Second Harmonic Generation in Topological Insulators under Quantizing Magnetic Fields

TL;DR

This paper provides a theoretical analysis of second harmonic generation in topological insulator surface states under magnetic fields, revealing high tunability and the importance of hexagonal warping effects in nonlinear optical responses.

Contribution

It introduces a microscopic theory incorporating hexagonal warping effects to calculate SHG spectra, offering analytical insights and high susceptibility predictions.

Findings

Resonant peaks in SHG spectra linked to Landau level transitions

High SHG susceptibility surpassing conventional materials

Tunable SHG response via magnetic field and doping levels

Abstract

We theoretically investigate the second harmonic generation (SHG) of topological insulator surface states in a perpendicular magnetic field. Our theory is based on the microscopic expression of the second-order magneto-optical conductivity developed from the density matrix formalism, taking into account hexagonal warping effects on the surface states' band structure. Using numerically exact Landau level energies and wavefunctions including hexagonal warping, we calculate the spectrum of SHG conductivities under normal incidence for different values of magnetic field and chemical potential. The imaginary parts of the SHG conductivities show prominent resonant peaks corresponding to one-photon and two-photon inter-Landau level transitions. Treating the hexagonal warping term perturbatively, these transitions are clarified analytically within a perturbation theory from which approximate selection rules for the allowable optical transitions for SHG are determined. Our results show extremely high SHG susceptibility that is easily tunable by magnetic field and doping level for topological surface states in the far-infrared regime, exceeding that of many conventional nonlinear materials. This work highlights the key role of hexagonal warping effects in generating second-order optical responses and provides new insights on the nonlinear magneto-optical properties of the topological insulators.