Commensurate moir\'e superlattices in anisotropically strained twisted bilayer graphene

Abstract

We investigate how anisotropic strain reorganizes commensurate moir\'e superlattices and electronic structure in twisted bilayer graphene (TBG) across a finite range of reference twist angles. Motivated by experiments showing robust moir\'e phenomenology under angular disorder and heterostrain (Kapfer et al., Science 381,677 (2023)), we construct commensurate strained supercells generated by a general anisotropic deformation of the top graphene layer of TBG. The results show that anisotropic strain does not generically destroy the electronic structure of nearby pristine moir\'e systems; rather, its effect depends sensitively on whether the strained commensurate geometry remains two dimensional or crosses over toward a quasi one dimensional regime. This provides a geometric perspective on the persistence of moir\'e electronic features over a finite window of twist angle and heterostrain. Within this framework, the allowed strained configurations naturally separate into tilted two dimensional moir\'e patterns and quasi one dimensional stripe like patterns. We find that several such strained two dimensional solutions occur near a given pristine twist angle, and that nearby solutions retain triangular like AA-region localization, comparable low energy bandwidths, and a low field Hofstadter spectrum close to the unstrained system. In contrast, quasi one dimensional strained configurations show stronger dimensional reduction, reduced Dirac point multiplicity, stripe like spatial localization, and stronger Hofstadter splitting.