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 Δ1↑ − Δ2↑ = 44 meV. Even in 2g-CrI3 system, we also found valley splitting of Δ1↑ − Δ2↑ = 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 Δ1↑ > Δ2↑ at zero field to Δ1↑ < Δ2↑ 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.
Highlights
Valleytronics is an emerging field in the condensed matter physics and extensive research efforts have been performed to utilize the valley index for device applications.[1,2,3,4,5] the study on the valley physics started in the late 1970s using the twodimensional (2D) electron gases in silicon inversion layers
The valley index can behave as a distinguishable pseudospin in momentum space due to the opposite Berry curvature and extensive studies have been focused on the valley physics for potential device application by breaking the valley degeneracy.[3,4,9]
The pair of valley coincides with massless Dirac quasiparticles centered on these two inequivalent ±K corners of the Brillouin zone and this makes graphene a prime candidate for observing the physical properties associated with quantum Hall effects.[10]
Summary
Valleytronics is an emerging field in the condensed matter physics and extensive research efforts have been performed to utilize the valley index for device applications.[1,2,3,4,5] the study on the valley physics started in the late 1970s using the twodimensional (2D) electron gases in silicon inversion layers. The valley degeneracy and inter-valley coupling were investigated.[6,7,8] After the discovery of graphene, the interest in the valley physics began to grow substantially and the surge is everincreasing with the help of advanced experimental technique to fabricate various types of 2D materials. The valley index can behave as a distinguishable pseudospin in momentum space due to the opposite Berry curvature and extensive studies have been focused on the valley physics for potential device application by breaking the valley degeneracy.[3,4,9] In the graphene system, the pair of valley coincides with massless Dirac quasiparticles centered on these two inequivalent ±K corners of the Brillouin zone and this makes graphene a prime candidate for observing the physical properties associated with quantum Hall effects.[10]
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