A position-dependent ab initio tight-binding model for twisted TMD bilayers

The discovery of superconducting and correlated insulating states in magic-angle twisted bilayer graphene has led to intense interest in other moiré materials. Twisted bilayer transition metal dichalcogenides (TMDs), for example, have been shown to exhibit correlated insulating states at different fillings, possible superconducting behaviour [1], and exotic optical properties [2].

The large size of the moiré unit cells of small-angle twisted TMD bilayers renders electronic structure calculations based on density functional theory (DFT) unsuitable for the routine study and exploration of their large chemical and structural phase space. Therefore, atomistic tight-binding models are often used. Whilst tight-binding models with position-dependent interlayer hoppings have been developed, a model that captures position dependence within a layer doesn’t exist. This is essential to describe the effect of intralayer atomic relaxations on the emergence and nature of flat bands in the electronic structure [3], as well as to calculate electron-phonon coupling.

In this work, we develop a position-dependent intralayer TMD tight-binding Hamiltonian. Our model is based on Slater-Koster relations that are parametrized to hoppings obtained from first-principles DFT Hamiltonians of strained monolayer TMDs in a basis of maximally localized Wannier functions.

[1] Wang L. et al., Nat. Mat. 19, pages 861–866 (2020)

[2] Tran, K., et al., Nature 567, 71–75 (2019)

[3] Li, H., et al., Nat. Mater. 20, 945–950 (2021