| ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
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Photogalvanic effects in surface states of topological insulators under perpendicular magnetic fields |
| Haoyu Li(李浩宇)1,2, Kainan Chang(常凯楠)1,2,†, Wang-Kong Tse1,2,‡, and Jin Luo Cheng(程晋罗)3,§ |
1 GPL Photonics Laboratory, State Key Laboratory of Luminescence Science and Technology, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China;
2 University of Chinese Academy of Science, Beijing 100049, China;
3 Department of Physics and Astronomy, The University of Alabama, Alabama 35487, USA |
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Abstract We present a theoretical study of the nonlinear magneto-optical shift conductivity in the surface states of the prototypical topological insulator Bi$_2$Se$_3$ under a perpendicular quantizing magnetic field. By describing the electronic states as Landau levels and using a perturbative approach, we derive the microscopic expression for the shift conductivity $\sigma^{(2);\alpha\beta\gamma}(-\omega,\omega)$, where $\alpha,\beta,\gamma=\pm$ stand for the circular polarization of light and $\omega$ is the light frequency; the spectra are further decomposed into contributions from the interband and intraband optical transitions, for which the selection rules are identified. Considering that the system possesses $C_3$ point group of symmetry, the nonzero components of the conductivity tensor are $\sigma^{(2);-++}=[\sigma^{(2);+-}]^\ast$. Therefore, a pure circularly polarized light generates zero shift current. In the clean limit, the conductivities are nonzero only for discrete photon energies because of the discrete Landau levels and energy conservation, and they become Lorentzian lineshapes with the inclusion of damping, which relaxes the condition of energy conservation. The dependence of the spectra on the damping parameters, the magnetic fields, and the chemical potentials is investigated in detail. Our results reveal that the shift current is highly tunable by the chemical potential and the magnetic field. These results underscore the potential of topological insulators for tunable, strong nonlinear magneto-optical applications.
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Received: 16 December 2025
Revised: 05 February 2026
Accepted manuscript online: 03 March 2026
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PACS:
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42.65.-k
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(Nonlinear optics)
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73.20.At
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(Surface states, band structure, electron density of states)
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71.70.Di
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(Landau levels)
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| Fund: Work in China (Chang K N and Cheng J L) was supported by the National Natural Science Foundation of China (Grant No. 12034003). Work in U.S. (Tse W K) was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Early Career Award (Grant No. DESC0019326). |
Corresponding Authors:
Kainan Chang, Wang-Kong Tse, Jin Luo Cheng
E-mail: changkainan@126.com;wktse@ua.edu;jinluocheng.phys@gmail.com
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Cite this article:
Haoyu Li(李浩宇), Kainan Chang(常凯楠), Wang-Kong Tse, and Jin Luo Cheng(程晋罗) Photogalvanic effects in surface states of topological insulators under perpendicular magnetic fields 2026 Chin. Phys. B 35 054203
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