Switchable valley splitting by external electric field effect in graphene/CrI3 heterostructures

Abstract Achieving and controlling valley splitting is a core issue for valleytronics applications. Conventionally, valley splitting was achieved by applying an external magnetic field or structural manipulation. However, this approach is less efficient. Here, we explored single layer and bilayer graphene on CrI₃ (g-CrI₃ and 2g-CrI₃) heterostructures to induce valley splitting. In g-CrI₃, we found a valley splitting with the majority gap difference of Δ_1↑ − Δ_2↑ = 44 meV. Even in 2g-CrI₃ system, we also found valley splitting of Δ_1↑ − Δ_2↑ = 21 meV. Moreover, we also investigated the electric field effect on valley splitting. In both systems, we observed that valley splitting could be switched in the majority spin band. For instance, the sign of gap difference at ±K changed from Δ_1↑ > Δ_2↑ at zero field to Δ_1↑ < Δ_2↑ at a small applied electric field of 0.1 V/Å_. With further increase of the electric field to 0.2 V/Å, valley splitting disappeared. Thus, we propose that a large value of valley splitting can be achieved and the sign of splitting can also be switched with electric field instead of magnetic field. This feature may be beneficial for designing of valleytronic based information process devices.