Effective tight-binding model for MX2 under electric and magnetic fields

Abstract

We present a systematic method for developing a five band Hamiltonian for the metal d orbitals that can be used to study the effect of electric and magnetic fields on multilayer MX2 (M=Mo,W and X=S,Se) systems. On a hexagonal lattice of d orbitals, the broken inversion symmetry of the monolayers is incorporated via fictitious s orbitals at the chalcogenide sites. A tight-binding Hamiltonian is constructed and then downfolded to get effective d orbital overlap parameters using quasidegenerate perturbation theory. The steps to incorporate the effects of multiple layers, external electric and magnetic fields are also detailed. We find that an electric field produces a linear-k Rashba splitting around the Γ point, while a magnetic field removes the valley pseudospin degeneracy at the ±K points. Our model provides a simple tool to understand the recent experiments on electric and magnetic control of valley pseudospin in monolayer dichalcogendies.