Valley-Hall alternatively changing conductivity in gapped and strained graphene.

Abstract

We investigated the alternatively changing (ac) valley-Hall effect in a graphene/h-BN structure under the modulations of a static electric field E0, magnetic field B0, and light field EA1. The proximity to the h-BN film leads to a mass gap and strain-induced pseudopotential for electrons in graphene. Starting from the Boltzmann equation, we derive the ac conductivity tensor σ, including the orbital magnetic moment, Berry curvature, and anisotropic Berry curvature dipole. It is found that under B0 ≠ 0, σ for the two valleys can have different amplitudes and even have the same sign, leading to a net ac Hall conductivity. The ac Hall conductivities and the optical gain can be altered by both the amplitude and the direction of E0. These features can be understood from the changing rate of σ with E0 and B0, which is valley-resolved and varies nonlinearly with the chemical potential.