Moir; patterns: a simple analytical model

By considering a straightforward geometrical construction in reciprocal space we derive simple analytical equations that describe the geometry (period and angle) of the moir; patterns (MPs) formed by superposition of any 2D material on any substrate (including other 2D materials). These equations should be valuable tools for interpreting experimentally observed MPs and for designing van der Waals heterostructures in which MPs are used to modulate the topological and/or electronic states of a device.