- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Nonperturbative topological current in Weyl and Dirac semimetals in laser fields

Renato M. A. Dantas1,2,*, Zhe Wang3,4, Piotr Surówka1,2,5,†, and Takashi Oka6,1,7,‡

  • 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
  • 2Würzburg-Dresden Cluster of Excellence ct.qmat, 01187 Dresden, Germany
  • 3Institute of Physics II, University of Cologne, 50937 Cologne, Germany
  • 4Fakultät Physik, Technische Universität Dortmund, 44227 Dortmund, Germany
  • 5Department of Theoretical Physics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
  • 6The Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
  • 7Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany

  • *rmad@pks.mpg.de
  • †surowka@pks.mpg.de
  • ‡oka@pks.mpg.de
PDF

Phys. Rev. B 103, L201105 – Published 6 May, 2021

DOI: https://doi.org/10.1103/PhysRevB.103.L201105

Abstract

We study nonperturbatively the anomalous Hall current and its high harmonics generated in Weyl and Dirac semimetals by strong elliptically polarized laser fields in the context of kinetic theory. We find a crossover between perturbative and nonperturbative regimes characterized by the electric field strength E*=μω2evF (ω, laser frequency; μ, Fermi energy; vF, Fermi velocity). In the perturbative regime, the anomalous Hall current depends quadratically on the field strength (E), whereas the higher-order corrections, as well as high harmonics, vanish at zero temperature. In the nonperturbative regime, the anomalous Hall current saturates and decays as (lnE)/E, while even-order high harmonics are generated when in-plane rotational symmetry is broken. Based on the analytical solution of the Boltzmann equation, we reveal the topological origin of the sharp crossover: the Weyl monopole stays inside or moves outside of the Fermi sphere, respectively, during its fictitious motion in the perturbative or nonperturbative regimes. Our findings establish a nonlinear response intrinsically connected to topology, characteristic of Weyl and Dirac semimetals.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (44)

  1. N. P. Armitage, E. J. Mele, and A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018).
  2. H. Gao, J. W. Venderbos, Y. Kim, and A. M. Rappe, Annu. Rev. Mater. Res. 49, 153 (2019).
  3. K. Landsteiner, Acta Phys. Pol. B 47, 2617 (2016).
  4. D. Xiao, J. Shi, and Q. Niu, Phys. Rev. Lett. 95, 137204 (2005).
  5. C. Duval, Z. Horváth, P. A. Horváthy, L. Martina, and P. C. Stichel, Mod. Phys. Lett. B 20, 373 (2006).
  6. D. Xiao, M.-C. Chang, and Q. Niu, Rev. Mod. Phys. 82, 1959 (2010).
  7. E. J. Sie, J. W. McIver, Y.-H. Lee, L. Fu, J. Kong, and N. Gedik, Nat. Mater. 14, 290 (2014).
  8. R. Loganayagam and P. Surówka, J. High Energy Phys. 04 (2012) 097.
  9. D. T. Son and N. Yamamoto, Phys. Rev. Lett. 109, 181602 (2012).
  10. M. A. Stephanov and Y. Yin, Phys. Rev. Lett. 109, 162001 (2012).
  11. D. T. Son and B. Z. Spivak, Phys. Rev. B 88, 104412 (2013).
  12. J.-Y. Chen, D. T. Son, M. A. Stephanov, H.-U. Yee, and Y. Yin, Phys. Rev. Lett. 113, 182302 (2014).
  13. R. M. A. Dantas, F. Peña-Benitez, B. Roy, and P. Surówka, J. High Energy Phys. 12 (2018) 069.
  14. S. A. Mikhailov and K. Ziegler, J. Phys.: Condens. Matter 20, 384204 (2008).
  15. P. Bowlan, E. Martinez-Moreno, K. Reimann, T. Elsaesser, and M. Woerner, Phys. Rev. B 89, 041408(R) (2014).
  16. A. Cortijo, Phys. Rev. B 94, 235123 (2016).
  17. F. Giorgianni, E. Chiadroni, A. Rovere, M. Cestelli-Guidi, A. Perucchi, M. Bellaveglia, M. Castellano, D. D. Giovenale, G. D. Pirro, M. Ferrario, R. Pompili, C. Vaccarezza, F. Villa, A. Cianchi, A. Mostacci, M. Petrarca, M. Brahlek, N. Koirala, S. Oh, and S. Lupi, Nat. Commun. 7, 11421 (2016).
  18. N. Yoshikawa, T. Tamaya, and K. Tanaka, Science 356, 736 (2017).
  19. F. de Juan, A. G. Grushin, T. Morimoto, and J. E. Moore, Nat. Commun. 8, 15995 (2017).
  20. Q. Ma, S.-Y. Xu, C.-K. Chan, C.-L. Zhang, G. Chang, Y. Lin, W. Xie, T. Palacios, H. Lin, S. Jia, P. A. Lee, P. Jarillo-Herrero, and N. Gedik, Nat. Phys. 13, 842 (2017).
  21. H. A. Hafez, S. Kovalev, J.-C. Deinert, Z. Mics, B. Green, N. Awari, M. Chen, S. Germanskiy, U. Lehnert, J. Teichert, Z. Wang, K.-J. Tielrooij, Z. Liu, Z. Chen, A. Narita, K. Müllen, M. Bonn, M. Gensch, and D. Turchinovich, Nature (London) 561, 507 (2018).
  22. H. Rostami and M. Polini, Phys. Rev. B 97, 195151 (2018).
  23. J. W. McIver, B. Schulte, F.-U. Stein, T. Matsuyama, G. Jotzu, G. Meier, and A. Cavalleri, Nat. Phys. 16, 38 (2019).
  24. T. Oka and S. Kitamura, Annu. Rev. Condens. Matter Phys. 10, 387 (2019).
  25. G. B. Osterhoudt, L. K. Diebel, M. J. Gray, X. Yang, J. Stanco, X. Huang, B. Shen, N. Ni, P. J. W. Moll, Y. Ran, and K. S. Burch, Nat. Mater. 18, 471 (2019).
  26. N. Sirica, R. I. Tobey, L. X. Zhao, G. F. Chen, B. Xu, R. Yang, B. Shen, D. A. Yarotski, P. Bowlan, S. A. Trugman, J.-X. Zhu, Y. M. Dai, A. K. Azad, N. Ni, X. G. Qiu, A. J. Taylor, and R. P. Prasankumar, Phys. Rev. Lett. 122, 197401 (2019).
  27. Y. Gao, S. Kaushik, E. J. Philip, Z. Li, Y. Qin, Y. P. Liu, W. L. Zhang, Y. L. Su, X. Chen, H. Weng, D. E. Kharzeev, M. K. Liu, and J. Qi, Nat. Commun. 11, 720 (2020).
  28. S. Kovalev, R. M. A. Dantas, S. Germanskiy, J.-C. Deinert, B. Green, I. Ilyakov, N. Awari, M. Chen, M. Bawatna, J. Ling, F. Xiu, P. H. M. van Loosdrecht, P. Surówka, T. Oka, and Z. Wang, Nat. Commun. 11, 2451 (2020).
  29. B. Cheng, N. Kanda, T. N. Ikeda, T. Matsuda, P. Xia, T. Schumann, S. Stemmer, J. Itatani, N. P. Armitage, and R. Matsunaga, Phys. Rev. Lett. 124, 117402 (2020).
  30. T. Morimoto, S. Zhong, J. Orenstein, and J. E. Moore, Phys. Rev. B 94, 245121 (2016).
  31. N. M. R. Peres, Y. V. Bludov, J. E. Santos, A.-P. Jauho, and M. I. Vasilevskiy, Phys. Rev. B 90, 125425 (2014).
  32. Y. Gao, S. A. Yang, and Q. Niu, Phys. Rev. Lett. 112, 166601 (2014).
  33. Y. Gao, S. A. Yang, and Q. Niu, Phys. Rev. B 91, 214405 (2015).
  34. I. Sodemann and L. Fu, Phys. Rev. Lett. 115, 216806 (2015).
  35. L. E. Golub and E. L. Ivchenko, Phys. Rev. B 98, 075305 (2018).
  36. In our analysis, interband transitions are neglected because we deal with the condition μ≫ℏω. Nevertheless, we stress that interband, when allowed, can lead to a circular photogalvanic effect in Weyl semimetals [19, 42, 43]. Otherwise, intraband effects can be responsible for such a response even in systems other than Weyl and Dirac semimetals [44].
  37. Equation (11) trivially generalizes for the existence of multiple crossings between the perturbative and nonperturbative regions, i.e., for the existence of multiple pairs of u1* and u2*.
  38. H. Nielsen and M. Ninomiya, Phys. Lett. B 105, 219 (1981).
  39. H. Nielsen and M. Ninomiya, Nucl. Phys. B 185, 20 (1981).
  40. H. Nielsen and M. Ninomiya, Nucl. Phys. B 193, 173 (1981).
  41. H. Ishizuka, T. Hayata, M. Ueda, and N. Nagaosa, Phys. Rev. Lett. 117, 216601 (2016).
  42. C.-K. Chan, N. H. Lindner, G. Refael, and P. A. Lee, Phys. Rev. B 95, 041104(R) (2017).
  43. N. V. Leppenen, E. L. Ivchenko, and L. E. Golub, J. Exp. Theor. Phys. 129, 139 (2019).
  44. L. E. Golub, E. L. Ivchenko, and B. Spivak, Phys. Rev. B 102, 085202 (2020).

Outline

Information

Phys. Rev. B 103, L201105– Published 6 May, 2021
  • Received 20 August 2020
  • Revised 19 January 2021
  • Accepted 16 April 2021
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation