Quantum magnetotransport in a bilayer MoS2: influence of a perpendicular electric field

Abstract

We first derive the energy dispersion of bilayer MoS$_{2}$ in the presence of a perpendicular electric field $E_z$. We show that the band gap and layer splitting can be controlled by the field $E_z$. Away from the $k$ point, the intrinsic SOC splitting increases in the conduction band but is weakly affected in the valence band. We then analyze the band structure in the presence of a perpendicular magnetic field $B$ and the field $E_z$, including spin and valley Zeeman terms, and evaluate the Hall and longitudinal conductivities. We discuss the numerical results as functions of the fields $B$ and $E_z$ for finite temperatures. The field $B$ gives rise to a significant spin splitting in the conduction band, to a beating in the Shubnikov-de Haas (SdH) oscillations when it's weak, and to their splitting when it's strong. The Zeeman terms and $E_{z}$ suppress the beating and change the positions of the beating nodes of the SdH oscillations at low $B$ fields and enhance their splitting at high $B$ fields. Similar beating patterns are observed in the spin and valley polarizations at low $B$ fields. Interestingly, a $90\%$ spin polarization and a $100\%$ square-wave-shaped valley polarization are observed at high $B$ fields. The Hall-plateau sequence depends on $E_z$. These findings may be pertinent to future spintronic and valleytronic devices.