# Strain-Fluctuation-Induced Near-Quantization of Valley Hall Conductivity in Graphene Systems

## TL;DR

This paper presents a theory explaining near-quantized valley Hall conductivity in graphene caused by strain-induced gauge potentials, highlighting the role of gauge disorder in anomalous Hall phenomena.

## Contribution

The paper introduces a theoretical framework for valley Hall effect in graphene considering strain fluctuation-induced gauge potentials as the main disorder source.

## Key findings

- Near-quantized valley Hall conductivity in the band transport regime.
- Reproduction of temperature and gap dependence of the valley Hall effect.
- Identification of gauge disorder as a key factor in anomalous Hall physics.

## Abstract

We develop a theory of the valley Hall effect in high-quality graphene samples, in which strain fluctuation-induced random gauge potentials have been suggested as the dominant source of disorder. We find a near-quantized value of valley Hall conductivity in the band transport regime, which originates from an enhanced side jump of a Dirac electron when it scatters off the gauge potential. By assuming a small residue charge density our theory reproduces qualitatively the temperature- and gap-dependence of the observed valley Hall effect at the charge neutral point. Our study suggests that the valley Hall effect in graphene systems represents a new paradigm for the anomalous Hall physics where gauge disorder plays an important role.