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 E_A1. 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.

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