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

Abstract

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.

5 pages, 4 figures

References in corpus (9)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• A tight-binding approach to uniaxial strain in graphene
• All-graphene integrated circuits via strain engineering
• Single Layer Behavior and Its Breakdown in Twisted Graphene Layers
• Edge states in Graphene: from gapped flat band to gapless chiral modes
• Charge Transport in Disordered Graphene-Based Low Dimensional Materials
• Strained graphene: tight-binding and density functional calculations

Cited by in corpus (12)

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• Dynamical Floquet spectrum of Kekulé-distorted graphene under normal incidence of electromagnetic radiation
• Topological edge states on time-periodically strained armchair graphene nanoribbons
• Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons
• Topological origin of flat-bands as pseudo-Landau levels in uniaxial strained graphene nanoribbons and induced magnetic ordering due to electron-electron interactions
• Spectral butterfly, mixed Dirac-Schrödinger fermion behavior and topological states in armchair uniaxial strained graphene
• Effective magnetic field induced by inhomogeneous Fermi velocity in strained honeycomb structures
• Topological phase-diagram of time-periodically rippled zigzag graphene nanoribbons
• Floquet spectrum and electronic transitions of tilted anisotropic Dirac materials under electromagnetic radiation: monodromy matrix approach
• Flat bands without twists: periodic holey graphene
• Interaction-driven charge textures and unconventional superconductivity in strained monolayer graphene
• Emergence of an aperiodic Dirichlet space from the tetrahedral units of an icosahedral internal space