Hofstadter butterflies and metal/insulator transitions for moiré heterostructures
Published 2022-06-23Version 1
We consider a tight-binding model recently introduced by Timmel and Mele for strained moir\'e heterostructures. We consider two honeycomb lattices to which layer antisymmetric shear strain is applied to periodically modulate the tunneling between the lattices in one distinguished direction. This effectively reduces the model to one spatial dimension and makes it amenable to the theory of matrix-valued quasi-periodic operators. We then study the transport and spectral properties of this system, explaining the appearance of a Hofstadter-type butterfly. For sufficiently incommensurable moir\'e length and strong coupling between the lattices this leads to the occurrence of localization phenomena.