Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials

TL;DR

This paper reveals a quantum nonlinear Hall effect in time-reversal invariant materials caused by Berry curvature dipole, enabling transverse currents without breaking time-reversal symmetry, with potential for novel electronic applications.

Contribution

It introduces the concept of a nonlinear Hall effect driven by Berry curvature dipole in time-reversal invariant materials, expanding understanding of Hall phenomena.

Findings

Nonlinear Hall effect occurs in time-reversal invariant, inversion-breaking materials.

The effect depends on the Berry curvature dipole and symmetry properties.

Candidate materials include topological insulators, transition metal dichalcogenides, and Weyl semimetals.

Abstract

It is well-known that a non-vanishing Hall conductivity requires time-reversal symmetry breaking. However, in this work, we demonstrate that a Hall-like transverse current can occur in second-order response to an external electric field in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the optical frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. We show that the nonlinear Hall coefficient is a rank-two pseudo-tensor, whose form is determined by point group symmetry. We discus optimal conditions to observe this effect and propose candidate two- and three-dimensional materials, including topological crystalline insulators, transition metal dichalcogenides and Weyl semimetals.