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The electronic properties of graphene under any arbitrary uniaxial strainfield are obtained by an exact mapping of the corresponding tight-bindingHamiltonian into an effective one-dimensional modulated chain. For a periodicmodulation, the system displays a rich behavior, including quasicrystals andmodulated crystals with a complex spectrum, gaps at the Fermi energy andinteresting localization properties. These features are explained by theincommensurate or commensurate nature of the potential, which leads to a densefilling of the reciprocal space in the former case. Thus, the usualperturbation theory approach breaks down in some cases, as is proved byanalyzing a special momentum that uncouples the model into dimers.

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