arXiv Analytics

Sign in

arXiv:2206.11891 [math-ph]AbstractReferencesReviewsResources

Hofstadter butterflies and metal/insulator transitions for moiré heterostructures

Simon Becker, Lingrui Ge, Jens Wittsten

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.

Related articles: Most relevant | Search more
arXiv:1112.0634 [math-ph] (Published 2011-12-03, updated 2014-08-14)
Galilean conformal algebras in two spatial dimension
arXiv:2103.13770 [math-ph] (Published 2021-03-25)
Ultraviolet Renormalisation of a quantum field toy model I
arXiv:1412.4191 [math-ph] (Published 2014-12-13)
A note on homotopic versus isomorphic topological phases