Nonlinear Valley Hall Effect

TL;DR

This paper introduces a nonlinear valley Hall effect mechanism that generates valley currents in symmetric systems by leveraging electric field corrections to Berry curvature, demonstrated in strained graphene and organic semiconductors.

Contribution

It proposes a novel nonlinear valley Hall effect in inversion and time-reversal symmetric systems, expanding valleytronics beyond traditional symmetry-breaking methods.

Findings

Nonlinear valley Hall signals emerge from electric field corrections to Berry curvature.

Demonstrated in tilted massless Dirac fermions in strained graphene.

Potential for controlling valley degrees of freedom via nonlinear effects.

Abstract

The valley Hall effect arises from valley contrasting Berry curvature and requires inversion symmetry breaking. Here, we propose a nonlinear mechanism to generate a valley Hall current in systems with both inversion and time-reversal symmetry, where the linear and second-order charge Hall currents vanish along with the linear valley Hall current. We show that a second-order valley Hall signal emerges from the electric field correction to the Berry curvature, provided a valley-contrasting anisotropic dispersion is engineered. We demonstrate the nonlinear valley Hall effect in tilted massless Dirac fermions in strained graphene and organic semiconductors. Our work opens up the possibility of controlling the valley degree of freedom in inversion symmetric systems via nonlinear valleytronics.