Theory of lattice relaxation in homobilayer twist moirés

Lattice relaxation in moiré materials can strongly modify the electronic moiré bands. This is especially true in moirés made from transition metal dichalcogenides (TMDs) for which relaxation is an order of magnitude stronger compared to graphene moirés. Here we present analytical results for relaxation in homobilayer twist moirés based on symmetry constraints and continuum elasticity. We focus on twist moirés with D6 and D3 stacking symmetry such as parallel and antiparallel stacked homobilayer TMDs, respectively. In particular, we consider both the perturbative regime (large twist angles) and the regime of domain formation (tiny twist angles). Our results agree well with numerical solutions and molecular dynamics simulations. Finally, we demonstrate how our theory yields expressions for the strain-induced pseudo gauge fields and modified moiré potentials in the presence of lattice relaxation.