Temperature-tunable Fano resonance induced by strong coupling between Weyl fermions and phonons in TaAs

Abstract

Strong coupling between discrete phonon and continuous electron-hole pair excitations can induce a pronounced asymmetry in the phonon line shape, known as the Fano resonance. This effect has been observed in various systems. Here we reveal explicit evidence for strong coupling between an infrared-active phonon and electronic transitions near the Weyl points through the observation of a Fano resonance in the Weyl semimetal TaAs. The resulting asymmetry in the phonon line shape, conspicuous at low temperatures, diminishes continuously with increasing temperature. This behaviour originates from the suppression of electronic transitions near the Weyl points due to the decreasing occupation of electronic states below the Fermi level (E_F ) with increasing temperature, as well as Pauli blocking caused by thermally excited electrons above E_F . Our findings not only elucidate the mechanism governing the tunable Fano resonance but also open a route for exploring exotic physical phenomena through phonon properties in Weyl semimetals.

ARTICLE

Received 1 Sep 2016 | Accepted 9 Feb 2017 | Published 30 Mar 2017

B. Xu1,2,*, Y.M. Dai3,*, L.X. Zhao1, K. Wang1, R. Yang1, W. Zhang1, J.Y. Liu1, H. Xiao2, G.F. Chen1,4, S.A. Trugman3,5,

J.-X. Zhu3,5, A.J. Taylor6, D.A. Yarotski3, R.P. Prasankumar3 & X.G. Qiu1,4

Strong coupling between discrete phonon and continuous electronhole pair excitations can induce a pronounced asymmetry in the phonon line shape, known as the Fano resonance. This effect has been observed in various systems. Here we reveal explicit evidence for strong coupling between an infrared-active phonon and electronic transitions near the Weyl points through the observation of a Fano resonance in the Weyl semimetal TaAs. The resulting asymmetry in the phonon line shape, conspicuous at low temperatures, diminishes continuously with increasing temperature. This behaviour originates from the suppression of electronic transitions near the Weyl points due to the decreasing occupation of electronic states below the Fermi level (EF) with increasing temperature, as well as Pauli blocking caused by thermally excited electrons above EF. Our ndings not only elucidate the mechanism governing the tunable Fano resonance but also open a route for exploring exotic physical phenomena through phonon properties in Weyl semimetals.

1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China. 2 Center for High Pressure Science and Technology Advanced Research, Beijing 100094, China. 3 Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. 4 Collaborative Innovation Center of Quantum Matter, Beijing 100190, China. 5 Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. 6 Associate Directorate for Chemistry, Life and Earth Sciences, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to Y.M.D. (email: mailto:[email protected]

Web End [email protected] ) or to R.P.P. (email: mailto:[email protected]

Web End [email protected] ) or to X.G.Q. (email: mailto:[email protected]

Web End [email protected] ).

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DOI: 10.1038/ncomms14933 OPEN

Temperature-tunable Fano resonance induced by strong coupling between Weyl fermions and phonons in TaAs

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14933

The Weyl semimetal (WSM) phase, a novel topological state of quantum matter, has been proposed to exist in materials with two non-degenerate bands crossing at EF in three-

dimensional momentum space1. At the band crossing points (Weyl points), the electronic dispersion is linear in all three directions, resembling a three-dimensional version of graphene, and the low-energy excitations can be described by Weyl equations, producing a condensed-matter realization of Weyl fermions2. Recently, such a WSM state has been discovered in non-centrosymmetric transition-metal monoarsenides and monophosphides (TaAs, TaP, NbAs and NbP)38, where 12 pairs of Weyl points have been found. Since the Weyl points are located in close proximity to EF in these materials, interband electronic transitions near the Weyl points occur at a very low energy, 2|m|, where |m| represents the chemical potential with respect to the Weyl points9,10. This energy scale overlaps optical phonon frequencies11. Consequently, strong coupling between electronic transitions near the Weyl points (Weyl fermions) and phonons may arise, manifested through a temperature-tunable Fano resonance.

This is actually a rare occurrence. Fano resonances generally do not occur in conventional metals or semiconductors, since the energy scale of interband electronic transitions in these materials is usually much higher than phonon excitations. However, this interesting phenomenon has been reported in bilayer or few-layer graphene1214, topological insulators15,16 and some strongly correlated electron systems, such as stripe-phase nickelates17 and high-Tc superconductors18,19. The observed

Fano resonance in strongly correlated materials is very weak, with 1/q2, a parameter that describes the asymmetry of the Fano line shape, only reaching B0.04 (refs 1719). In topological insulators, the effect is also weak 1=q2 0:02 0:06

and cannot

be observed without manipulating extrinsic parameters, such as magnetic eld15, chemical doping16 or micro-fabrication on the surface20. In contrast, bilayer or few-layer graphene exhibits a strong Fano resonance, with 1/q2Z1, but the resonance energy is B1,600 cm 1 (200 meV), much greater than EF, making it impossible to tune the resonance via temperature1214. Moreover, the Fano physics revealed in all the above materials is associated with or has considerable contributions from coupling between phonons and conventional massive fermions.

Here we observe an intrinsic, strong 1=q2 1:1

and

temperature-tunable Fano resonance, which arises purely from quantum interference between phonons and massless Weyl fermions, in the recently discovered Weyl semimetal TaAs. We further demonstrate that the Fano line shape can be tuned by changing the occupation of the electronic states near the Weyl points. These observations not only open a novel avenue for exploring exotic quantum phenomena in WSMs, such as the chiral anomaly2124, but also set the stage for a variety of potential applications that take advantage of the ability to tune the Fano resonance using different parameters (for example, temperature, light or magnetic/electric elds).

ResultsSample growth and characterization. High-quality single crystals of TaAs were synthesized through a chemical vapour transport method23. The as-grown crystals are polyhedrons with shiny facets up to 1.5 mm in size. X-ray diffraction measurements reveal that the as-grown facets are the (001), (107) and (112) surfaces (Supplementary Fig. 1). Systematic optical measurements were carried out on all three surfaces.

Reectivity and optical conductivity. Figure 1a shows the far-infrared reectivity R(o) measured on the (107) surface of

TaAs at 11 different temperatures from 5 to 300 K (ref. 10). The relatively high R(o) that approaches unity at zero frequency is consistent with the metallic nature of TaAs. A well-dened plasma edge in the far-infrared region suggests very low carrier density, in agreement with the tiny volumes enclosed by the Fermi surfaces in this material36. In addition to the broad features in R(o), a sharp feature can be clearly identied at B253 cm 1 (31 meV), as indicated by the arrow, which is associated with the infrared-active

A1 phonon mode (Supplementary Note 1).

In order to gain direct information about this mode, we calculated the optical conductivity s1(o) from R(o) using a KramersKronig analysis10 (more details in Methods section). Figure 1b displays s1(o) of TaAs on the (107) surface in the far-infrared region at different temperatures. The low-frequency s1(o) is dominated by a narrow Drude response alongside prominent linear features, whose origin and temperature dependence have been previously discussed in detail10. The A1 mode manifests itself as a sharp peak in the s1(o) spectrum, as indicated by the arrow. Figure 1c shows an enlarged view of s1(o)

in the frequency region of 240270 cm 1, where the A1 mode can be seen more clearly. It is well known that, in the absence of strong electronphonon coupling, the phonon exhibits a symmetric line shape in s1(o) that can be described by a Lorentz oscillator, as schematically illustrated in Fig. 1d. In contrast, strong electronphonon coupling gives rise to an asymmetric phonon prole in s1(o), known as the Fano line shape13,14,25 (Fig. 1e). As shown in Fig. 1c, the A1 mode in

TaAs exhibits a striking asymmetric line shape at low temperatures, which is an unequivocal signature of strong electronphonon coupling. More interestingly, the asymmetry of the phonon line shape diminishes as the temperature rises, suggesting that the coupling-induced Fano resonance in TaAs can be tuned by temperature.

Mechanism governing the temperature-tunable Fano resonance. To quantify the temperature dependence of the A1 mode, we extract the phonon line shape by subtracting a linear electronic background in a narrow frequency range at all measured temperatures, as shown in Fig. 2a. At each temperature, the phonon is t with the Fano line shape25,

s1

o

2p

Z0

O2 g

q2 4q o o0g 1

q2 1 4 o o0

2 ; 1

where Z0 is the vacuum impedance; o0, g and O correspond to the resonance frequency, linewidth and strength of the phonon, respectively; q is a dimensionless parameter that describes the asymmetry of the Fano prole. A larger 1/q2 indicates more conspicuous asymmetry in the phonon line shape, while for 1/q2 0, the symmetric Lorentz line shape is fully recovered.

The solid lines in Fig. 2a represent the tting curves, which describe the measured phonon line shapes reasonably well at all temperatures. This procedure also returns the temperature dependence of the tting parameters.

Figure 2b depicts 1/q2 as a function of temperature. While 1/q2 adopts a large value of 1.1 at 5 K (refs 1214,18), it decreases dramatically with increasing temperature. This suggests that the A1 mode is strongly coupled to a continuum of electronhole excitations, and the resulting Fano resonance varies signicantly with temperature. We rst trace the origin of this coupling by examining the band structure of TaAs. Both rst-principle calculations and angle-resolved photoemission spectroscopic measurements have revealed 12 pairs of Weyl points in TaAs36. These Weyl points are categorized into two types3. Four pairs in the kz 0 plane, about 2 meV above EF, are dened

g2

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a b c d

1.8

300

5

T(K)

T (K)

3 1 cm 1 )

6

1.2

0.6

0.0240 250 260 270 4 0

2

[afii9846] 1([afii9853]) (a.u.)

0

1.0

0.9

0.8 0

3 1 cm 1 )

e

Reflectivity

4

[afii9846] 1([afii9853]) (10

0

[afii9846] 1([afii9853]) (10

2

0 0

100Wave number (cm1) Wave number (cm1)

2 4

[afii9853] (cm1) ([afii9853] -[afii9853]0) / [afii9828]

200 200

300 400 400 600

Figure 1 | Reectivity and optical conductivity of TaAs. (a) Reectivity of TaAs in the far-infrared region measured at different temperatures on the (107) surface. (b) Optical conductivity of TaAs on the (107) surface up to 600 cm 1 at different temperatures. (c) Enlarged view of the optical conductivity in the region of the infrared-active A1 mode at B253 cm 1. (d) Schematic of the symmetric Lorentz oscillator, which describes the phonon line shape in the optical conductivity without strong electronphonon coupling. (e) Schematic of the asymmetric Fano resonance, used to describe the phonon line shape in the presence of strong electronphonon coupling.

1.5

1.0

a b c

10

T (K)

A

[afii9846] 1([afii9853]) (103 1cm1)

2.0

1.5

1.0

0.5

0.0

8

1/q2

[afii9828](cm1 )

6

0.5

4

0.0

0 100 200 300 0

2

240 250 260 270

[afii9853] (cm1) T (K)

100 200 300

T (K)

Figure 2 | Fano t and temperature dependence of tting parameters. (a) Line shape of the A1 phonon, with the electronic background subtracted at different temperatures. The black solid lines through the data denote the Fano tting results. (b,c) Temperature dependence of the Fano parameter 1/q2 and the line width g of the A1 mode, respectively. Error bars for both parameters are estimated by tting the phonon line shape to the Fano equation in different frequency ranges at all measured temperatures. The red solid lines through the data in each panel represent the modelling results.

as W1, while another eight pairs off the kz 0 plane, lying about

21 meV below EF, are named W2. Interband electronic transitions in the vicinity of a Weyl point start at o 2|m| (refs 9,10), making

it easy to calculate that electronic transitions near W2 turn on at o 42 meV (B336 cm 1). Thus electronic transitions at

the frequency of the A1 mode (253 cm 1) do not occur near W2. This implies that the A1 mode is unlikely to be coupled to the electronic transitions near W2. However, electronic transitions near W1 set in at o44 meV (B32 cm 1) and can therefore overlap with the frequency of the A1 mode, suggesting that this mode is coupled to the electronic transitions near W1.

Having attributed the asymmetric line shape of the A1 mode to its strong coupling with the electronic transitions near W1, we proceed to understand the temperature dependence of this mode. In WSMs, since the Weyl points are in close proximity to EF,

electronic transitions near the Weyl points can be dramatically affected by thermal excitations, thus changing the line shape of the phonon that is coupled to these transitions. Figure 3 shows the band structure along three momentum directions near W1 in TaAs. The occupation probabilities of the electronic states in these bands (colour maps) are calculated using the FermiDirac distribution function at three different temperatures (5, 150 and 300 K), from which we see that the occupation of the electronic

states near W1 depends strongly on the temperature. At5 K (Fig. 3ac), the electronic states below EF are fully occupied (blue), while the states above EF are empty (white). In this case, interband transitions at the energy of the A1 mode :o0 are strong, as indicated by the thick arrows. As the temperature increases from 5 to 300 K, thermal excitations cause vacant states to appear below EF and electronic states above EF to be partially occupied. Electronic transitions at :o0 are signicantly suppressed (illustrated by the thin arrows in Fig. 3), because the available initial states for these transitions decrease, and many of the nal states are Pauli blocked by thermally excited electrons. This suppression of the electronic transitions near W1 is directly responsible for the change in the A1 phonon line shape.

For a more quantitative analysis, the dimensionless parameter q in the Fano theory is given by13,25

q

; 2

where Ve ph is the electronphonon coupling strength;

De h(o0, T) is the joint electronhole pair density of states at

the frequency of the A1 mode o0 for a given temperature T; and mph and me h represent the optical matrix elements for phonon

and electronhole pair excitations, respectively. In this equation, we note that raising T mainly modies De h(o0, T) by thermally

1

mph

me h

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E(meV)

E(meV)

E(meV)

0

1

Figure 3 | Occupation probability of the electronic states near W1. Band structure along three different momentum directions near the Weyl points W1 in TaAs. The black and red dashed lines in each panel correspond to the Fermi level and the energy of W1 ( m

j j 2 meV), respectively. The colour maps,

which are calculated from the FermiDirac distribution function f(E), denote the occupation probability of the electronic states at different temperatures of5 K (ac), 150 K (df) and 300 K (gi). The red arrows represent the electronic transitions at the energy of the A1 mode :o0. The thickness of each arrow schematically depicts the transition amplitude.

exciting electrons to the electronic states above EF and creating holes below EF. Near the Weyl points, the nite-temperature joint electronhole pair density of states at :o0 takes the form

De h o0; T

D0e h o0

f

!

o0

e 2kBT

1

where f E1= eE m=kBT 1

is the Fermi function, with E representing the energy of the single-particle state with respect to the Weyl points and D0e h o0

being the zero-

temperature joint electronhole pair density of states at :o0. The red solid curve in Fig. 2b is the least-squares t to the experimental temperature dependence of 1/q2 (blue solid circles) using equation (2). The excellent agreement between our experimental data and the model further underlines the intimate link between the line shape of the A1 mode and the electronic transitions near W1, which are continuously suppressed with increasing temperature due to the reduced occupation of the electronic states below EF and Pauli blocking from thermally excited electrons above EF.

A careful examination of the temperature dependence of the A1 phonon linewidth g (Fig. 2c) leads us to the same conclusion.

In the case of weak electronphonon coupling, phonon decay is dominated by the anharmonic effect: a zone-centre phonon decays into two acoustic modes with the same frequencies and opposite momenta26,27. The temperature dependence of the

phonon linewidth gph ph(T) for this process follows

gph phTgph ph0 1

2

; 4

where g0ph ph is the residual linewidth at zero temperature. Apparently, this model does not account for the behaviour of the

A1 mode in TaAs, since it gives an increasing g as the temperature is raised, which is opposite to our experimental observation. Instead, strong electronphonon coupling must be taken into account to understand the temperature dependence of g in

TaAs. In a system with strong electronphonon coupling, a phonon can also decay by creating an electronhole pair28. This process is sensitive to De h(o0, T) and is thus suppressed with increasing temperature due to thermal excitations, resulting in a temperature-dependent phonon linewidth ge ph(T)

ge phTge ph0 f

o0 2

f o0

2

; 3

o0 2

f o0

2

; 5

where g0e ph represents a residual linewidth. Consequently, the temperature-dependent linewidth of a phonon mode that is strongly coupled to electronic excitations is given by g(T) gph ph(T) ge ph(T). This equation gives an excellent

description to the measured temperature dependence of the linewidth for the A1 mode in TaAs, as shown by the red solid curve in Fig. 2c. The above observations explicitly demonstrate that the A1 mode is strongly coupled to the electronic transitions near W1, and both the line shape and linewidth of this phonon are closely tied to these transitions, which can be

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continuously tuned by temperature through varying the occupation of the electronic states near W1.

To lend further credence to our experimental results and analysis, we performed optical measurements at 12 different temperatures on the (112) surface. Essentially identical behaviour was revealed for the A1 mode (Supplementary Fig. 3). We then utilized the same methods and models to analyse the line shape and linewidth of this mode observed on the (112) surface (Supplementary Fig. 4), reaching the same conclusions.

Finally, we note that although electronic transitions at :o0 are absent near W2 at low temperatures, Fermi smearing at high temperatures may relax the Pauli blocking, allowing these transitions to occur. From equations (2 and 3), we can easily calculate the asymmetry of the A1 mode arising from coupling to W2 at 300 K: 1=q2W2 300 K

0:07. This small value of 1/q2W2,

which vanishes quickly with decreasing temperature, suggests that electronic transitions near W2 do not give rise to a noticeable Fano resonance in the A1 mode of TaAs over the measured temperature range (5300 K). However, the enhancement of these transitions with increasing temperature may produce a strong Fano resonance at high enough temperatures. It is also worth pointing out that changing the occupation of the electronic states near W1 via other methods, such as electrical gating or femtosecond optical excitation, should induce a similar change in the Fano line shape of the A1 mode in TaAs.

DiscussionThe strong coupling between Weyl fermions and phonons enables the study of exotic quantum phenomena in WSMs by tracking the properties of phonons. One interesting proposal derived from our ndings is to provide experimental evidence for the chiral anomaly2124, in which the application of parallel electric (E) and magnetic (B) elds pumps electrons from one Weyl point to the other with opposite chirality at a rate proportional to E B, leading to a shift of EF in opposite

directions at different Weyl points. This EF shift caused by the chiral anomaly can signicantly affect the electronic transitions near the Weyl points, which accordingly changes the line shape of the phonon that is coupled to these transitions.

For more insight, we can calculate the chiral anomaly-induced EF shift, given by9,29

DEF

3e2 v3Ft

p ) form for the low-frequency extrapolation. Above the highest measured frequency, we assumed a constant reectivity up to 12.5 eV, followed by a free-electron (o 4) response.

Data availability. All data that support the ndings of this study are available from the corresponding authors upon request.

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2 E B

1=3

6

where vF is the Fermi velocity and t is the scattering time between different Weyl points. To obtain a realistic estimate, we take vF 5 105 m s 1 (refs 6,23,30), t 5 10 11 s (refs 9,24,29),

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Experimental observation of this effect would be a strong evidence for the chiral anomaly in WSMs.

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In conclusion, we have found compelling evidence for strong coupling between the infrared-active A1 phonon mode and electronic transitions near W1 (Weyl fermions) in TaAs through the observation of a Fano resonance. Varying the temperature, which changes the occupation of the electronic states in proximity to EF, can continuously tune the amplitude of the electronic transitions near W1, thus manipulating the line shape of the A1 mode. Our ndings not only suggest a new approach for investigating exotic quantum phenomena in WSMs, such as the chiral anomaly, through the behaviour of phonons, but also imply a broad range of potential applications, such as in thermo-, magneto- and electro-optical devices. Please note that, after our manuscript was submitted, we noticed two preprints (refs 33,34) that theoretically propose detecting the chiral anomaly in WSMs through phonon dynamics.

Methods

Sample synthesis. High-quality TaAs single crystals were grown througha chemical vapour transport method23. A previously reacted polycrystalline TaAs was lled in a quartz ampoule using iodine (2 mg cm 3) as the transporting agent.

After evacuating and sealing, the ampoule was kept at the growth temperature for 3 weeks. Large polyhedral crystals with dimensions up to 1.5 mm are obtained in a temperature eld of DT 1,1501,000 C.

Optical measurements. Near normal incident reectivity R(o) was measured over a broad frequency range on a Bruker VERTEX 80v FTIR spectrometer.

In order to accurately measure the absolute R(o) of the samples, an in situ gold overcoating technique35 was used. R(o) from 40 to 15,000 cm 1 were measured at 11 different temperatures from 300 down to 5 K on three different surfaces of as-grown single crystals in an ARS-Helitran cryostat. Since a broad spectral range is required for a Kramers-Kronig analysis, we extended our data to the ultraviolet range (up to 50,000 cm 1) at room temperature using an AvaSpec-2048 14 ber

optic spectrometer.

KramersKronig analysis. The real part of the optical conductivity s1(o) has been determined via a KramersKronig analysis of R(o)36. Below the lowest measured frequency, we used a HagenRubens (R 1 A

o

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Acknowledgements

We thank Ricardo Lobo, Yongkang Luo, Simin Nie and Hongming Weng for illuminating discussions. Work at IOP CAS was supported by MOST (973 Project Nos. 2015CB921303 and 2015CB921102) and NSFC (Grant Nos. 91121004, 91421304 and 11374345). Work at LANL was performed at the Center for Integrated Nanotechnologies, a US Department of Energy, Ofce of Basic Energy Sciences user facility, and funded by the LANL LDRD program and by the UC Ofce of the President under the UC Lab Fees Research Program, Grant ID No. 237789. H.X. is supported by NSFC, Grant No. U1530402.

Author contributions

B.X. carried out the optical measurements with the assistance of K.W., R.Y., W.Z. and J.Y.L.; L.X.Z. and G.F.C. synthesized the single crystals; B.X., Y.M.D., H.X., A.J.T., D.A.Y., R.P.P. and X.G.Q. analysed the data; S.A.T. and J.-X.Z. contributed to theoretical models; Y.M.D. wrote the manuscript; all authors made comments on the manuscript; R.P.P. andX.G.Q. supervised the project.

Additional information

Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications

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Competing interests: The authors declare no competing nancial interests.

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How to cite this article: Xu, B. et al. Temperature-tunable Fano resonance induced by strong coupling between Weyl fermions and phonons in TaAs. Nat. Commun. 8, 14933 doi: 10.1038/ncomms14933 (2017).

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6 NATURE COMMUNICATIONS | 8:14933 | DOI: 10.1038/ncomms14933 | http://www.nature.com/naturecommunications

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