Semiclassical framework for electronic structure of Moir\'{e} systems

We show that Moir\'{e} systems can be extensively studied in emergent semiclassical framework, with small parameter being the Moir\'{e} parameter $\theta$ of mismatch between lattices. A variety of known tunable physical phenomena, including the appearance and stability of flat bands, are described. The study starts with analysis of one-dimensional Moir\'{e} chains, strained and twisted bilayer square lattices. We then focus on applying the developed methods to real materials, such as strained graphene, TBG, graphene/hBN bilayers and MoSe2/WSe2 heterostructure.