Moiré pattern as a magnifying glass for strain and dislocations in van der Waals heterostructures

We consider the role of deformations in graphene heterostructures with hexagonal crystals (including strain, wrinkles and dislocations) on the geometrical properties of moiré patterns characteristic for a pair of two incommensurate misaligned isostructural crystals. By employing a phenomenological theory to describe generic moiré perturbations in van der Waals heterostructures of graphene and hexagonal crystals we investigate the electronic properties of such heterostructures.