Nonlinear magneto-optic effects in doped graphene and gapped graphene: a perturbative treatment

TL;DR

This paper investigates the nonlinear magneto-optic responses of doped and gapped graphene under magnetic fields, revealing strong field-dependent effects and resonant Landau level transitions that significantly alter optical conductivities.

Contribution

It provides a perturbative analysis of nonlinear magneto-optic effects in doped and gapped graphene, including detailed spectra and resonance behavior of conductivities under magnetic fields.

Findings

Nonlinear conductivities depend strongly on magnetic field strength.

Resonant peaks in conductivities are caused by Landau level transitions.

Conductivities can vary by orders of magnitude with magnetic field and gap parameters.

Abstract

The nonlinear magneto-optic responses are investigated for gapped graphene and doped graphene in a perpendicular magnetic field. The electronic states are described by Landau levels, and the electron dynamics in an optical field is obtained by solving the density matrix in the equation of motion. In the linear dispersion approximation around the Dirac points, both linear conductivity and third order nonlinear conductivities are numerically evaluated for infrared frequencies. The nonlinear phenomena, including third harmonic generation, Kerr effects and two photon absorption, and four wave mixing, are studied. All optical conductivities show strong dependence on the magnetic field. At weak magnetic fields, our results for doped graphene agree with those in the literature. We also present the spectra of the conductivities of gapped graphene. At strong magnetic fields, the third order conductivities show peaks with varying the magnetic field and the photon energy. These peaks are induced by the resonant transitions between different Landau levels. The resonant channels, the positions, and the divergences of peaks are analyzed. The conductivities can be greatly modified, up to orders of magnitude. The dependence of the conductivities on the gap parameter and the chemical potential is studied.