# 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.

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## 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.

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## 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

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.

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## Supplementary information

### Supplementary Information

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

## Rights and permissions

Reprints and Permissions

Ji, Z., Liu, G., Addison, Z. et al. Spatially dispersive circular photogalvanic effect in a Weyl semimetal. Nat. Mater. 18, 955–962 (2019) doi:10.1038/s41563-019-0421-5

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