▎ 摘　　要

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.