Related papers: Quantum graph spectra of a graphyne structure
We construct the new one-dimensional Dirac Hamiltonians that are spectrally isomorphic (not isospectral) with the known exactly solvable models. Explicit formulas for their spectra and eigenstates are provided. The operators are utilized…
We analyze spectral properties of a quantum graph in the form of a ring chain with a $\delta$ coupling in the vertices exposed to a homogeneous magnetic field perpendicular to the graph plane. We find the band spectrum in the case when the…
We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. Using the transfer matrix method, we explicitly determine the dispersion relation in terms of different…
In some previous works, the analytic structure of the spectrum of a quantum graph operator as a function of the vertex conditions and other parameters of the graph was established. However, a specific local coordinate chart on the…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary…
Studying the spectral theory of Schroedinger operator on metric graphs (also known as quantum graphs) is advantageous on its own as well as to demonstrate key concepts of general spectral theory. There are some excellent references for this…
We describe some basic tools in the spectral theory of Schr\"odinger operator on metric graphs (also known as "quantum graph") by studying in detail some basic examples. The exposition is kept as elementary and accessible as possible. In…
We study the dynamics of carriers in graphene subjected to an inhomogeneous magnetic field. For a magnetic field with an hyperbolic profile the corresponding Dirac equation can be analyzed within the formalism of supersymmetric quantum…
We consider periodic Schr\"{o}dinger operators on the hexagonal lattice with self-adjoint vertex conditions that allow discontinuity and concentrated mass at the vertices. This model generalizes the periodic Schr\"{o}dinger operator on the…
Spectroscopic studies of electronic phenomena in graphene are reviewed. A variety of methods and techniques are surveyed, from quasiparticle spectroscopies (tunneling, photoemission) to methods probing density and current response (infrared…
We study the band dispersion of graphene with randomly distributed structural defects using two complementary methods, exact diagonalization of the tight-binding Hamiltonian and implementing a self-consistent T matrix approximation. We…
We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under influence of a magnetic field assuming a $\delta$-coupling at the points where the rings touch. We start…
A number of interesting properties of graphene and graphite are postulated to derive from the peculiar bandstructure of graphene. This bandstructure consists of conical electron and hole pockets that meet at a single point in momentum (k)…
We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a…
We provide an introductory review of some topics in spectral theory of Laplacians on metric graphs. We focus on three different aspects: the trace formula, the self-adjointness problem and connections between Laplacians on metric graphs and…
We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac…
Chiral graphene nanoribbons are extremely interesting structures due to their low bandgaps and potential development of spin-polarized edge states. Here, we study their band structure on low work function silver surfaces and assess the…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
We consider discrete Schr\"odinger operators with real periodic potentials on periodic graphs. The spectra of the operators consist of a finite number of bands. By "rolling up" a periodic graph along some appropriate directions we obtain…