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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, gaps at the Fermi energy and interesting localization properties. These features are explained by the incommensurate or commensurate nature of the potential, which leads to a dense filling of the reciprocal space in the former case. Thus, the usual perturbation theory approach breaks down in some cases, as is proved by analyzing a special momentum that uncouples the model into dimers.