Algebraic theory of crystal vibrations: Singularities and zeros in vibrations of 1D and 2D lattices
arXiv:1506.01707 · doi:10.1103/PhysRevB.91.214307
Abstract
A novel method for the calculation of the energy dispersion relation (EDR) and density of states (DOS) in one (1D) and two (2D) dimensions is introduced and applied to linear lattices (1D) and square and hexagonal lattices (2D). The (van Hove) singularities and (Dirac) zeros of the DOS are discussed. Results for the 2D hexagonal lattice (graphene-like materials) are compared with experimental data in microwave photonic crystals.
References in corpus (17)
- Electric Field Effect in Atomically Thin Carbon Films
- The electronic properties of graphene
- Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
- Andreev reflection and Klein tunneling in graphene
- Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
- Strain-induced pseudomagnetic field and Landau levels in photonic structures
- Artificial graphene as a tunable Dirac material
- Phases of the one-dimensional Bose-Hubbard model
- Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice
- Topological transition of Dirac points in a microwave experiment
- Artificial graphene with tunable interactions
- Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene
- Quantum and Wave Dynamical Chaos in Superconducting Microwave Billiards
- Dirac Point and Edge States in a Microwave Realization of Tight-Binding Graphene-like Structures
- Lifshitz and Excited State Quantum Phase Transitions in Microwave Dirac Billiards
- Extremal transmission through a microwave photonic crystal and the observation of edge states in a rectangular Dirac billiard
- Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states
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- Probing the excited-state quantum phase transition through statistics of Loschmidt echo and quantum work
- Excited state quantum phase transitions in the bending spectra of molecules
- Symmetries of the squeeze-driven Kerr oscillator
- Phase diagram of the two-fluid Lipkin model: a butterfly catastrophe
- Properties of the eigenmodes and quantum-chaotic scattering in a superconducting microwave Dirac billiard with threefold rotational symmetry
- Symmetries of Liouvillians of squeeze-driven parametric oscillators
- Van Hove Singularities and Excited-State Quantum Phase Transitions in Graphene-like Microwave Billiards