Related papers: Spectral gaps in graphene antidot lattices
Our research focuses on the transmission gaps of charge carriers passing through phosphorene superlattice, which are made up of a series of barriers and wells generating $n$ identical cells. We determine the solutions of the energy spectrum…
In this paper, we study the opening of a spectral gap for a class of 2-dimensional periodic Hamiltonians which include those modelling multilayer graphene. The kinetic part of the Hamiltonian is given by $\sigma \cdot F(-i\nabla)$, where…
Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of…
We prove that the spectral gap of a finite planar graph $X$ is bounded by $\lambda_1(X)\le C(\frac{\log(\diam X)}{\diam X})^2$ where $C$ depends only on the degree of $X$. We then give a sequence of such graphs showing the the above…
We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. For a given number $N$ we construct periodic (i.e. covering) manifolds such that the essential spectrum of the corresponding…
The physical mechanism underlying scattering properties of matter wave gap-solitons by linear optical lattice defects is investigated. The occurrence of repeated reflection, transmission and trapping regions for increasing strengths of an…
Graphene plasmonics has become a highlighted research area due to the outstanding properties of deep-subwavelength plasmon excitation, long relaxation time, and electro-optical tunability. Although the giant conductivity of a graphene layer…
Graphene outstanding properties directly come from its pecular electronic structure and thus from the honeycomb lattice symmetry. The way interaction with the substrate impact this lattice is of primary importance. This is peculiarly true…
The procedure of evaluating of the spectrum for discrete periodic operators perturbed by operators of smaller dimensions is obtained. This result allows to obtain propagative, guided, localised spectra for different kind of physical…
We study the mechanism of wrinkling of suspended graphene, by means of atomistic simulations. We argue that the structural instability under edge compression is the essential physical reason for the formation of periodic ripples in…
We study the density of states in monolayer and bilayer graphene in the presence of a random potential that breaks sublattice symmetries. While a uniform symmetry-breaking potential opens a uniform gap, a random symmetry-breaking potential…
Intrinsic ripples with various configurations and sizes were reported to affect the physical and chemical properties of 2D materials. By performing molecular dynamics simulations and theoretical analysis, we use two geometric models of the…
Collisions between electrons and holes can dominate the carrier scattering in clean graphene samples in the vicinity of charge neutrality point. While electron-hole limited resistance in pristine gapless graphene is well-studied, its…
Topological defects (e.g. pentagons, heptagons and pentagon-heptagon pairs) have been widely observed in large scale graphene and have been recognized to play important roles in tailoring the mechanical and physical properties of…
The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their…
We investigate the persistence of spectral gaps of one-dimensional frustration free quantum lattice systems under weak perturbations and with open boundary conditions. Assuming the interactions of the system satisfy a form of local…
We study the disorder effect on the excitonic gap generation caused by strong Coulomb interaction in graphene. By solving the self-consistently coupled equations of dynamical fermion gap $m$ and disorder scattering rate $\Gamma$, we found a…
Symmetry arguments are used to describe all possible two-dimensional periodic corrugations of graphene ("nanomeshes") capable of inducing tangible semiconducting gap. Such nanomeshes or superlattices break the initial graphene translational…
We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported, we show that the S-matrix for all energies in any open set in the continuous…
We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…