Valence Band Splitting on Multilayer MoS2: Mixing of Spin-Orbit Coupling and Interlayer Coupling.

Understanding the origin of valence band splitting is important because it governs the unique spin and valley physics in few-layer MoS2. We explore the effects of spin-orbit coupling and interlayer coupling on few-layer MoS2 using first-principles methods. We find spin-orbit coupling has a major contribution to the valence band splitting at K in multilayer MoS2. In double-layer MoS2, the interlayer coupling leads to the widening of the gap between the already spin-orbit split states. This is also the case for the bands of the K-point in bulk MoS2. In triple-layer MoS2, the strength of interlayer coupling of the spin-up channel becomes different from that of spin-down at K. This combined with spin-orbit coupling results in the band splitting in two main valence bands at K. With the increase of pressure, this phenomenon becomes more obvious with a decrease of main energy gap in the splitting valence bands at the K valley.