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.