Spatially dispersive circular photogalvanic effect in a Weyl semimetal


Weyl semimetals (WSMs) are gapless topological states of matter with broken inversion and/or time reversal symmetry. WSMs can support a circulating photocurrent when illuminated by circularly polarized light at normal incidence. Here, we report a spatially dispersive circular photogalvanic effect (s-CPGE) in a WSM that occurs with a spatially varying beam profile. Our analysis shows that the s-CPGE is controlled by a symmetry selection rule combined with asymmetric carrier excitation and relaxation dynamics. By evaluating the s-CPGE for a minimal model of a WSM, a frequency-dependent scaling behaviour of the photocurrent is obtained. Wavelength-dependent measurements from the visible to mid-infrared range show evidence of Berry curvature singularities and band inversion in the s-CPGE response. We present the s-CPGE as a promising spectroscopic probe for topological band properties, with the potential for controlling photoresponse by patterning optical fields on topological materials to store, manipulate and transmit information.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Polarization-dependent photocurrent measurements on 1T′ and Td (Weyl) phases of MoTe2.
Fig. 2: Measurement of circulating current in the Td (Weyl) phase of Mo0.9W0.1Te2 at room temperature under circularly polarized optical excitation.
Fig. 3: Spatial location and Gaussian spot size dependence of the s-CPGE current in Mo0.9W0.1Te2 at room temperature.
Fig. 4: Numerical and experimental results for s-CPGE current over a broad wavelength range (visible to mid-infrared).

Data availability

The data presented in this study are available from the corresponding author upon reasonable request.

Code availability

The code for calculating the s-CPGE in this study is available from the corresponding author upon reasonable request.


  1. 1.

    Kane, C. L. & Mele, E. J. Z 2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).

  2. 2.

    Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

  3. 3.

    Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

  4. 4.

    Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).

  5. 5.

    Armitage, N., Mele, E. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).

  6. 6.

    Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).

  7. 7.

    Burkov, A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011).

  8. 8.

    Nielsen, H. B. & Ninomiya, M. The Adler–Bell–Jackiw anomaly and Weyl fermions in a crystal. Phys, Lett. B 130, 389–396 (1983).

  9. 9.

    Zyuzin, A. & Burkov, A. Topological response in Weyl semimetals and the chiral anomaly. Phys. Rev. B 86, 115133 (2012).

  10. 10.

    Potter, A., Kimchi, I. & Vishwanath, A. Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5, 5161 (2014).

  11. 11.

    Hosur, P. & Qi, X.-L. Recent developments in transport phenomena in Weyl semimetals. CR Phys. 14, 857–870 (2013).

  12. 12.

    Xiong, J. et al. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350, 413–416 (2015).

  13. 13.

    Ma, Q. et al. Direct optical detection of Weyl fermion chirality in a topological semimetal. Nat. Phys. 13, 842–847 (2017).

  14. 14.

    Wu, L. et al. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys. 13, 350–355 (2017).

  15. 15.

    Morimoto, T., Zhong, S., Orenstein, J. & Moore, J. E. Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals. Phys. Rev. B 94, 245121 (2016).

  16. 16.

    Chan, C.-K., Lindner, N. H., Refael, G. & Lee, P. A. Photocurrents in Weyl semimetals. Phys. Rev. B 95, 041104 (2017).

  17. 17.

    König, E., Xie, H.-Y., Pesin, D. & Levchenko, A. Photogalvanic effect in Weyl semimetals. Phys. Rev. B 96, 075123 (2017).

  18. 18.

    Zhang, Y., Sun, Y. & Yan, B. Berry curvature dipole in Weyl semimetal materials: an ab initio study. Phys. Rev. B 97, 041101 (2018).

  19. 19.

    de Juan, F., Grushin, A. G., Morimoto, T. & Moore, J. E. Quantized circular photogalvanic effect in Weyl semimetals. Nat. Commun. 8, 15995 (2017).

  20. 20.

    Wang, Z. et al. MoTe2: a type-II Weyl topological metal. Phys. Rev. Lett. 117, 056805 (2016).

  21. 21.

    Huang, L. Spectroscopic evidence for a type-II Weyl semimetallic state in MoTe2. Nat. Mater. 15, 1155–1160 (2016).

  22. 22.

    Belopolski, I. et al. Discovery of a new type of topological Weyl fermion semimetal state in MoxW1−xTe2. Nat. Commun. 7, 13643 (2016).

  23. 23.

    Chang, T.-R. et al. Prediction of an arc-tunable Weyl Fermion metallic state in MoxW1−xTe2. Nat. Commun. 7, 10639 (2016).

  24. 24.

    Zhang, K. et al. Raman signatures of inversion symmetry breaking and structural phase transition in type-II Weyl semimetal MoTe2. Nat. Commun. 7, 13552 (2016).

  25. 25.

    Deng, K. et al. Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2. Nat. Phys. 12, 1105–1110 (2016).

  26. 26.

    Belopolski, I. et al. Topological Weyl phase transition in MoxW1−xTe2. Preprint at (2016).

  27. 27.

    Dhara, S., Mele, E. J. & Agarwal, R. Voltage-tunable circular photogalvanic effect in silicon nanowires. Science 349, 726–729 (2015).

  28. 28.

    McIver, J., Hsieh, D., Steinberg, H., Jarillo-Herrero, P. & Gedik, N. Control over topological insulator photocurrents with light polarization. Nat. Nanotech. 7, 96–100 (2012).

  29. 29.

    Ivchenko, E. & Ganichev, S. in Spin Physics in Semiconductors (ed. Dyakonov, M. I.) Ch. 9 (Springer, 2008).

  30. 30.

    Ganichev, S. D. & Prettl, W. Spin photocurrents in quantum wells. J. Phys. Condens. Matter 15, R935–R983 (2003).

  31. 31.

    Shalygin, V., Moldavskaya, M., Danilov, S., Farbshtein, I. & Golub, L. Circular photon drag effect in bulk tellurium. Phys. Rev. B 93, 045207 (2016).

  32. 32.

    Karch, J. et al. Terahertz radiation driven chiral edge currents in graphene. Phys. Rev. Lett. 107, 276601 (2011).

  33. 33.

    He, X. et al. Anomalous photogalvanic effect of circularly polarized light incident on the two-dimensional electron gas in AlxGa1−xN/GaN heterostructures at room temperature. Phys. Rev. Lett. 101, 147402 (2008).

  34. 34.

    Sipe, J. & Shkrebtii, A. Second-order optical response in semiconductors. Phys. Rev. B 61, 5337–5352 (2000).

  35. 35.

    Sekine, A., Culcer, D. & MacDonald, A. H. Quantum kinetic theory of the chiral anomaly. Phys. Rev. B 96, 235134 (2017).

  36. 36.

    Sturman, P. J. Photovoltaic and Photo-refractive Effects in Noncentrosymmetric Materials Vol. 8 (CRC Press, 1992).

  37. 37.

    Wang, Z. et al. Dirac semimetal and topological phase transitions in A 3Bi (A = Na, K, Rb). Phys. Rev. B 85, 195320 (2012).

  38. 38.

    Olbrich, P. et al. Room-temperature high-frequency transport of Dirac fermions in epitaxially grown Sb2Te3- and Bi2Te3-based topological insulators. Phys. Rev. Lett. 113, 096601 (2014).

  39. 39.

    Hirsch, J. Spin Hall effect. Phys. Rev. Lett. 83, 1834–1837 (1999).

  40. 40.

    Rubin, L. & Sample, H. The Hall Effect and Its Applications (Plenum Press, 1980).

  41. 41.

    Deyo, E., Golub, L., Ivchenko, E. & Spivak, B. Semiclassical theory of the photogalvanic effect in non-centrosymmetric systems. Preprint at (2009).

  42. 42.

    Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

  43. 43.

    Rappe, A. M., Rabe, K. M., Kaxiras, E. & Joannopoulos, J. Optimized pseudopotentials. Phys. Rev. B 41, 1227–1230 (1990).

  44. 44.

    Souza, I., Marzari, N. & Vanderbilt, D. Maximally localized Wannier functions for entangled energy bands. Phys. Rev. B 65, 035109 (2001).

  45. 45.

    Mostofi, A. A. et al. wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178, 685–699 (2008).

Download references


R.A. acknowledges the support from the Office of Naval Research MURI (grant no. N00014-17-1-2661), US Army Research Office (grant no. W911NF-17-1-0436) and the RAISE-EQuIP-NSF-ECCS-1842612 grant from the NSF (USA). Calculation of the s-CPGE response by E.J.M. and Z.A. was supported by the Department of Energy (grant no. DE FG02 84ER45118). The crystal growth effort (P.Y. and Z.L.) was supported by the Singapore National Research Foundation under NRF RF Award No. NRF-RF2013-08 and Tier 2 MOE2016-T2-2-153. A.M.R. acknowledges support from the US Department of Energy, Office of Science, Basic Energy Sciences Program under grant DE-FG02-07ER46431. R.A., C.L.K. and A.M.R. acknowledge the support from the Penn’s MRSEC Seed Grant (DMR-1720530). Computational support was provided by the National Energy Research Scientific Computing Center of the DOE.

Author information

R.A. supervised the project. Z.J. and R.A. conceived and designed the project and experiments. Z.J. and G.L. performed all the measurements with some assistance from W.L.; Z.J. and G.L. fabricated the devices and analysed the data with R.A.; Z.J. and Z.A. developed the microscopic theory under the supervision of E.J.M. and C.L.K.; Z.J. performed real-band calculations with the help of H.G. and A.M.R.; P.Y. and Z.L. grew the single crystals on which all the optoelectronic measurements were performed. Z.J., R.A. and E.J.M. wrote the manuscript. All the authors discussed the results and commented on the manuscript.

Correspondence to Ritesh Agarwal.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–12, Supplementary Notes 1–6, Supplementary Refs. 1–12

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ji, Z., Liu, G., Addison, Z. et al. Spatially dispersive circular photogalvanic effect in a Weyl semimetal. Nat. Mater. 18, 955–962 (2019).

Download citation

Further reading