Semiclassical quantization conditions in strained moir\'e lattices

Abstract

In this article we generalize the Bohr-Sommerfeld rule for scalar symbols at a potential well to matrix-valued symbols having eigenvalues that may coalesce precisely at the bottom of the well. As an application, we study the existence of approximately flat bands in moir\'e heterostructures such as strained two-dimensional honeycomb lattices in a model recently introduced by Timmel and Mele.