The electrical and spin properties of monolayer and bilayer Janus HfSSe under vertical electrical field

In this paper, the electrical and spin properties of mono- and bilayer HfSSe in the presence of a vertical electric field are studied. The density functional theory is used to investigate their properties. Fifteen different stacking orders of bilayer HfSSe are considered. The mono- and bilayer demonstrate an indirect bandgap, whereas the bandgap of bilayer can be effectively controlled by the electric field. While the bandgap of bilayer closes at large electric fields and a semiconductor to metal transition occurs, the effect of a normal electric field on the bandgap of the monolayer HfSSe is quite weak. Spin-orbit coupling causes band splitting in the valence band and Rashba spin splitting in the conduction band of both mono- and bilayer structures. The band splitting in the valence band of the bilayer is smaller than a monolayer, however, the vertical electric field increases the band splitting in bilayer one. The stacking configurations without mirror symmetry exhibit Rashba spin splitting which is enhanced with the electric field.