Abstract
A Weyl semimetal is a novel topological phase of matter^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}, in which Weyl fermions arise as pseudomagnetic monopoles in its momentum space. The chirality of the Weyl fermions, given by the sign of the monopole charge, is central to the Weyl physics, since it directly serves as the sign of the topological number^{5,15} and gives rise to exotic properties such as Fermi arcs^{5,9,12} and the chiral anomaly^{15,16,17,18,19}. Here, we directly detect the chirality of the Weyl fermions by measuring the photocurrent in response to circularly polarized midinfrared light. The resulting photocurrent is determined by both the chirality of Weyl fermions and that of the photons. Our results pave the way for realizing a wide range of theoretical proposals^{15,16,20,21,22,23,24,25,26,27,28,29,30} for studying and controlling the Weyl fermions and their associated quantum anomalies by optical and electrical means. More broadly, the two chiralities, analogous to the two valleys in twodimensional materials^{31,32}, lead to a new degree of freedom in a threedimensional crystal with potential novel pathways to store and carry information.
Main
In 1929, H. Weyl discovered that all elementary fermions that have zero mass must attain a definitive chirality determined by whether the directions of spin and motion are parallel or antiparallel^{1}. Such a chiral massless fermion is called the Weyl fermion (WF). Although none of the fundamental particles in highenergy physics was identified as WFs, condensed matter researchers have found an analogue of this elusive particle in a new class of topological materials, the Weyl semimetal (WSM)^{2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}. Similar to the case in highenergy physics, the WFs in a WSM also have a definitive chirality. A righthanded Weyl node (χ = +1) is a monopole (a source) of Berry curvature whereas a lefthanded Weyl node (χ = −1) is an antimonopole (a drain) of Berry curvature. Any Fermi surface enclosing a right(left)handed Weyl node (χ = ±1) has a unit Berry flux coming out (in) and hence carries a Chern number C = ±1 (Fig. 1a). As a result, the chirality of the WF serves as its topological number.
The distinct chirality directly leads to exotic, topologically protected phenomena in a WSM. First, the separation between WFs of opposite chirality in k space protects them from being gapped out^{5}. Second, the opposite Chern numbers of the bulk Fermi surfaces guarantee the existence of topological Fermi arc surface states^{5} that connect between Weyl nodes of opposite chirality (Fig. 1a, b). Third, applying parallel electric and magnetic fields can break the apparent conservation of chirality, making a Weyl metal, unlike ordinary nonmagnetic metals, more conductive with an increasing magnetic field^{17,18,19}. Besides its fundamental importance in the topological physics of WSM, the chirality also gives rise to a new degree of freedom in threedimensional (3D) materials, analogous to the valley degree of freedom in the twodimensional (2D) transition metal dichalcogenides (TMDs) that have gathered great attention recently^{31,32}. The potential to control the chirality^{15,16,20,21,22,23,24,25,26,27,28,29}, combined with the high electron mobility found in the WSMs^{18}, may offer new schemes to encode and process information.
Therefore, it is of crucial importance to detect the chirality of the WFs. This requires identifying physical observables that are sensitive to the WF chirality. The band structures, quasiparticle interferences, magnetoresistances measured by angleresolved photoemission spectroscopy (ARPES)^{9,11,12,13,14}, scanning tunnelling microscope^{33,34,35}, and transport experiments^{17,18,19}, respectively, are not sensitive to the chirality of WFs (see also Supplementary Information VII). One proposal to detect the chirality is to use pump–probe ARPES to measure the transient spectral weight upon shining circularly polarized pump light^{36}. However, this requires an ARPES with a midinfrared pump and a soft Xray probe, which is technically very challenging. On the other hand, optical experiments on WSMs have remained very limited^{37,38}, although they are promising approaches to achieve these goals^{15}. In this paper, we detect the chirality of the WFs in the WSM TaAs by measuring its midinfrared photocurrent response. Photocurrents induced by circularly polarized light, also called the circular photogalvanic effect (CPGE), have been previously measured in other systems^{39,40,41,42,43}, but have not been experimentally studied in WSMs.
We first discuss the theoretical picture of the CPGE for optical transitions from the lower part of the Weyl cone to the upper part^{20}. There are two independent factors important for the CPGE here. The first is the chirality selection rule (Fig. 1c, e). For a right circularly polarized (RCP) light propagating along and a χ = +1 WF, the optical transition is allowed on the +k_{z} side but forbidden on the −k_{z} side due to the conservation of angular momentum^{20,24,36}. The second is the Pauli blockade, which is present only when the chemical potential is away from the Weyl node. In the presence of a finite tilt (Fig. 1d), the Pauli blockade becomes asymmetric about the nodal point. If we consider only a single Weyl cone, in general we expect a nonzero current (Fig. 1c, d). However, having a nonzero total photocurrent depends on whether contributions from different WFs cancel each other. In an inversionbreaking WSM with mirror symmetries, ref. 20 shows that the total photocurrent becomes nonvanishing when both factors are present (Supplementary Information IV.1).
TaAs has been experimentally established as an inversionbreaking WSM with mirror symmetries^{7,8,9,12}. The tilt of the WFs is significant (for example, v_{+}/v_{−} ≥ 2, see Fig. 1d and Supplementary Information III.3) and the chemical potential is ∼18 meV away from the W_{1} Weyl nodes (Supplementary Information III.2). These factors make TaAs a promising system in which to observe the WFinduced CPGE as discussed above. We describe the following properties of TaAs relevant for our study. Although TaAs has twentyfour WFs, only two are independent, which are highlighted in Fig. 1j and named W_{1} and W_{2}. The other twentytwo Weyl nodes can be related by the system’s symmetries (see Supplementary Information I), including time reversal (), fourfold rotation around (C_{4c}) and two mirror reflections about the (b, c) and (a, c) planes ( and ). Moreover, since the crystal lacks mirror symmetry , can be unambiguously defined as the direction going from the Ta atom to the As atom across the dotted line in Fig. 1h. With this welldefined lattice (Fig. 1g–i) as an input, firstprinciples calculations have predicted the energy dispersion and the chirality of each WF (Fig. 1j). Although the energy dispersion has been observed by ARPES^{9,11,12,13,14}, the chirality configuration (Fig. 1j) has not been measured.
To detect the CPGE, we utilize a midinfrared scanning photocurrent microscope (Fig. 2a) equipped with a CO_{2} laser source (wavelength λ_{CO}_{2} = 10.6 μm and energy ℏω ≃ 120 meV). We note that this photon energy fits our purpose because we specifically want to excite electrons from the lower part of Weyl cone to the upper part. A much lower photon energy (in the terahertz range) will probably fall into the intraband regime unless the chemical potential is tuned very close to the Weyl nodes, whereas a much higher photon energy would excite electrons to bands at much higher energy, making the process of marginal relevance to the Weyl physics. Throughout the paper, we assign the direction of propagation of the light as . Our TaAs sample (Fig. 2b) is purposely filed down so that the outofplane direction is . We have performed singlecrystal Xray diffraction (XRD, see SI.III.5), which allows us to determine the direction (Fig. 2b). Throughout Fig. 2, the lab and sample coordinates are identical (for example, ). The black data points in Fig. 2c show the current along , when the laser spot is near the sample’s centre (the black dot in Fig. 2b). We observe that the current reaches maximum value for RCP light, minimum for LCP light, and zero for linearly polarized light. The whole data curve fits nicely to a cosine function. In sharp contrast, we see no observable current along the direction (the black data points in Fig. 2d).
We move the light spot horizontally to the blue and pink dots in Fig. 2b. The corresponding photocurrents (the blue and pink data points in Fig. 2c) show the same polarization dependence but with an additional, polarizationindependent shift. We also see the same polarizationindependent shift for the currents along (Fig. 2d). These data reveal two distinct mechanisms for photocurrent generation. To understand the polarizationindependent component, in Fig. 2e, we show the photocurrent along with a fixed polarization (RCP), while the laser spot is varied in (y, z) space. We see the current flowing to the opposite directions depending on whether the light spot is closer to the left or right contact. This spatial dependence shows that the polarizationindependent component arises from the photothermal effect^{39,40,44}. Essentially, because the sample and contact have different thermopower, a current is generated by the laserinduced temperature gradient. Figure 2f shows the photocurrent as a function of polarization and the z position of the laser spot, where both the polarizationdependent and polarizationindependent components can be seen. In order to separate these two components, we Fourier transform from the polarization angle space to the frequency space. As shown in Fig. 2g, aside from the lowfrequency intensities that correspond to the polarizationindependent photothermal current, we observe a sharp peak exclusively at a frequency of 1/π. This peak disappears at the z values outside the sample, confirming that the observed current is the sample’s intrinsic property. We show the frequencyfiltered photocurrent only at a frequency of 1/π. The RCP (Fig. 2h) light induced photocurrent is along the direction irrespective of the location of the laser. This spatial configuration is different from that of the photothermal effect (Fig. 2e). In Supplementary Fig. 4, we further show the temperature and laser power dependences of the photocurrent. In particular, we found that the photothermal effect and the CPGE have opposite temperature trends. These systematic polarization, position, temperature and powerdependent measurements further confirm the CPGE and isolate it from the photothermal effect.
We now present two important characteristics of the observed photocurrent. The first is the cancellation of photocurrent along certain directions. For RCP light along (Fig. 2), we observe zero current along . On another TaAs sample (Supplementary Fig. 24), we shine light along . We observe zero current along both the and directions. The second is the sign reversal of the photocurrent upon rotating the sample by 180° while fixing the properties of the light (Fig. 3). The lab coordinate remains constant while the sample coordinate changes upon rotations. The measured photocurrent I > 0 is consistently defined as in the lab coordinate. For a given polarization, the direction of the photocurrent reverses if one rotates the sample by 180° around or (Fig. 3b, c), while it remains the same upon a rotation around (Fig. 3d). To explain these observations, we consider the secondorder photocurrent response tensor η_{αβγ} (the tensor indices span the sample coordinate components {a, b, c}) since our CPGE shows a linear dependence on the laser power (Supplementary Fig. 4c). η_{αβγ} is defined through:
where J is the total photocurrent and E is the electric field. The CPGE corresponds to the imaginary part of η_{αβγ} (refs 38,41,42,43). Because the η_{αβγ} tensor is an intrinsic property, it has to obey the symmetries of the system. Therefore, symmetry dictates many important properties of the CPGE, independent of the details of the band structure, the wavelength of the light, or the underlying microscopic mechanism for the optical transition. In TaAs, the presence of and forces η_{αβγ} to vanish when it contains an odd number of momentum index a or b. In Supplementary Information IV.2, we show that both observations can be explained by symmetry analysis of the tensor η_{αβγ}, which further confirms the intrinsic nature of the observed CPGE.
Whereas the cancellation and sign reversal are dictated solely by symmetry, the absolute direction of the current—that is, the sign of η_{bbc} and η_{bcb}—depends on the microscopic mechanism. Specifically, when we shine light along , symmetry tells us the current will be nonzero along but it cannot decide whether the current flows to or (Fig. 2). Unlike a high photon energy, which would probably involve many bands irrelevant to the WFs, the photon energy of 120 meV creates excitations from the lower part of the Weyl cone to the upper part, which directly relies on the chirality of the WFs (Fig. 1). Moreover, the microscopic theory describing this optical transition is available^{20}, which allows us to theoretically calculate the photocurrent (in Supplementary Information V, we further exclude other mechanisms). Specifically, the photocurrent from a single WF is given by
where C is a constant determining the magnitude of the current that is the same for all 24 WFs, is a dimensionless vector that gives the direction of the current, q is the momentum vector from the Weyl node, E_{±}, v_{±}, and n_{±}^{0}(μ, q) are the energies, group velocities, and equilibrium distribution functions for the upper (+) and lower (−) parts of the Weyl cone (the Pauli blockade sets in through the chemical potential μ in n_{±}^{0}), ω and A are the frequency and vector potential of the light, and V_{+−} is the optical transition matrix element, which depends on the chirality selection rule through χ and A. Interestingly, the chemical potential of TaAs is known from previous transport experiments^{18,19} to be very close to the W_{2} Weyl node. Our quantum oscillation measurements (Supplementary Information III.2) confirmed this case (μ is 17.8 meV above W_{1} and 4.8 meV above W_{2}). Since the Pauli blockade vanishes for chemical potential at the Weyl node, the photocurrent contribution from W_{2} WFs is negligibly small. Therefore, our photocurrent solely probes the chirality of a single W_{1} WF (the other seven W_{1} WFs are automatically related by symmetries). Assuming RCP light propagating along , this theory predicts a photocurrent () along given by (Supplementary Information III.4 and Supplementary Information IV.3)
where χ_{W}_{1} is the chirality of the W_{1} WF highlighted in Fig. 4a. In other words, theory predicts that, if χ_{W}_{1} = +1, then is along and that if χ_{W1} = −1, then is along . In our data (Fig. 4b), because we shine RCP light along and measure a current flowing to and because we have measured from singlecrystal XRD, we observe the following relation from our data:
By comparing equation (3) with equation (4), we determine χ_{W}_{1} = +1. We find that the chirality of the W_{1} WF determined by the photocurrent agrees with that predicted by first principles (Fig. 1j). The agreement further confirms our detection of the WF chirality in TaAs.
Looking forward, it would be valuable to test the observed CPGE effect in holedoped samples, where the contribution from the W2 Weyl nodes may dominate. Since, at present, all asgrown TaAs samples haven been found to be electrondoped with a chemical potential similar to ours^{18,19}, the holedoped TaAs may be achieved by chemical doping (for example, Ti, Zr, Si, or Ge) or by electrical gating in thinfilm samples. It would also be interesting to investigate the dependence on the photon energy, especially in the terahertz range (for example, ℏω ≤ 10 meV). Finally, it is helpful to study the relaxation time τ via optical pump–probe experiments in the midinfrared regime.
Finally, we discuss how our results can open up new experimental possibilities for studying and controlling the WFs and their associated quantum anomalies. Analogous to two valleys in two dimensions (Fig. 4c), the key is to identify ways to interact with the two chiralities in a WSM distinctly. In the present study, this is achieved because the circularly polarized light excites opposite sides of the WFs of opposite chirality (Fig. 4d). Another approach to differentiate the two chiralities is to create a population imbalance (Fig. 4e). Interestingly, doing so in a WSM fundamentally requires breaking the apparent conservation of chirality (the chiral anomaly). This can be achieved electrically by applying parallel electric and magnetic fields (Fig. 4e)^{16,17,18,19}, or optically through the chiral magnetic effect by shining a light on a special kind of WSM, where Weyl nodes of opposite chirality have different energies^{21,27,28,29,30}. Apart from the present study and the proposed anomalyrelated physics^{16,21,27,28,29,30}, the nontrivial Berry curvatures in WSMs can also lead to various novel optical phenomena such as photocurrents^{22,23,24,25}, Hall voltages^{26}, Kerr rotations^{23}, and secondharmonic generations^{23,25}. Although these novel phenomena^{16,21,22,23,24,25,26,27,28,29,30} may arise from different aspects of Weyl physics, they are ultimately rooted in the existence of two distinct chiralities (χ = ±1) of WFs, as demonstrated here.
Methods
Midinfrared photocurrent microscopy setup.
In our experiment, the sample is contacted with metal wires and placed in an optical scanning microscope setup that combines electronic transport measurements with light illumination^{44,45}. The laser source is a temperaturestabilized CO_{2} laser with a wavelength λ = 10.6 μm (energy ℏω ≃ 120 meV). A focused beam spot (diameter d ≈ 50 μm) is scanned (using a twoaxis piezocontrolled scanning mirror) over the entire sample and the current is recorded at the same time to form a colour map of photocurrent as a function of spatial positions. Reflected light from the sample is collected to form a simultaneous reflection image of the sample. The absolute location of the photoinduced signal is therefore found by comparing the photocurrent map to the reflection image. The light is first polarized by a polarizer and the chirality of light is further modulated by a rotatable quarterwave plate characterized by an angle θ (Fig. 2a).
Singlecrystal growth.
Single crystals of TaAs were prepared by the standard chemical vapour transfer (CVT) method^{46}. The polycrystalline samples were prepared by heating up stoichiometric mixtures of highquality Ta (99.98%) and As (99.999%) powders in an evacuated quartz ampoule. Then the powder of TaAs (300 mg) and the transport agent were sealed in a long evacuated quartz ampoule (30 cm). The end of the sealed ampoule was placed horizontally at the centre of a singlezone furnace. The central zone of the furnace was slowly heated up to 1,273 K and kept at the temperature for five days, while the cold end was less than 973 K. Magnetotransport measurements were performed using a Quantum Design Physical Property Measurement System.
Firstprinciples calculations.
Firstprinciples calculations were performed by the OPENMX code within the framework of the generalized gradient approximation of density functional theory^{47}. Experimental lattice parameters were used^{46}. A realspace tightbinding Hamiltonian was obtained by constructing symmetryrespecting Wannier functions for the As p and Ta d orbitals without performing the procedure for maximizing localization.
Photocurrent calculations.
We elaborate on the methods of photocurrent calculation. For a single Weyl node, the photocurrent density due to a deviation of the electronic distribution δn_{l}(q) = n_{l}(q) − n_{l}^{0}(q) is:
where l = +, − represents the upper part (+) and lower part (−) of the Weyl cone, Δv(q) = v_{+}(q) − v_{−}(q) is the velocity of each particle–hole pair. Then, based on the relaxation time approximation and Fermi’s golden rule, we have:
where V is the electron–light coupling responsible for photoexcitations from q_{−}〉 to q_{+}〉 and ΔE(q) = E_{+}(q) − E_{−}(q). We first numerically extract an effective k ⋅ p Weyl Hamiltonian H(k) from ab initio band structure calculation. Then, by the Peierls substitution, the coupling Hamiltonian is calculated as V = H(k + A(t)) − H(A), where A is the vector potential. Rewriting the integrand in dimensionless quantities,
C determines the order of magnitude of the current. The dimensionless vector , which is of order one, determines the direction of the current. We note that the terms in depend on system details. For example, δ((ΔE(q)/ℏω) − 1) and n_{−}^{0}(q) − n_{+}^{0}(q) depend on the band structure of the sample; 〈q_{+} (V/(ℏv_{F}A/2)) q_{−}〉 depends on both the wavefunctions of the WFs in the sample and the properties of the light.
In the following, we show calculation results of in TaAs under different conditions measured in experiments.
For RCP along , and .
For RCP along , and .
Indeed, we see that the current along is finite for a RCP along . In the other three cases, the current is zero due to cancellation.
Data availability.
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
Additional Information
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
 1
Weyl, H. Elektron und gravitation. Z. Phys. 56, 330–352 (1929).
 2
Volovik, G. E. The Universe in a Helium Droplet (Oxford Univ. Press, 2003).
 3
McEuen, P. L. et al. Disorder, pseudospins, and backscattering in carbon nanotubes. Phys. Rev. Lett. 83, 5098–5101 (1999).
 4
Murakami, S. Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase. New J. Phys. 9, 356 (2007).
 5
Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermiarc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).
 6
Burkov, A. A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011).
 7
Huang, S. M. et al. A Weyl fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat. Commun. 6, 7373 (2015).
 8
Weng, H. et al. Weyl semimetal phase in noncentrosymmetric transition metal monophosphides. Phys. Rev. X 5, 011029 (2015).
 9
Xu, S.Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).
 10
Lu, L. et al. Observation of Weyl points in a photonic crystal. Science 349, 622–624 (2015).
 11
Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).
 12
Lv, B. Q. et al. Observation of Weyl nodes in TaAs. Nat. Phys. 11, 724–727 (2015).
 13
Yang, L. X. et al. Weyl semimetal phase in the noncentrosymmetric compount TaAs. Nat. Phys. 11, 728–733 (2015).
 14
Belopolski, I. et al. Criteria for directly detecting topological Fermi arcs in Weyl semimetals. Phys. Rev. Lett. 116, 066802 (2016).
 15
Jia, S., Xu, S.Y. & Hasan, M. Z. Weyl semimetals, Fermi arcs and chiral anomalies. Nat. Mater. 15, 1140–1144 (2016).
 16
Parameswaran, S. A. et al. A. Probing the chiral anomaly with nonlocal transport in threedimensional topological semimetals. Phys. Rev. X 4, 031035 (2014).
 17
Xiong, J. et al. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350, 413–416 (2015).
 18
Zhang, C. et al. Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl semimetal. Nat. Commun. 7, 10735 (2016).
 19
Huang, X. et al. Observation of the chiral anomaly induced negative magnetoresistance in 3D Weyl semimetal TaAs. Phys. Rev. X 5, 031023 (2015).
 20
Chan, C.K., Lindner, N. H., Refael, G. & Lee, P. A. Photocurrents in Weyl semimetals. Phys. Rev. B 95, 041104 (2017).
 21
Taguchi, K., Imaeda, T., Sato, M. & Tanaka, Y. Photovoltaic chiral magnetic effect in Weyl semimetals. Phys. Rev. B 93, 201202(R) (2016).
 22
Ishizuka, H., Hayata, T., Ueda, M. & Nagaosa, N. Emergent electromagnetic induction and adiabatic charge pumping in Weyl semimetals. Phys. Rev. Lett. 117, 216601 (2016).
 23
Morimoto, T., Zhong, S., Orenstein, J. & Moore, J. E. Semiclassical theory of nonlinear magnetooptical responses with applications to topological Dirac/Weyl semimetals. Phys. Rev. B 94, 245121 (2016).
 24
de Juan, F., Grushin, A. G., Morimoto, T. & Moore, J. E. Quantized circular photogalvanic effect in Weyl semimetals. Preprint at http://arXiv.org/abs/1611.05887 (2016).
 25
Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in timereversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).
 26
Chan, C.K., Lee, P. A., Burch, K. S., Han, J. H. & Ran, Y. When chiral photons meet chiral fermions: photoinduced anomalous Hall effects in Weyl semimetals. Phys. Rev. Lett. 116, 026805 (2016).
 27
Chen, Y., Wu, S. & Burkov, A. A. Axion response in Weyl semimetals. Phys. Rev. B 88, 125105 (2013).
 28
Hosur, P. & Qi, X.L. Tunable circular dichroism due to the chiral anomaly in Weyl semimetals. Phys. Rev. B 91, 081106(R) (2015).
 29
Goswami, P., Sharma, G. & Tewari, S. Optical activity as a test for dynamic chiral magnetic effect of Weyl semimetals. Phys. Rev. B 92, 161110(R) (2015).
 30
Ma, K. & Pesin, D. A. Chiral magnetic effect and natural optical activity in (Weyl) metals. Phys. Rev. B 92, 235205 (2015).
 31
Xu, X. et al. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014).
 32
Mak, K.F. & Shan, J. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photon. 10, 216–226 (2016).
 33
Zheng, H. et al. Atomic scale visualization of quantum interference on a Weyl semimetal surface by scanning tunneling microscopy/spectroscopy. ACS Nano 10, 1378–1385 (2016).
 34
Inoue, H. et al. Quasiparticle interference of the Fermi arcs and surfacebulk connectivity of Weyl semimetals. Science 351, 1184–1187 (2016).
 35
Batabyal, R. et al. Visualizing ‘Fermi arc’ in the Weyl semimetal TaAs. Sci. Adv. 2, e1600709 (2016).
 36
Yu, R. et al. Determine the chirality of Weyl fermions from the circular dichroism spectra of timedependent angleresolved photoemission. Phys. Rev. B 93, 205133 (2016).
 37
Xu, B. et al. Optical spectroscopy of the Weyl semimetal TaAs. Phys. Rev. B 93, 121110(R) (2016).
 38
Wu, L. et al. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys. 13, 350–355 (2017).
 39
McIver, J. W. et al. Control over topological insulator photocurrents with light polarization. Nat. Nanotech. 7, 96–100 (2012).
 40
Yuan, H. et al. Generation and electric control of spinvalleycoupled circular photogalvanic current in WSe2 . Nat. Nanotech. 9, 851–857 (2014).
 41
Ivchenko, E. L. & Ganichev, S. in Spin Physics in Semiconductors (ed. Dyakonov, M. I.) (Springer, 2008).
 42
Ganichev, S. D. & Prettl, W. Spin photocurrents in quantum wells. J. Phys. Condens. Matter 15, R935–R983 (2003).
 43
Diehl, H. et al. Spin photocurrents in (110)grown quantum well structures. New J. Phys. 9, 349 (2007).
 44
Gabor, N. M. et al. Hot carrier assisted intrinsic photoresponse in graphene. Science 334, 648–652 (2011).
 45
Herring, P. K. et al. Photoresponse of an electrically tunable ambipolar graphene infrared thermocouple. Nano Lett. 14, 901–907 (2014).
 46
Murray, J. J. et al. Phase relationships and thermodynamics of refractory metal pnictides: the metalrich tantalum arsenides. J. LessCommon Met. 46, 311–320 (1976).
 47
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Acknowledgements
We thank L. Ye and J. Checkelsky for the help with sample preparation. N.G. and S.Y.X. acknowledge support from US Department of Energy, BES DMSE, Award number DEFG0208ER46521 (initial planning), the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4540 (data analysis), and in part from the MRSEC Program of the National Science Foundation under award number DMR1419807 (data taking, manuscript writing, and using shared experimental facilities). Work in the P.J.H. group was partly supported by the Center for Excitonics, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences under Award Number DESC0001088 (fabrication and measurement) and partly through AFOSR grant FA95501610382 (data analysis), as well as the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4541 to P.J.H. P.A.L. acknowledges the support by DOE under grant DEFG0203ER46076 (theoretical analyses). T.P. and Y.L. acknowledge partial funding support from the ONR PECASE project (Award No. 021302001) and the MIT/Army Institute for Soldier Nanotechnologies (Award No. 023674) (experimental setup). G.C. and H.L. were supported by the National Research Foundation (NRF), Prime Minister’s Office, Singapore, under its NRF fellowship NRF Award No. NRFNRFF201303 (firstprinciples band structure calculations). C.L.Z. and S.J. were supported by National Basic Research Program of China (grant Nos. 2013CB921901 and 2014CB239302) (single crystal growth). W.X. was supported by the startup funding through LSU College of Science (single crystal XRD measurements).
Author information
Affiliations
Contributions
N.G., P.J.H., S.Y.X. and Q.M. designed the experiment. N.G. and P.J.H. supervised the project. Q.M. and S.Y.X. performed the measurements and analysed the data. Y.L. and T.P. assisted with the measurements. C.L.Z. and S.J. grew the single crystal. G.C. and H.L. provided the firstprinciples band structures. C.K.C. and P.A.L. provided theoretical analysis and calculated the photocurrents. W.X. performed the singlecrystal XRD measurement. S.Y.X. and Q.M. wrote the manuscript with input from all authors.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary information
Supplementary information (PDF 3211 kb)
Rights and permissions
About this article
Cite this article
Ma, Q., Xu, SY., Chan, CK. et al. Direct optical detection of Weyl fermion chirality in a topological semimetal. Nature Phys 13, 842–847 (2017). https://doi.org/10.1038/nphys4146
Received:
Accepted:
Published:
Issue Date:
Further reading

Topology and geometry under the nonlinear electromagnetic spotlight
Nature Materials (2021)

Spin photogalvanic effect in twodimensional collinear antiferromagnets
npj Quantum Materials (2021)

Weyl, Dirac and highfold chiral fermions in topological quantum matter
Nature Reviews Materials (2021)

Dynamical evolution of anisotropic response of typeII Weyl semimetal TaIrTe4 under ultrafast photoexcitation
Light: Science & Applications (2021)

Cycling Fermi arc electrons with Weyl orbits
Nature Reviews Physics (2021)