Recently, twisted bilayers of transition metal dichalcogenides (TMDs) have gained interest as a novel and robust platform for simulating quantum phases of matter on emergent 2D lattices. These systems exhibit rich phase diagrams as function of twist angle, carrier density and temperature, including correlated insulating, superconducting and topologically non-trivial phases. The emergence of these correlated phases is attributed mainly to strong electron-electron interactions among electrons in flat bands near the Fermi level.

Studying the atomic and electronic structure of these systems using first-principles methods is computationally highly challenging because for small twist angles the moiré unit cells contain thousands of atoms. To overcome this problem, we employ a multi-scale approach in which classical force fields are used to find the equilibrium atomic structures and tight-binding calculations are carried out on the relaxed structures to determine electronic band structures. We present results for twisted bi-, tri- and quadlayer TMDs and discuss the dependence of the flat bands on the twist angle and the stacking arrangement.