Mapping of strained graphene into one-dimensional Hamiltonians: Quasicrystals and modulated crystals

The electronic properties of graphene under any arbitrary uniaxial strain field are obtained by an exact mapping of the corresponding tight-binding Hamiltonian into an effective one-dimensional modulated chain. For a periodic modulation, the system displays a rich behavior, including quasicrystals and modulated crystals with a complex spectrum, including gaps and peaks at the Fermi energy and localization transitions. All these features are explained by the incommensurate or commensurate nature of the potential, which leads to a dense filling by diffraction spots of the reciprocal space in the former case. The essential features of strain are made specially clear by analyzing a special momenta that uncouples the model into dimers.