Atomic relaxation and strain in twisted bilayer transition metal dichalcogenides

Twisted bilayer transition metal dichalcogenides (TMDs) exhibit a variety of exotic correlated phases, including the fractional quantum anomalous Hall state and superconductivity. While atomic relaxation is known to modify flat-band conditions, its influence on the electronic structure has not been systematically investigated, and no continuum model has yet incorporated its effects. Here, we develop a configuration-space continuum model for moiré TMDs that accounts for both twist angle and lattice mismatch. We show that the twist angle introduces antisymmetric strain (corresponding to local rotations), whereas lattice mismatch gives rise to symmetric strain. We incorporate atomic relaxation directly into the continuum model and show that it gives rise to both scalar and vector potentials.