$\mathit{\text{Ab-initio}}$ Tight-Binding Hamiltonian for Transition Metal Dichalcogenides

We present an accurate $\mathit{\text{ab-initio}}$ tight-binding hamiltonian for the transition-metal dichalcogenides, MoS${}_2$, MoSe${}_2$, WS${}_2$, WSe${}_2$, with a minimal basis (the $\mathit{\text{d}}$ orbitals for the metal atoms and $\mathit{\text{p}}$ orbitals for the chalcogen atoms) based on a transformation of the Kohn-Sham density function theory (DFT) hamiltonian to a basis of maximally localized Wannier functions (MLWF). The truncated tight-binding hamiltonian (TBH), with only on-site, first and partial second neighbor interactions, including spin-orbit coupling, provides a simple physical picture and the symmetry of the main band-structure features. Interlayer interactions between adjacent layers are modeled by transferable hopping terms between the chalcogen $\mathit{\text{p}}$ orbitals. The full-range tight-binding hamiltonian (FTBH) can be reduced to hybrid-orbital k $\cdot$ p effective hamiltonians near the band extrema that captures important low-energy excitations. These $\mathit{\text{ab-initio}}$ hamiltonians can serve as the starting point for applications to interacting many-body physics including optical transitions and Berry curvature of bands, of which we give some examples.