We have investigated the valley Chern number and gapless edge states in wide-gap semiconductor SiC and BN monolayers by using the density functional theory calculations. We found that while SiC monolayer has a non-quantized valley Chern number due to a partial mixing of the Berry curvature peaks pertaining to the opposite valleys, there exist topologically protected gapless edge states within the bulk gap, leading to a quantum valley Hall effect. Doping of the opposite charge carriers causes a backscattering-free valley current flowing on the opposite edge, which can be used for experimental confirmation and application at room temperature. BN monolayer, on the other hand, was found to have gapped edge states due to the too large staggered AB-sublattice potentials.
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