Algebraic theory of crystal vibrations: Singularities and zeros in vibrations of 1D and 2D lattices

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 (8)

• 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
• Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice
• 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

Cited by in corpus (7)

• Excited-state quantum phase transitions
• Excited-state quantum phase transition in the Rabi model
• Excited-state quantum phase transitions in systems with two degrees of freedom: III. Interacting boson systems
• Excited state quantum phase transitions in the bending spectra of molecules
• Symmetries of the squeeze-driven Kerr oscillator
• 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