Strain-Induced Quasi-1D Channels in Twisted Moire Lattices

We study the effects of strain in moire ' systems composed of honeycomb lattices. We elucidate the formation of almost perfect one-dimensional moire ' patterns in twisted bilayer systems. The formation of such patterns is a consequence of an interplay between twist and strain which gives rise to a collapse of the reciprocal space unit cell. As a criterion for such collapse we find a simple relation between the two quantities and the material specific Poisson ratio. The induced one-dimensional behavior is characterized by two, usually incommensurate, periodicities. Our results offer explanations for the complex patterns of one-dimensional channels observed in low angle twisted bilayer graphene systems and twisted bilayer dicalcogenides. Our findings can be applied to any hexagonal twisted moire ' pattern and can be easily extended to other geometries.