estimated to be ≈5 nm.

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PiFM investigation of vdW materials is still at the early stage, having many possibilities to examine defect properties. Tumkur et al. scanned a WS₂ sample at three separate wavelengths to observe different regions being highlighted, asserting that this showed spectrally selective defect mapping (Figure 8b).^[87] PiFM scanning under excitation of photon energy with 2.28 eV revealed potential defect states, while scanning with 2.72 eV did not show any distinct features.

By contrast, Yu et al. attempted to compare PiFM results with the topography mapping simultaneously for WS₂ encapsulated in 10 nm above and 20 nm below with hBN (Figure 8c)^[180] to improve the quality of monolayer interface. From the PiFM spectrum, slight decrease of linewidth and redshift of exciton peak were observed in region B where WS₂ was encapsulated with hBN, compared with region A without hBN. Nevertheless, the greater tip–sample distance due to the additional 10 nm thick hBN layer on top of the WS₂ monolayer contributes to decreasing the field locally confined between the tip and the WS₂ surface. Additionally, Yu et al. observed polymer residues remaining on the sample surface after the sample preparation process. The increased tip–sample distance and surface contamination consequently caused the degradation of spatial resolution in the PiFM mapping.

Careful sample preparation covering the entire TMD with repeat measurements should be taken to confirm their results, and a thinner hBN layer could potentially improve the mapping clarity.^[181–183] PiFM measurements are expected to enable further explorations for defects in vdW materials with high spatial resolution.^[143]

Nanoscale Strain Characterization via Near-Field Optical Microscopy

2D materials’ mechanical responses are profoundly distinct from that of their bulk counterparts, such as ultrahigh elastic modulus, high fracture strain, and high out-of-plane flexibility. Tailoring 2D materials’ properties by mechanical strain have been explored as a promising pathway to enrich fundamental phenomena and novel functionalities in the field of condensed matter physics and materials science. Moreover, spatially heterogeneous strain often plays a crucial role in quantum confinement-driven phenomena, including pseudomagnetic quantum Hall effects^[184,185] and antibunched photon emission.^[186,187] For rational design and enhanced performance of local strain-engineered devices, it is highly desired to realize control and characterization of nanoscale strain distribution, while it has been a persistent challenge to achieve spatial resolution below optical diffraction limit with nondestructive approaches. In this regard, near-field optical characterization has shown promise in the analysis of strain distribution and strain-induced phenomena at nanometer scale. We will discuss the methodologies and strategies of various near-field optical characterization of 2D strain analysis in this section.

s-SNOM Imaging of Nanoscale Strain

Nanoscale strain analysis using s-SNOM is based on the modulation of phonon band structure or free carrier in the locally strained materials and resulting shifts of resonance vibration frequencies. The incident beam is turned into a tightly confined and enhanced electromagnetic near-field at the vicinity of the AFM tip, allowing for imaging and spectroscopy of local strain distribution at ≈20 nm of spatial resolution. Using s-SNOM for local strain and residual stress analysis was first reported for nanoindented bulk SiC crystal,^[188,189] as residual stress modulated the longitudinal optical phonon and PhP resonance frequencies. While complex strain tensors in 3D bulk semiconductors hampered quantitative interpretation of local strain distribution from phonon or PhP, strained 2D materials opened up new opportunities for highly precise and quantitative analysis of local strain due to its reduced dimensionality and high strain sensitivity.^[107] For instance, Lyu et al. studied strain-induced modulation of local dielectric properties of hBN.^[190] Nanoscale hBN wrinkles were created by thermal annealing due to a mismatch between the thermal expansion coefficient of hBN and Si substrate (Figure 9a, left). In-plane compressive strain exerted at the end of a wrinkle modifies the local dielectric constant of hBN, causing the shift in the resonance frequency of in-plane transverse optical (TO) phonon mode (1372 cm⁻¹). The intensity contrast was observed between strained and unstrained regions in the nanoscale s-SNOM imaging due to compressive strain-induced blueshift of resonant TO phonon frequency, resulting in decreased s-SNOM intensity at the strained regime when the excitation energy is lower than the energy of TO phonon (Figure 9a, center). Moreover, the near-field signal was strongly affected by the nonlocal PhP propagation in hBN when the excitation wavelength exceeded the TO phonon frequency, resulting in an interference pattern near the wrinkles and hBN edges. In addition to the nanoimaging with ≈20 nm of spatial resolution, the nano-spectroscopy was carried out via broadband synchrotron IR nano-spectroscopy which showed phonon frequency shift up to ≈2 cm⁻¹ by local strain near hBN wrinkle (Figure 9a, right). The detection limit of s-SNOM in this work was estimated at the local strain level of 0.01%. Vincent et al. also investigated the strain-induced enhancement of IR absorption of hBN-encapsulated graphene nanobubbles using s-SNOM.^[191] It was found that strong light absorption at the nanobubble was observed at ≈1000 cm⁻¹ excitation with distinct absorption domains within the nanobubbles. The coincidence between the domain boundary and ridges of the nanobubbles indicated that localized strain tunes the optical conductivity and plasmonic dispersion of graphene.

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In addition to localized strain near isolated out-of-plane structures, large-area distribution of strain gradient in 2D materials also provides unique opportunities for exploring fundamental physical properties. For instance, the tensile strain distributed randomly in graphene can lead to Anderson localization in which increased disorder in a medium brings about a higher probability of constructive scattering and strong localization of the coherent scattering wave. Theoretical prediction indicated that polaritons in highly disordered 2D metal films can undergo Anderson localization and manifest by enhanced near-field amplitude inversely proportional to localization length.^[194] Duan et al. reported that s-SNOM can record the transition to Anderson localization of PPs in flat graphene with varied degrees of strain disorder.^[195] While unstrained graphene exhibited quasi-expansion of polariton waves and plane-wave fringe pattern, the increased level of strain disorder in the graphene gives rise to lateral confinement of the PPs, showing a transition to weak localization and Anderson localization. Anderson localization was observed in graphene with high strain disorder and accompanied by enhanced near-field scattering amplitude and tight confinement (≈250 nm) which is comparable to the plasmonic wavelength of graphene (≈200 nm). On the other hand, Dobrik et al. reported more controlled deformation of large-area graphene at the sub-nanometer scale for modulation of polariton dynamics.^[192] Cyclic thermal annealing of flat graphene induced compressive strain on graphene and formed a large-area corrugated structure. Interestingly, the corrugated graphene enabled visible plasmon as demonstrated in graphene-enhanced Raman scattering and theoretically predicted electron energy-loss spectroscopy. The confocal SNOM measurement showed that visible wavelength excitation (400 nm) on corrugated graphene resulted in the fringe pattern at the layer boundaries similar to that of PPs pattern in IR s-SNOM measurement, while the fringe pattern was not observed in flat graphene samples (Figure 9b).

Understanding nanoscale local strain in vertically stacked 2D heterostructures is another critical research area requiring the improved spatial resolution of strain analysis. Recent investigations on twisted 2D heterostructures, such as unconventional superconductivity of magic-angle twisted bilayer graphene^[196] and moiré-trapped 2D excitons,^[197] revealed the profound influence of interlayer coupling and lattice relaxation on the correlated electronic band structure. Especially, localized relaxation to increase commensurate domains gives rise to the formation of soliton boundaries at which strain is mostly concentrated.^{[135,193,198]} In this regard, s-SNOM has shown promising features, especially for strain-induced soliton boundaries and nanoscale phase imaging. For instance, Geisenhof et al. investigated the stacking transition between trilayer graphene with Bernal and rhombohedral stacking by post-procedure driven straining.^[199] Stacking transitions imaged by s-SNOM characterizations were attributed to anisotropic compressive strain during metal electrode deposition and hBN encapsulation with post-processing, and the resultant movement of the strain soliton boundary. Ni et al. also investigated the soliton network formed on the twisted hBN via s-SNOM.^[193] Varied symmetry of hBN domains was created and separated by soliton boundaries formed on the subsurface, which was manifested at the PhPs resonance frequency of hBN (1368 cm⁻¹) (Figure 9c). This is attributed to the modulation of dielectric constant and lattice dynamics under localized strain accumulated along solitons.

TERS/TEPL Imaging of Nanoscale Strain

While s-SNOM provides a nanoscale resolution (≈20 nm) in imaging of strain and strain-induced quasiparticle dynamics, the excitation wavelength is often limited to an IR laser that is sensitive to local dielectric constant and specific phonon modes. Describing light–matter interaction with visible wavelength light is desirable to analyze various resonance vibration modes and PL properties, which can be directly correlated to the observations in far-field optical characterization. In this regard, TERS and TEPL have drawn great attention as a promising methodology for strain characterization. The peak shift and broadening in TERS and TEPL provide rich information on strain-induced modulation of phonon Raman bands and electronic band structure. Strain analysis using TERS was first carried out in Si-based semiconductors^[200] and 1D nanostructures such as carbon nanotubes^[160] and recently adopted to 2D materials and heterostructures. In particular, emerging quantum phenomena in 2D materials, such as room-temperature exciton confinement, have been demonstrated by TERS and TEPL that are not accessible without high spatial resolution and strong confinement of near-field electromagnetic waves.

Studies using TERS and TEPL have demonstrated significant advantages for real-time and high-sensitivity detection of nanoscale strain distribution in 2D materials. Beams et al. utilized TERS for nanoscale strain characterization of strained graphene on nanoparticles.^[201] The TERS hyperspectral Raman scanning across nanoparticle-supported graphene showed a redshift of the G peak (1580 cm⁻¹) and 2D peak (2630 cm⁻¹) as well as a broadening of the 2D peak, without any changes in D peak. Based on the experimental Raman shift and mechanical modeling of the radially strained membrane, the local strain profile of graphene was obtained, which revealed that a 5 nm nanoparticle can induce 0.37% of total strain on monolayer graphene in radial and circumferential direction over 170 nm of lateral distance. Strain analysis with TERS was also performed on 2D TMDs in which nanoscale strain is induced by underlying nanostructures such as nano-triangles^[202] and nanopyramid,^[203] or by indented with an AFM tip.^[146] Park et al. demonstrated hybrid TERS/TEPL nano-spectroscopy for defect analysis and local strain tuning in monolayer WSe₂ (Figure 10a).^[146] PL emission is quenched as well as blueshifted at the edges, nucleation sites, and twin boundaries of monolayer WSe₂ by nonradiative recombination of exciton at defects. The local compressive strain was applied by using an AFM tip, enabling reversible bandgap tuning up to 24 meV and irreversible modification of bandgap by 48 meV. This allows for distinguishing the effects of defect-induced PL emission quenching or energy shift from strain-induced modulation of the electronic band structure.

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The presence of spatially nonuniform strain applied on 2D semiconductors creates potential energy gradient due to bandgap variation with respect to the local strain. This allows for directional drift of excitons toward the regime with local energy minima, which is called exciton funneling. In 2D semiconductors, funneling and localization of strongly bound excitons into nanoscale strain field play a critical role in quantum optical phenomena such as antibunched photon emission, while conventional PL measurement is not capable of resolving nanoscale strain gradient. In this regard, TEPL has been employed to demonstrate exciton funneling with a nanoscale spatial resolution (≈20 nm).^{[204,206–208]} For instance, Koo et al. demonstrated dynamic control of exciton funneling in wrinkled WSe₂ on Au substrate.^[204] Employing adaptive TEPL with bottom illumination and wavefront shaping enhanced spatial resolution (≈15 nm). The increased quantum yield and high TEPL intensity were observed at the wrinkle apex compared to the flat area, which was attributed to strain-induced exciton funneling to tensile strained WSe₂ (ΔE = 10 meV) wrinkle apex with lower exciton energy (Figure 10b). In addition, the reconfigurable tuning of strain and exciton funneling was realized by pressing the wrinkle structure with a metallic tip. Similarly, Shao et al. reported exciton funneling of twisted bilayer MoS₂ using TEPL with ≈10 nm of spatial resolution.^[208] The bilayer wrinkle induced ≈1.2% of uniaxial tensile strain and 50 meV of A exciton energy shift. Higher TEPL intensity was observed at the center of the wrinkle within few tens of nanometer, which was narrower than the width of wrinkle, indicating exciton funneling toward the highly strained wrinkle apex. Albagami et al. also elucidated strain-induced modulation of optical properties in freestanding lateral 2D heterostructure of WSe₂ and MoSe₂.^[207] Several competing mechanisms in TEPL measurements have been discussed including 1) near-field plasmonic enhancement, 2) local strain-induced exciton funneling, 3) charge transfer from 2D material sample to tip, and 4) hot carrier injection from the plasmonic tip to the sample. In addition, Albagami et al. observed strain-induced redshift in freestanding MoSe₂ at the hetero-nanobubbles with increased TEPL intensity, implying exciton funneling toward tensile-strained MoSe₂.

Strain-induced exciton funneling plays a critical role in antibunched photon emission in 2D TMD quantum emitters. However, single photon emission has been observed only at cryogenic temperatures for 2D TMD emitters due to the thermalization of exciton out of the confinement trap at elevated temperatures. Recently, researchers have shown that localized exciton can be observed even at room temperature utilizing near-field TEPL measurement. Lee et al. investigated that localized exciton of monolayer WSe₂ can be detected at ambient temperature by employing a triple-sharp-tip plasmonic cavity, which is composed of sharp Au bowtie plasmonic nanostructure and an AFM tip.^[145] While neutral exciton exhibited redshift corresponding to 0.3% of local tensile strain, they observed the emergence of a broad exciton peak at the low-energy shoulder of the PL spectrum only when the tip is located within the 30 nm region from the center of the bowtie structure. The localized exciton has lower exciton emission energy (1.58 eV) compared to that of the neutral exciton (1.67 eV) or trions (1.64 eV). Interestingly, the localized exciton is only detectable when a metallic tip induces strong z-polarized emitters, whereas far-field spectroscopy of nanogap plasmonic PL did not show any evidence of exciton localization. This is attributed to the high emission rate and tight near-field localization in the triple-sharp-tip cavity structure in the TEPL measurement. Similarly, Darlington et al. reported exciton localization at room temperature from monolayer WSe₂ nanobubbles.^[205] TEPL measurement with sub-34 nm of spatial resolution allowed for imaging and spectroscopy of localized exciton (1.56 eV) versus neutral exciton (1.65 eV) (Figure 10c). Hyperspectral mapping shows an extraordinary feature of the donut-like distribution of localized exciton emission along the periphery of the nanobubble, which is not intuitive to the prediction of continuum mechanics modeling and exciton funneling toward the center of a nanobubble. Theoretical modeling of the confinement potential, electron-hole overlay, and the shear strain shows a deep potential trap along the periphery due to atomic-scale wrinkle, which agreed well with the experimental observation of donut-like localized excitonic states.

Summary and Outlook

In this review, we surveyed advances and principles of near-field optical imaging techniques (s-SNOM, TERS/TEPL, and PiFM) and their recent applications to investigate the light–matter interactions, defects, and strain in 2D vdW materials. The physical origins of s-SNOM and tip-enhanced spectroscopy are near-field coupled tip–sample polarization via the field localization and enhancement by the tip apex. The lightning rod effects and plasmonic resonances enhance the light intensity with elastic scattering (s-SNOM), inelastic scattering (TERS), and photoluminescence (TEPL). PiFM detects photo-induced electromagnetic force including optical tweezer force, image dipole force, and optical binding force from dipole–dipole interaction, via force gradient measurement assisting suppression of scattering force and photothermal effect on cantilever. Each near-field optical imaging technique has been reported to achieve a spatial resolution of less than 10 nm and to enable hyperspectral imaging, which far-field optical techniques cannot obtain.

Near-field optical imaging techniques have been extensively utilized to explore light–matter interactions, defects, and strain in 2D vdW materials and heterostructures. Particularly, 2D quasiparticles, such as PPs in graphene, EPs in TMDs, and PhPs in hBN have been evaluated to demonstrate strong light–matter interaction in 2D vdW materials. Using s-SNOM, researchers attained signatures of 2D polaritons using s-SNOM amplitude, phase, and fringe patterns at the edge to observe the propagation length of polaritons and postulated the dispersion relation. TERS/TEPL spectra and imaging distinctly improved the spectral and spatial resolution and enabled distinguishing overlapped vibration modes or exciton peaks compared with conventional confocal micro-Raman/PL. PiFM was complementarily used with s-SNOM to capture the E-field confinement in graphene plasmon and PhPs in hBN excited under IR light illumination. In addition, diverse kinds of defects, including adlayer defects, grain boundaries, and step edges, were investigated with near-field imaging techniques. Mapping local defects with better spatial resolution enabled research into finding the reasons for unwanted defects and the strategies to utilize them. For localized or large-area distributed strain gradients in 2D vdW materials, s-SNOM established the modulation of phonon band structure and measured the shifts in resonance vibration frequencies. TERS and TEPL revealed the nanoscale spatial distribution of strain rate and strain-induced exciton funneling phenomena, which assists antibunched photon emission in 2D TMDs.

As for the perspective of nano-optical imaging techniques, s-SNOM, and tip-enhanced spectroscopy have been leading the near-field imaging field with increasing spatial resolution by decreasing the probe volume of the tip–sample cavity. Modulating the precise tip–sample distance in either classical or quantum regimes with the feedback loop is expected to control the optical field enhancement, unveiling the effect of directly tunneling electrons between the metal tip and sample or regulating the relative rate of radiative and nonradiative pathways. Adopting pump-probe or in situ measurements in s-SNOM and TERS/TEPL contributed to the investigation of the time-resolved ultrafast dynamics of 2D polaritons.^{[113,123,133]} Also, attempts to alter the measurement environment, such as cryogenic s-SNOM in a liquid state^[130] or ultrahigh vacuum-TERS^[209] were explored to acquire enhanced near-field signal. Meanwhile, PiFM is growing its presence in 2D materials research, starting from probing 2D polaritons. Several research groups are working to elucidate the physical meanings of the PiFM signals and extend their excitation wavelengths beyond IR to visible wavelengths. Further efforts are needed to optimize the PiFM tip and select proper substrates to exclude the thermal expansion contribution.^[90,105]

Although we already have covered the near-field studies of 2D vdW materials and diverse combinations of heterostructures, interface phenomena remain an interesting topic and should be appropriately examined further. For instance, the integration of 2D vdW materials with 3D metal nanostructures produces enhanced light absorption and emission even in 2D monolayers, with the assistance of the electric field confinement followed by generation of photogenerated charge carriers at the interface by coupling of exciton-PPs.^[210–212] Near-field optical imaging is expected to play a crucial role for studying the interactive modulation of EPs, PPs, and PhPs in 2D vdW heterostructures and the resulting resonance mode changes. Furthermore, the mapping of moiré potentials depending on the stacking angle will provide perspective to utilize the trapped 2D quasiparticles at the heterointerface. In addition, the visualization of moiré superlattices determined by lattice constant mismatch and twist angle will bring strategies to engineer nanoscale defects and strain on 2D materials. Based on recent research on moiré local bandgap measurement via scanning tunneling techniques^[213] and hyperspectral imaging of exciton confinement within a moiré unit cell via electron microscopic techniques,^[214] near-field imaging is expected to advance the understanding of 2D moiré potentials and moiré exciton behaviors when engineering the strain or introducing defect states.

Acknowledgements

This work was supported by the Air Force Office of Scientific Research (AFOSR) (Grant No. FA2386-21-1-4129) and the National Science Foundation (NSF) (Grant Nos. CMMI-2135734, CBET-2035584, and ECCS-2201054). This research was primarily supported by the NSF Materials Research Science and Engineering Center (MRSEC) program through the Illinois MRSEC.

Conflict of Interest

The authors declare no conflict of interest.

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