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.
@article{arxiv.1905.05952,
title = {Strain-Fluctuation-Induced Near-Quantization of Valley Hall Conductivity in Graphene Systems},
author = {Wen-Yu Shan and Di Xiao},
journal= {arXiv preprint arXiv:1905.05952},
year = {2019}
}