On the spectra of carbon nano-structures

Abstract

An explicit derivation of dispersion relations and spectra for periodic Schrödinger operators on carbon nano-structures (including graphen and all types of single-wall nano-tubes) is provided.

25 pages, 7 figures

References in corpus (6)

• Kirchhoff's Rule for Quantum Wires
• Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs
• Spectra of Schroedinger operators on equilateral quantum graphs
• Band spectra of rectangular graph superlattices
• Branched quantum wave guides with Dirichlet boundary conditions: the decoupling case
• On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators

Cited by in corpus (38)

• Soliton solutions of nonlinear Schroedinger equation on simple networks
• Elliptic operators with honeycomb symmetry: Dirac points, Edge States and Applications to Photonic Graphene
• Observation of edge waves in a two-dimensional Su-Schrieffer-Heeger acoustic network
• Spectral analysis on infinite Sierpinski fractafolds
• Bifurcations of standing localized waves on periodic graphs
• Dirac and magnetic Schrödinger operators on fractals
• Spectral Theory of Infinite Quantum Graphs
• Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures
• Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics
• Universality of the momentum band density of periodic networks
• Transport in simple networks described by integrable discrete nonlinear SchrÄodinger equation
• Scattering on periodic metric graphs
• Dirac cones for point scatterers on a honeycomb lattice
• Characterization of edge states in perturbed honeycomb structures
• Continuity of the integrated density of states on random length metric graphs
• Topological two-dimensional Su-Schrieffer-Heeger analogue acoustic networks: Total reflection at corners and corner induced modes
• Cantor spectrum of graphene in magnetic fields
• Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs
• Inverse scattering for Schrödinger operators on perturbed lattices
• Reducible Fermi surface for multi-layer quantum graphs including stacked graphene
• Topics on Fermi varieties of discrete periodic Schrödinger operators
• Physics of the fundamental limits of nonlinear optics: A theoretical perspective
• Symmetry breaking in two-dimensional square grids: persistence and failure of the dimensional crossover
• Dispersion relations of periodic quantum graphs associated with Archimedean tiling (I)
• Continuum limit of the lattice quantum graph Hamiltonian
• Dispersion relations of periodic quantum graphs associated with Archimedean tilings (II)
• Hermitian unitary matrices with modular permutation symmetry
• Spectrum of a dilated honeycomb network
• Optimum topology of quasi-one dimensional nonlinear optical quantum systems
• Optimization of eigenstates and spectra for quasi-linear nonlinear optical systems
• Quantum graphs whose spectra mimic the zeros of the Riemann zeta function
• Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs
• Dirac cones for bi- and trilayer Bernal-stacked graphene in a quantum graph model
• Non-compact quantum graphs with summable matrix potentials
• Robustness of flat bands on the perturbed Kagome and the perturbed Super-Kagome lattice
• General solution to nonlinear optical quantum graphs using Dalgarno-Lewis summation techniques
• Spectra of semi-infinite quantum graph tubes
• The curious spectra and dynamics of non-locally finite crystals