Photogalvanic Effects in Surface States of Topological Insulators under Perpendicular Magnetic Fields

TL;DR

This paper provides a theoretical analysis of the nonlinear magneto-optical shift conductivity in the surface states of topological insulators under perpendicular magnetic fields, highlighting the effects of Landau levels, symmetry, and damping.

Contribution

The study derives a microscopic expression for shift conductivity in topological insulator surface states, considering Landau levels and symmetry, and explores its tunability via magnetic field and chemical potential.

Findings

Shift current is zero for pure circularly polarized light due to symmetry.

Conductivities are nonzero only at discrete photon energies in the clean limit.

Shift current can be tuned by chemical potential and magnetic field.

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.