Lattice Relaxation in Twisted Homotrilayer Transition Metal Dichalcogenides

The experimental observations of fractional quantum anomalous Hall states in twisted bilayer transition metal dichalcogenides (TMDs) demonstrated the existence of these exotic topological states with time-reversal symmetry breaking in real materials without the application of an external magnetic field. These phases occur at the so-called magic twist angles in which the band structure hosts topological flat bands possessing non-zero Chern numbers. The continuum Hamiltonian of K-valley twisted TMD homobilayers under the adiabatic approximation possesses skyrmions in the layer pseudospin field that lead to an effective magnetic field, which motivates a study of twisted homotrilayer TMDs. However, the relative energies of different stacking configurations of the constituent layers cause the moiré pattern to relax in order to expand areas of energetically favourable stacking configurations. This lattice relaxation must be taken into account in the continuum model description, and so we use elasticity theory in order to develop an algorithm that computes the lattice relaxation of twisted homotrilayer TMDs. We present these lattice reconstruction results as well as the effect on the electronic band structure.