Effective tight-binding model for transition metal dichalcogenides

For transition metal dichalcogenides, various band models have been developed to describe the novel subband features. In this work, we propose a new effective minimum-band model by preforming a canonical transformation on the full-band Hamiltonian. We found that, depending on the form of transformation, both the $\Gamma$- and $K$-valley electrons can be well captured, including the frequency and band effective mass. And, for the full-band parameters used, starting from Wannier function basis set leads to a better result than from Slater-Koster basis set. A close inspection of the transformation projection also enables us to extract the modification on the site energy, as well as the orbital hopping between several nearest neighboring atoms. Instead of pure empirical fitting, our effective models preserve rich orbital physics inside, which is shown to be versatile in studying a variety of fundamental physical properties.