Strain-dependent ab-initio tight binding Hamiltonians for T-type transition metal dichalcogenides

Many transition metal dichalcogenides (TMDs) adopt a T-structure in which the metal atom is octahedrally coordinated by the chalcogens. In particular, MX₂ with M=(Nb, Ta, Ti) and X=(S, Se) all exhibit fascinating electronic properties including various charge density wave phases. Using Density Functional Theory followed by a Wannier transformation we extract the strain-dependent tight binding parameters for single-layer TMDs. The resulting tight binding Hamiltonian respects the crystal symmetry and gives a very accurate yet simple description of the electronic band structure which is easily augmented to include spin-orbit effects and interlayer couplings. The knowledge of the strain dependence of the electronic properties is critical in order to correct for the effects of relaxation in realistic simulations of twisted nanostructures.