Numerical study of the quantum valley Hall effect

S. K. Wang, Jun Wang, Jun-Feng Liu

Published 2016-07-12Version 1

Recently, the topological valley current flowing in the gapped graphene was observed in a four-terminal Hall-bar device by measuring the nonlocal resistivity signal [{{Gorbachev \emph{et al.}, Science {\bf{346}}, 448 (2014)}}]. In this work, we study numerically the quantum valley Hall effect in the same Hall bar geometry based on a lattice model and the multiple-terminal Landauer-B\"{u}ttiker formula. It is found that in the clean limit, the nonlocal resistivity $R_{NL}$ is quantized, $R_{NL}={h}/{e^2}$, as long as the Hall-bar width exceeds its length $w>l$ and in the opposite case $l>w$, it decreases exponentially, $R_{NL}{\sim}e^{-l/w}$. The quantization of $R_{NL}$ originates from the quantized valley Hall conductivity of the gapped graphene, while its requirement of $w>l$ relates to the fact that the valley degree of freedom is defined in the reciprocal space and sensitive to the device profile. The quantization of $R_{NL}$ is also shown robust against both the rough edges of graphene and static disorders. Our findings may shed light on the fabrication of valley-based devices.