Resonant second harmonic generation in a two-dimensional electron system

TL;DR

This paper investigates the nonlinear second harmonic response in disordered two-dimensional electron systems with broken inversion symmetry, highlighting resonant excitation mechanisms influenced by magnetic fields, spin-orbit coupling, and quantum confinement.

Contribution

It introduces a detailed analysis of resonant second harmonic generation in 2D electron systems, including local, Berry-dipole, and nonlocal contributions, with emphasis on resonance conditions and magnetic field effects.

Findings

Resonant second harmonic generation occurs near spin-orbit split band energies.

Magnetic fields induce nonreciprocal current responses.

Local contributions can be resonantly excited by external radiation.

Abstract

We consider the nonlinear response of a disordered two-dimensional electronic system, lacking inversion symmetry, to an external alternating electric field. The application of an in-plane static magnetic field induces local contributions to the current density that are quadratic in the electric field and linear in the magnetic field. This current oscillates at twice the frequency of the external irradiation and there are two linearly independent vector combinations that contribute to the current density. This particular mechanism coexists with the topological Berry-dipole contribution to the second harmonic of the current density, which can be generated by quantum confinement. Additional nonlocal terms in the current density are possible in the regime away from the normal incidence. The total current exhibits a nonreciprocal character upon reversal of the magnetic field direction. We evaluate the magnitude of this effect by computing its dependence on the strength of spin-orbit coupling and the disorder scattering rate. Importantly, we show that these local second-harmonic contributions can be resonantly excited when the frequency of the external radiation approaches the energy separation between the spin-orbit split bands.