Dynamics of the (spin-) Hall effect in topological insulators and graphene

TL;DR

This paper investigates how strong electric fields affect the (spin-) Hall effect in topological insulators and graphene, revealing quantization breakdown and a conductivity decrease proportional to 1/sqrt{E}.

Contribution

It provides a detailed analysis of the non-equilibrium dynamics of the (spin-) Hall effect under strong electric fields in topological materials.

Findings

Hall conductivity remains quantized under weak fields

Quantization breaks down at strong fields due to Landau-Zener transitions

Conductivity decreases as 1/sqrt{E} in strong electric fields

Abstract

A single two-dimensional Dirac cone with a mass gap produces a quantized (spin-) Hall step in the absence of magnetic field. What happens in strong electric fields? This question is investigated by analyzing time evolution and dynamics of the (spin-) Hall effect. After switching on a longitudinal electric field, a stationary Hall current is reached through damped oscillations. The Hall conductivity remains quantized as long as the electric field (E) is too weak to induce Landau-Zener transitions, but quantization breaks down for strong fields and the conductivity decreases as 1/sqrt{E}. These apply to the (spin-) Hall conductivity of graphene and the Hall and magnetoelectric response of topological insulators.