Nonlinear transverse current on $\mathcal{C}_{3v}$-symmetric honeycomb lattice

TL;DR

This paper investigates the nonlinear transverse current in a $ ext{C}_{3v}$-symmetric honeycomb lattice, revealing that second-order currents can be transverse despite vanishing Hall conductivity at lower orders, with calculations based on quantum kinetic equations.

Contribution

It demonstrates that nonlinear transverse currents exist in $ ext{C}_{3v}$-symmetric honeycomb lattices even when Hall conductivity vanishes, providing explicit tensor calculations.

Findings

Second-order current is transverse for fields perpendicular to mirror lines.

Conductivity tensors have only one independent component each.

Zero-frequency current switches sign with polarization rotation.

Abstract

At nonlinear orders in the electric field, the vanishing of the Hall conductivity does not prevent the nonlinear component of the current from being transverse for selected field directions. We study electrons on $\mathcal{C}_{3v}$-symmetric honeycomb lattice for which the Hall conductivity vanishes at first and second order. Nevertheless, the second-order current component is transverse for fields perpendicular to the three mirror lines. The $\mathcal{C}_{3v}$ symmetry constrains the first-order and second-order conductivity tensors to have only one independent component each, which we calculate using the quantum kinetic equation. In linearly\hyp{}polarized oscillating field, the current has a zero\hyp{}frequency component switching sign upon $\pi/2$-rotation of the polarization angle.