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.

实现和控制波谷分割是Valleytronics应用程序的核心问题。通常，谷值分裂是通过施加外部磁场或结构操纵来实现的。但是，这种方法效率较低。在这里，我们探索了CrI ₃（g-CrI ₃和2g-CrI ₃）异质结构上的单层和双层石墨烯，以引起谷裂。在g-CrI _3中，我们发现了一个谷峰分裂，其多数间隙差为Δ1 _↑  -Δ2 _↑  = 44 meV。即使在2g-CrI ₃系统中，我们也发现了Δ1 _↑  -Δ2 _↑的谷裂 = 21兆电子伏 此外，我们还研究了电场对谷值分裂的影响。在这两个系统中，我们观察到谷值分裂可以在多数自旋带中切换。例如，在±K处的间隙差的符号从零场的Δ1 _↑  >Δ2 _↑变为在0.1 V /Å的小外加电场下的Δ1 _↑  <Δ2 _{↑ 。}随着电场进一步增加到0.2 V /Å，波谷分裂消失了。因此，我们提出可以实现大的谷值分裂，并且也可以通过电场而不是磁场来切换分裂的符号。该特征对于基于山谷电子的信息处理设备的设计可能是有益的。