Gapped edge states and quantum valley Hall effect in a planar honeycomb monolayer of group III–V binary compounds of the form BX (X = N, P, and As)

Although a gapless edge state is a characteristic of topologically nontrivial insulators, we show that in quantum valley Hall insulators with staggered AB-sublattice potentials, a gapless edge state can be shifted by large on-site potentials of an abrupt domain wall, leading to a gapped edge state. At a smooth domain wall, a gapless edge state occurs regardless of the strength of the staggered potentials. Our density functional theory calculations show that a wide-gap semiconductor BX (X = N, P, and As) monolayer can be a quantum valley Hall insulator with gapped edge states. We found that a BX monolayer has gapped edge states at an abrupt domain wall. However, robust gapless edge states for ripple-induced smooth scattering potentials were identified at the bare edge of BP and BAs nanoribbons. In the BN monolayer, only gapped edge states were found, which appears to be due to too large on-site potentials.