Observation of a two-dimensional liquid of

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Received 23 Jan 2015 | Accepted 8 Sep 2015 | Published 22 Oct 2015

Frhlich polarons, or large polarons, at the bare SrTiO3 surface prepared by vacuum annealing. Systematic analyses of angle-resolved photoemission spectroscopy and X-ray absorption spectra show that these Frhlich polarons are two-dimensional and only exist with inversion symmetry breaking by two-dimensional oxygen vacancies. Our discovery provides a rare solvable eld theoretical model, and suggests the relevance of large (bi)polarons for superconductivity in perovskite oxides, as well as in high-temperature superconductors.

DOI: 10.1038/ncomms9585 OPEN

Observation of a two-dimensional liquid of Frhlich polarons at the bare SrTiO3 surface

Chaoyu Chen1, Jos Avila1, Emmanouil Frantzeskakis1,w, Anna Levy1,w & Maria C. Asensio1

1 Synchrotron SOLEIL, Beamline ANTARES, LOrme des Merisiers, Saint Aubin-BP 48, Gif surYvette 91192, France. w Present addresses: Institute of Physics (IoP), University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands (E.F.); Sorbonne Universits, UPMC, Paris 06, CNRS, INSP, UMR 7588, INSP, F-75005 Paris, France (A.L.). Correspondence and requests for materials should be addressed to M.C.A. (email: mailto:[email protected]

Web End [email protected] ).

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The concept of a polaron was set forth by Landau1 in 1933 and has attracted much attention over the following decades. It not only describes the specic physical

properties of charge carriers in polarizable solid, but also constitutes an interesting eld theoretical model consisting of a fermion interacting with a scalar boson eld2. Even today, there is ongoing research on polarons, including the basic theory3, as well as their behaviour in more compelling situations such as high-temperature superconductors46 and colossal magnetoresistance in rare-earth manganites7.

There are different types of polaron states in solids, such as Frhlich polaron, small polaron, spin polaron, bipolaron and hydrated polaron2. Originally polaron describes interaction between charge carrier and long-wavelength optical phonons, namely, Frhlich polaron8, of which the spatial extension exceeds the lattice constant. Frhlich polarons with low kinetic energy propagate through the lattice as free electrons but with an enhanced effective mass, thus directly measurable by spectroscopies like angle-resolved photoemission spectroscopy (ARPES).

SrTiO3 is the key material in the emerging eld of oxide electronics9. Structurally or electronically modied SrTiO3 presents a wide spectrum of phenomena such as superconductivity10, two-dimensional (2D) electron gas (2DEG)11,12, ferroelectricity13 and blue luminescence14, indicating versatile interplay of charge, spin, orbital and lattice degree of freedom15. However, previous studies give controversial information about the carrier type in SrTiO3 (see, for example, refs 16,17 and references therein), hampering the thorough distinction of these internal interplay. Recently, ARPES study on FeSe lm grown on SrTiO3 has revealed the enhancement of superconducting transition temperature Tc due to the coupling between FeSe electron and oxygen optical phonon in SrTiO3 (ref. 6).

In this article, by examining the surface electronic structure of vacuum-annealed SrTiO3, we report the observation of 2D liquid of Frhlich polaron, a new quasi-particle formed by conduction band electron coupled with one polar longitudinal optical (LO) phonon mode. By controlling the annealing temperature, we can precisely tune the surface oxygen vacancy concentration, which develops from 2D to 3D distribution of charges. Moreover, by compiling partial electron yield (PEY) and total uorescence yield (TFY) XAS spectrum, we are able to identify unambiguously these two distinctive distributions of oxygen vacancies. In the 2D case, oxygen defect dipoles break the inversion symmetry and initiate the coupling between electrons and polar LO phonons. This intermediate coupling leads to the formation of a new type of quasi-particles, Frhlich polarons, whose spectra function contains multiple replicas of original bands, equally spaced oLO

apart, with oLO the effective energy of LO phonons, as directly observed by ARPES here. Photon-energy-dependent ARPES measurements reveal the 2D nature of Frhlich polarons. In the 3D oxygen vacancy case, the 2D polarons collapse into 3D electron liquid due to the reversal of symmetry. Our ndings reveal the essential role of surface/interface LO-phonon-related large (bi)polarons in understanding superconductivity in perovskite oxides, as well as in high-temperature superconductors.

ResultsTunable oxygen vacancy concentration via vacuum annealing. Intrinsic SrTiO3 is a band insulator with a B3.2 eV gap, and experiences a second-order phase transition from cubic to tetragonal structure at the critical temperature of about 105 K (ref. 18). For the present study, both the XAS and ARPES measurements were performed B170 K while the low-energy-electron-diffraction (LEED) patterns were taken at room temperature.

Thus for our study, the bulk SrTiO3 is in the centre-symmetric equilibrium structure, that is, the Ti atom lying in the centre of the regular octahedron of oxygen atoms in the cubic perovskite structure (Fig. 1a). All the experiment data is from the (001) surface as shown in Fig. 1b.

To start with, we present the precisely regulation of surface carriers by controlling the amount of oxygen vacancies via vacuum annealing. We prove the existence of oxygen vacancies by reproducing the well-known LEED patterns (Fig. 2a and also see, for example, ref. 19 and references in), which reect the surface reconstruction due to the alignment of oxygen vacancies. Charge transfer from oxygen vacancies to Ti atoms (consequently, Ti4 to Ti3 ) allow us to derive the oxygen vacancy concentration [VO ] from the XAS spectra of Ti L2,3 edge, attributed to excitations of 2P3/2 and 2P1/2 subshells to unoccupied t2g and eg states, as shown in Fig. 2b,c. As indicated by the black arrow and more clearly shown in the insets, a 460 eV peak gradually increases with annealing temperature. According to the theoretical simulation20 (Fig. 2f, top), this peak comes from the Ti3 L3 edge. Since X-ray absorption near-edge spectroscopy is an atomic probe, strongly sensitive to its formal oxidation state and coordination chemistry21, we can calculate the Ti3 /Ti4 ratio by assuming the linear combination of Ti4 and Ti3 signals under the single inelastic electron scattering condition22,23. As exemplied in Fig. 2f (bottom) for the PEY XAS spectra from surface annealed at 1,000 C, the experimental spectra can be decomposed into 85% Ti4 and 15% Ti3 , using multiple least-squares t. Figure 2g schematically summarizes the tted PEY ratio corresponding to surfaces with different annealing temperature. The monotonic increase of oxygen vacancies with annealing temperature clearly demonstrates that we can control and reproduce the carrier concentration of the SrTiO3 samples.

This point has been further corroborated by the agreement between the Ti3 /Ti4 ratio calculated by PEY XAS and Ti 3p core levels shown in the Supplementary Fig. 1. Notice that we have chosen a similar energy window (B40 eV) to collect secondary electrons for XAS spectra and core level photoelectrons spectra, ensuring similar depth sensitivity in both data sets.

In addition, we can also prove the increase of surface oxygen vacancies from the O K-edge XAS spectra (Fig. 2d,e). As shown clearly in the insets, the A2 peak increases dramatically for the surface annealed at 1,200 C. This peak arises from the TiO pd-hybridization with a s-bonding character. Its increase indicates the lattice distortion caused by oxygen vacancies, in qualitatively agreement with our conclusion based on Ti L2,3-edge data. Given that each oxygen vacancy nominally transfers two electrons to the Ti d band24, and there are three O atoms but only one Ti atom in the unit cell, Ti3 ratio is six times the value of the oxygen vacancy concentration [VO ] (Fig. 2g), which allows XAS on Ti L2,3 edge be much more sensitive than O K edge. Thus it is sensible to calculate the [VO ] from the XAS spectra of Ti L2,3 edge.

More importantly, we show that the oxygen vacancy distribution displays a clear dimensionality change. Figure 2g also summarizes [VO] values tted from TFY-XAS spectra. For a given annealing temperature, both PEY and TFY spectra are recorded simultaneously from the same sample. Contrary to the monotonic increase of PEY [VO ], the TFY concentration remains at noise level at the beginning and only increases with annealing temperature above 1,000 C. This distinctive behaviour is based on the different depth sensitivity of PEY and TFY spectra25. The PEY signals, that is, energy-selected secondary electrons in present case, typically from an average depth of o1 nm (approximately two unit cells deep), are highly surface sensitive. In contrast, the TFY signals mainly give bulk information due to the long mean free path (MFP) of photons, (B100 nm). Thus, we

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SrTiO3 (001) 11

a b

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[afii9835]

[afii9835]i

Fluorescence detector

Photoelectron detector

Sample

[afii9850] AH

[afii9830]

h[afii9840]

Synchrotron radiation

Figure 1 | Lattice structure of SrTiO3 and measurement geometry. (a) The cubic unit cell, with the TiO6 octahedron shown as magenta surfaces. O atoms at O1 cites have TiO bonds along z direction, while O2 cites have TiO bonds parallel to the xy plane. (b) A 4 4 2 block of unit cells. The top layer

shown in light purple indicates the (001) surface. (c) Experimental geometry for XAS and ARPES measurements. AH(AV) is the vector potential of the incident light with linear horizontal (vertical) polarization; y and f denote the polar and azimuthal degree of freedom and yi is the polar angle of incidence.

The analyser slits permit photoelectron detection along the x axis. For all different y, the incident photon momentum, the photoelectron momentum and the surface normal lie on the same plane (e). For all the ARPES data, we set the yiB75, very close to the grazing angle, to enhance the surface contribution.

We use linear horizontal polarization (LH). The beam polarization is even to the scattering plane. According to the matrix element effect (MEE), only orbitals with even symmetry respect to the scattering plane can be excited and detected.

4.01013 cm2 4.61013 cm2 1.01014 cm2 3.61021 cm3

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530 540 550 530 540 550Photon energy (eV) Photon energy (eV) Photon energy (eV) Photon energy (eV) Photon energy (eV)

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Figure 2 | Creating 2D and 3D oxygen vacancies. (a) LEED patterns with surface reconstruction labelled for SrTiO3 surfaces prepared at different annealing temperature sequentially. The corresponding carrier densities are calculated by Ti3 ratio from PEY XAS spectra for 2D case (r1,000 C) and

TFY-XAS spectra for 3D case (1,200 C). See Methods for details. (be) Ti L2,3-edge and O K-edge XAS spectra from different surfaces. Black arrows indicate the peak intensity coming from Ti3 . (f) Top, numerically calculated XAS spectra of Ti3 and Ti4 ions in SrTiO3. Bottom, decomposition of experimental XAS spectra, exemplied by the PEY spectra for surfaces annealed at 1,000 C. (g) Schematic evolution of oxygen vacancy concentration and Ti3 ratio from PEY and TFY spectra. Vertical black line indicates the boundary between 2D and 3D oxygen vacancies.

conclude that vacuum annealing from 800 C to 1,000 C generates 2D oxygen vacancies conned at the surface. However, for samples annealed above 1,000 C, the high concentration of oxygen vacancies presents a 3D distribution of

charges. For the whole annealing temperature range, the concentration of induced surface charge carriers (2D and 3D) increases monotonously with temperature. In addition, judged from the sharp LEED pattern, the vacancies are well-aligned.

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These ordered defect dipoles break the local inversion symmetry, allow the Raman measurement of rst-order phonons26 and suggest a phase with ferroelectric-like polarization at the reduced surface of SrTiO3 (ref. 27).

Observation of Frhlich polaron spectra by ARPES. It is natural to ask what kind of electronic structure does this ferroelectric-like layer correspond to. Figure 3a shows the symmetrized Fermi surfaces (FSs) from the SrTiO3 surface annealed at 700 C.

Thanks to the matrix element effect, we can selectively excite electrons with different orbital symmetry (see Fig. 1c for measurement geometry). No ARPES spectral intensity can be detected at the rst Brillouin zone centre (G and G00 specically).

FSs at G10 and G01 are elliptical, with dxz (Fig. 3f) and dyz orbital character, respectively. The circular FS at G11 are from dxy orbital (Fig. 3b). Fitted dispersions (black dashed lines in Fig. 3b,c,f) show an effective mass of B0.6me (me the free electron mass) for dxy band, and B6me for dxz band (see Supplementary Fig. 2 for tting details). These lighter effective masses will contribute to the high carrier mobility12,28.

An extraordinary distinction is that there exist replica bands for each orbital (Fig. 3b,f), lying B90 meV higher than the original, which can be clearly distinguished from the energy-second-derivative spectra in Fig. 3c. The replica forms one more higher-lying electron pocket, as shown by the constant-energy contours in Fig. 3e. These replicas are attributed to the many-body effect, specically, the electronphonon coupling

(EPC)6,29. The characteristic energy, B90 meV, corresponds to one surface polar LO phonon mode30. These dispersions hence describe electrons weakly coupled to a lattice vibrational mode by the Coulomb interaction, which together can move coherently through the solid and composite a new type of quasi-particle, that is, large polaron. We use the weak-coupling eld-theoretical Frhlich Hamiltonian8 as the rst approximation to describe EPC in both 3D and 2D cases:

p22mb X

oLO;jay

kjakj X

Vk;jeik~rakj h:c:

Where r is the position coordinate operator of the electron with band mass mb, p is its canonically conjugate momentum operator; akjw(akj) is the creation (annihilation) operator for the j-th LO phonons of wave vector k and energy oLO,j. The Vkj

is the Fourier component of the EP interaction. Considering one branch of dispersion-less LO-phonon (Einstein model)3133, this interaction system becomes one of the exactly solvable models in many-body physics34. The spectra can be well-described by a FranckCondon model with Poisson distribution:

IlI0

gll ! 2

Here I0 is the quasi-particle peak intensity and Il the l-th replica intensity with l phonon(s) dressed. g is a constant, related with the EP interaction in 3D.

a b c d

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Figure 3 | Observation of Frhlich polaron spectra by ARPES at SrTiO3 surface prepared at 700 C. (a) Symmetrized Fermi surface of SrTiO3 in kx ky

space. G10 2p/a(1, 0)B(1.61, 0) 1. (b) Dispersion from G11 along [11] direction with dxy orbital character. Dispersion from G10 along [01] direction with

dxz orbital character is shown in f. The momentum cuts are shown in dashed while lines. (c) Energy-second-derivative image of spectra in b. (d) Simulated large polaron dispersions with dxy/dyz and dxz orbital characters. (e) Constant-energy contours of large polaron electronic structure, characterized by two (or more) similar electron pockets, indicated by dashed lines. (g) EDC stacks of spectra in b. Black empty circles indicate the EDC shown in h.

(h) FranckCondon line shape tting. The tted EDC (red line) is composed of three Gaussian peaks (blue line), separated in energy by 90 meV, and a hump-like background (red dashed line). Black dashed lines in b,c and f are tted dispersions for the zero-order bands. See Supplementary Fig. 2 for details.

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Considering the ARPES spectra in Fig. 3b,f, the lower-lying band corresponds to charge carriers without dressing phonons, while the higher one corresponds to charge carriers dressing one phonon. Other higher-order bands are nearly invisible but can be deduced from the energy distribution curves (EDCs) tted with FranckCondon line shape as shown in Fig. 3h (refs 6,29). The tting gives an energy separation oLOB90 meV and g 0.85. We

can also use other tting parameters a3D and a2D, to characterize the Frhlich coupling constant. Inferred from the zero-phonon peak intensity fraction of total weight, according to the diagrammatic quantum Monte Carlo simulation35, we have a3DB2.5. Using the scaling relation Z2D (a) Z3D (3pa/4) for

2D polarons36, we have a2DB1.1. Notably, here we use a common and available approach to estimate the 2D coupling strength indirectly. However, although beyond the scheme of present work, a more accurate model directly describing 2D Frhlich polaron spectra is highly desired.

It is worthy to note that the whole spectra with multiple bands we observed here describe the ground state of Frhlich polaron, not the excited state, since the temperature is set to zero for the theoretical spectra function34. In the ground state of Frhlich polaron, some probability exists that the charge carriers have different set of energy ol eb-D oLOl. Furthermore, this is

different from the characteristic peak-dip-hump spectra in cuprates37,38, in which case localized small polarons show no high-order dispersion. Our discovery only becomes possible because of the intermediate coupling strength. The discrete phonon mode energy is bigger than the electron bandwidth and most crucially, because the forward scattering is dominating the EPC, as discussed in the recent literature. Figure 3d shows the simulated dispersion of Frhlich polaron for both dxy and dxz/yz

orbitals, with the full width at half maximum (FWHM) set as constant, 25 meV and without multiple phonon contribution. Our discovery represents a rare eld theoretical model of Frhlich polaron, which is exactly solvable29,34.

One may wonder if these multiple bands arise from band bending effect due to the quantum connement of the conduction band bottom. In fact, the 2D electron gases/liquids at SrTiO3 surface have become model systems for engineering emergent behaviour and studying the quasi-particle dynamics in complex transition metal oxides11,12,15. Here we rule out this possibility due to the fact that the sub-bands in the quantum connement picture are real electronic structure, crossing Fermi level, but our observed shadow bands are the echo of EPC, without Fermi level crossing. See Supplementary Fig. 3 for schematic understanding. We also clarify that, contrary to previous works12,39, during our experiments, all the surfaces displayed no detectable dependence on synchrotron irradiation, as demonstrated by the core level and XAS spectra in Supplementary Fig. 4.

Many seminal studies have been recently done describing the 2DEG scenario, which provide a lot of information even if many important aspects of this phenomenon are still under inamed discussion. What is important, however, is that there is a quite robust consensus on the conditions in which the 2DEG is stable. Consequently, we have been able to identify three important parameters: carrier density, oxygen vacancy concentration and thickness of the surface layer where the 2DEG takes place. The reported value for the carrier density is close to 1014 cm 2 (see, for example, refs 11,15). For the oxygen vacancies, most of the works report a rather constant concentration11,12,40. Finally, the thickness is estimated in most of the important works around four to eight cell units11,12,15,40. For the polaron scenario, however, the formation appears when the carrier density, the oxygen vacancies and the thickness of the surface layer are in rather different ranges. In our manuscript, we have demonstrated that the polarons only form when the carrier density is close to

1013 cm 2, 1 order of magnitude lower than that for the case of 2DEG. For the oxygen concentration, the polarons appear for approximately half the concentration of oxygen vacancies reported for 2DEG systems (Supplementary Fig. 1). Finally, for the thickness, thanks to the parallel detection of XAS and ARPES we can conrm that the thickness of the surface polarons is not larger than one to two cell units, at least four to eight times smaller than that for the 2DEG surface layer.

Dimensionality and stability of the Frhlich polarons. As deduced from the XAS spectra, annealing below 1000 C creates 2D charge carrier localized mainly at the surface. From ARPES spectra we identify these charge carriers as Frhlich polarons. We then directly demonstrate the 2D nature of Frhlich polarons by ARPES. Photon-energy-dependent ARPES can map the FS at 3D momentum space (see Methods). Figure 4a shows the FS of dxy

orbital around one bulk G point in kx ky kz momentum space

from surface annealed at 800 C. To highlight the detail, we plot the second-derivative photoemission intensity versus momentum. Its cylindrical shape and the lack of dispersion along kz direction directly conrm the 2D nature of the FS. The projection of this 2D FS onto kx ky momentum space composes an open circle.

On the contrary, for surface annealed at 1,200 C, the corresponding kz dispersion of the FS shows a ellipsoid-like shape, whose projection shows lled circle feature (Fig. 4d), composing evidence of 3D carriers. Consequently, the EDCs analysis as a function of the annealing temperature (Fig. 4c) shows the polaronic bands till the oxygen vacancies present a 3D distribution. In fact, only one Gaussian peak could be tted to the 1,200 C EDC, with a non-vanishing background connecting the oxygen vacancy band (Supplementary Fig. 1c). This higher binding energy spectral weight commonly results from electron interaction, reminiscent of liquid behaviour12. Thus, both FSs and EDCs spectral analysis prove the 2D nature of Frhlich polarons. The transition from 2D Frhlich polaron to 3D electron liquid will be discussed in detail later.

Despite its ultimate collapse, 2D Frhlich polarons are relatively stable over a wide carrier density. The carrier density can be calculated from the Luttinger area of the FSs (see Methods), shown in Fig. 5a,b (see Supplementary Figs 5 and 2 for detailed FSs and tting). For 2D Frhlich polaron, we have n2DB5.7 1013 cm 2, 7.4 1013 cm 2 and 7.6 1013 cm 2

for surfaces prepared at 700 C, 800 C and 1,000 C, respectively. We have also estimated the carrier density according to the Ti3 /Ti4 ratio from PEY XAS spectra (see Methods). For 2D case, we got n2DB4.0 1013 , 4.6 1013 and 1.0 1014 cm 2 for

corresponding surfaces, in qualitative agreement with ARPES data. It is worthy to note that, for both ARPES and XAS, we assume an ideal 2D scenario. In reality the probe depth for our ARPES and XAS measurements are different since the photo-electron kinetic energy is about 95 eV for ARPES and 40 eV for XAS. As shown in Fig. 4c, from all samples annealed between 800 C and 1,000 C, FranckCondon line shape tting gave similar second and third order polaronic peak weight, indicating a constant EPC and relatively stable polarons, regardless of the vacancies organization or charge concentration.

Estimated from the 2D carrier density for 700 C case, the WignerSeitz radius rs (2pn2D) 1/2 is B5.3 and the average

separation between two Frhlich polarons is B11 (approximately three unit cells). Consequently, the momentum width Dk from ARPES spectra at Fermi momentum gives a polaron MFP lB10 . The FranckCondon tting in Fig. 4c also gave similar hump-like background for all the three surfaces. Note that, unlike the 1,200 C case with oxygen vacancy band observed at higher binding energy, this background can only originate from the

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a b

800 C

Low High

700 C 800 C 1,000 C 1,200 C

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Intensity (a.u.)

EDCFit Backgound

E EF (eV) E EF (eV) E EF (eV) E EF (eV)

Figure 4 | 2D nature and stability of large polarons in SrTiO3. (a,d) Fermi surface of SrTiO3 in kx ky kz space with dxy orbital character. The FSs are

centred at one Brillouin zone centre, G, which is one high-symmetric point in three-dimensional momentum space with (kx, ky , kz) 2p/a(1, 1, 3)B(1.61,

1.61, 4.83) 1. (b) Evolution of dispersions from the G11 cut as in Fig. 3b. (c) EDC curves (black empty circles) extracted from the momentum window shown in grey in b. FranckCondon line shape tted curves are shown with red lines. Blue lines represent individual Gaussian peaks.

a b

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5.71013 cm2 7.41013 cm2 7.61013 cm2 9.21020 cm3

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Figure 5 | Evolution of Fermi surfaces and dispersions. (a) Symmetrized Fermi surfaces of SrTiO3 in kx ky space for (001) surfaces annealed at different temperature. The raw data is shown in Supplementary Fig. 5. (b) Fitted FSs for all the three orbitals. The calculated carrier densities are shown for corresponding FSs. See Methods for calculation formula. The superimposed red and black curves indicate the size change for dxz FS and dxy FS, respectively.

(c) Fitted dispersions for different orbitals. See Supplementary Fig. 2 for tting details. The superimposed red and black curves indicate the band bottom change for dxz band and dxy band (zero order), respectively.

conduction band, and most likely, attributed to the interaction between polarons. In addition, the effective mass for Frhlich polaron (B0.6me for dxy orbital) is even lighter than that both for 3D liquid in our case (B1.1me) and for 2D electron gas from reported data (B0.7me)11, indicating its high mobility. Thus it is proper to conclude that 2D liquid of Frhlich polarons with high mobility can be created and conned at the surface of SrTiO3.

DiscussionThe ultimate collapse of 2D Frhlich polaron to 3D liquid is puzzling and deserves further examination. Here we interpret it exclusively from the point of view of symmetry. Considering that the EPC is local and linear, in lattice with space inversion symmetry, only phonons with even parity can contribute to the EPC. The linear contribution from polar LO phonons becomes possible only with inducing symmetry breaking. Intrinsic SrTiO3

has a centre-symmetric structure, with dxy and dxz/yz orbitals degenerate at the bottom of conduction band41. As annealed from 800 C to 1,000 C, the oxygen vacancies mainly locate at the O1 site (Fig. 1a). These highly restricted 2D defect dipoles break the inversion symmetry along z direction, resulting in the level splitting between dxy and dxz orbitals as shown in Fig. 5c. The sign change of splitting between 700 C and 800 C cases may attribute to the alignment and correlation of dipolar moment. Nevertheless, FranckCondon line shape tting yields similar phonon energy and coupling strength (Fig. 4c), indicating the robustness of Frhlich polaron with broken inversion symmetry. In the case of 1,200 C, oxygen vacancies expand to 3D and start to occupy O2 sites. These 3D defect dipoles generate relatively even potential along all the three directions. Thus somehow the surface lattices regain its symmetry, deduced by the re-degenerate orbital bands (see Fig. 5c for 1,200 C case). Consequently, EPC fails, and the many-body effect is dominated by electronelectron

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interaction, forming 3D liquid. Our scenario suggests that, besides vacuum annealing, other symmetry-breaking alternatives such as applying electric eld42 or capping layer6,43 may also initiate the electronLO phonon coupling and create Frhlich polarons.

The 2D Frhlich polaron density falls in the range of which superconductivity in perovskite oxide interfaces is observed42,44. It has been long proposed that a BoseEinstein condensation of 2D bipolarons into a superconducting uid be responsible for the high Tc in cuprates with multiple LO-phonon branches45. The recent discovery of high Tc in single unit cell thick iron selenide lm (1UC FeSe) grown on SrTiO3 substrate also suggests the intimate interplay between charge carriers in FeSe and LO-phonon in SrTiO3 (refs 6,46,47). The transport measurements48 rst conrm the very high-Tc superconductivity in single layer FeSe/STO system, in agreement with ref. 6. So if one considers these works together, it would be direct to deduce that this EPC is intrinsic for SrTiO3 and be responsible for the enhanced superconductivity in FeSe/STO system. However, even if there are several articles suggesting that the EPC of the SrTiO3 may be relevant in the mechanism of the high-Tc superconductivity, our manuscript is not dealing directly with this issue, in consequence further studies should be carried out to prove or disprove the relation between these two processes.

It is worthy to note that the phonon mode we observed here may not necessarily represent only one LO-branch, but could correspond to the approximation of multiple LO-phonon branches49. In this case, the calculated effective coupling constant a3D is 2.34(m*)1/2. Using the band effective mass (m*)

of dxy orbital in 3D liquid case, we have a3DB2.45, in excellent agreement with our experimental value. In this approximation, large bipolarons are found to have an extended stability region at low temperature. Thus our observation of Frhlich polaron liquid in SrTiO3 suggests signicant relevance of large (bi)polaron for superconductivity and should stimulate broad interest in exploring polaron behaviour in a wide range of perovskite-related materials, especially high-Tc cuprates and iron-based superconducting lm on SrTiO3 substrate.

Methods

Sample preparation. SrTiO3 (100) single crystals (crystal GmbH and SurfaceNet GmbH) were mounted on resistive Si heaters and cleaned by thermal annealing in vacuum conditions. Each sample was sequentially heated up to particular temperatures, and kept for 20 min, till characteristic LEED patterns are stabilized. At all stages of the cleaning procedure, the pressure was o10 9 mbar. All samples presented reproducible and stable phases, with a series of typical reconstructions.

X-ray Absorption Spectroscopy (XAS). For the XAS measurements, from the same sample surface secondary electrons were recorded by Scienta energy analyzer, while uorescence was recorded simultaneously by Bruker detector. XAS spectra simulation was performed by tetrahedral cluster model calculation. The cluster consists of a central Ti atom and its nearest neighbour ligand atoms, and the model calculation includes not only the full multiplets of 3d electrons but also conguration interaction.

ARPES. The angle and energy resolutions of the ARPES measurements (Scienta R4000) are set as 0.2o and B10 meV. The photon energy-dependent ARPES experiments were performed with photon energy varying from 70 eV to 115 eV. The kz was calculated by kz 1 2mEk cos2 y V0

1=2. The inner potential

V0 12 eV. Unless otherwise stated, we used photon energy at 100 eV for normal

ARPES measurements. The 2D and 3D carrier density can be calculated from the Luttinger area of the FSs. n2D k2F 2p

= and n3D k3F 3p2

= . From the Ti3 ratio, the carrier density can also be calculated by n2D ratio a 2 and

n3D ratio a 3 with the lattice constant a 3.9 .

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9585

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Acknowledgements

We thank Prof. Z.X. Shen for discussion. The Synchrotron SOLEIL is supported by the Centre National de la Recherche Scientique (CNRS) and the Commissariat lEnergie Atomique et aux Energies Alternatives (CEA), France.

Author contributions

C.C. managed the nal data analysis and manuscript writing with initial input from E.F. and M.C.A. ARPES and XAS experiments were performed by J.A., E.F. and A.L., and they have also partially participated in the data analysis. M.C.A. has initiated and designed this research. J.A. and M.C.A. have conducted the experimental research programme and data analysis. Also, the manuscript writing was improved by M.C.A. All authors discussed the results and commented on the manuscript.

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Abstract

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The polaron is a quasi-particle formed by a conduction electron (or hole) together with its self-induced polarization in a polar semiconductor or an ionic crystal. Among various polarizable examples of complex oxides, strontium titanate (SrTiO₃ ) is one of the most studied. Here we examine the carrier type and the interplay of inner degrees of freedom (for example, charge, lattice, orbital) in SrTiO₃ . We report the experimental observation of Fröhlich polarons, or large polarons, at the bare SrTiO₃ surface prepared by vacuum annealing. Systematic analyses of angle-resolved photoemission spectroscopy and X-ray absorption spectra show that these Fröhlich polarons are two-dimensional and only exist with inversion symmetry breaking by two-dimensional oxygen vacancies. Our discovery provides a rare solvable field theoretical model, and suggests the relevance of large (bi)polarons for superconductivity in perovskite oxides, as well as in high-temperature superconductors.

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Title

Observation of a two-dimensional liquid of Frohlich polarons at the bare SrTiO3 surface

Author

Chen, Chaoyu; Avila, José; Frantzeskakis, Emmanouil; Levy, Anna; Asensio, Maria C

Pages

8585

Publication year

2015

Publication date

Oct 2015

Publisher

Nature Publishing Group

e-ISSN

20411723

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1038/ncomms9585

ProQuest document ID

1725014262

Observation of a two-dimensional liquid of Frohlich polarons at the bare SrTiO3 surface

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