Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Spatially dispersive circular photogalvanic effect in a Weyl semimetal

Abstract

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.

from$8.99

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.

References

  1. 1.

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

    CAS  Article  Google Scholar 

  2. 2.

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

    CAS  Article  Google Scholar 

  3. 3.

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

    CAS  Article  Google Scholar 

  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).

    Article  Google Scholar 

  5. 5.

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

    CAS  Article  Google Scholar 

  6. 6.

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

    CAS  Article  Google Scholar 

  7. 7.

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

    CAS  Article  Google Scholar 

  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).

    Article  Google Scholar 

  9. 9.

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

    Article  Google Scholar 

  10. 10.

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

    CAS  Article  Google Scholar 

  11. 11.

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

    CAS  Article  Google Scholar 

  12. 12.

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

    CAS  Article  Google Scholar 

  13. 13.

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

    CAS  Article  Google Scholar 

  14. 14.

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

    CAS  Article  Google Scholar 

  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).

    Article  Google Scholar 

  16. 16.

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

    Article  Google Scholar 

  17. 17.

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

    Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  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).

    Article  Google Scholar 

  20. 20.

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

    Article  Google Scholar 

  21. 21.

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  23. 23.

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  25. 25.

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

    CAS  Article  Google Scholar 

  26. 26.

    Belopolski, I. et al. Topological Weyl phase transition in MoxW1−xTe2. Preprint at https://arxiv.org/abs/1612.07793 (2016).

  27. 27.

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  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).

    Article  Google Scholar 

  32. 32.

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

    CAS  Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  34. 34.

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

    CAS  Article  Google Scholar 

  35. 35.

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

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    CAS  Article  Google Scholar 

  39. 39.

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

    CAS  Article  Google Scholar 

  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 https://arxiv.org/abs/0904.1917 (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).

    Article  Google Scholar 

  43. 43.

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

    CAS  Article  Google Scholar 

  44. 44.

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

    Article  Google Scholar 

  45. 45.

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

    CAS  Article  Google Scholar 

Download references

Acknowledgements

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

Affiliations

Authors

Contributions

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.

Corresponding author

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). https://doi.org/10.1038/s41563-019-0421-5

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing