Related papers: Spectral gaps in graphene antidot lattices
Here we report a facile method to generate a high density of point defects in graphene on metal foil and show how the point defects affect the electronic structures of graphene layers. Our scanning tunneling microscopy (STM) measurements,…
The derived by us earlier electron scattering matrix for the short-range defects in monolayer graphene is applyed to description of the resistivity electron density dependence. It is argued that large charged defect density is unlikely in…
We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties of the graph. We show that it exhibits a striking number of parallels to the reciprocal of…
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…
Irradiation of graphene on SiO2 by 500 eV Ne and He ions creates defects that cause intervalley scattering as evident from a significant Raman D band intensity. The defect scattering gives a conductivity proportional to charge carrier…
Using a tight-binding model, we study a line defect in graphene where a bulk energy gap is opened by sublattice symmetry breaking. It is found that sublattice symmetry breaking may induce many configurations that correspond to different…
We establish a connection between gaps problems in Diophantine approximation and the frequency spectrum of patches in cut and project sets with special windows. Our theorems provide bounds for the number of distinct frequencies of patches…
This paper presents an analysis of the band structure of a spacetime potential lattice created by a standing electromagnetic wave. We show that there are energy band gaps. We estimate the effect, and propose a measurement that could confirm…
Gap opening at the Dirac point of the single-layer graphene with periodic scalar and vector potentials has been theoretically investigated under the continuum model. The symmetry analysis indicates that the two-fold degeneracy at the Dirac…
We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices…
Graphene on a dielectric substrate exhibits spatial doping inhomogeneities, forming electron-hole puddles. Understanding and controlling the latter is of crucial importance for unraveling many of graphene's fundamental properties at the…
The electronic transmission and conductance of a gapped graphene superlattice were calculated by means of the transfer-matrix method. The system that we study consists of a sequence of electron-doped graphene as wells and hole-doped…
We discuss upper and lower bounds for the size of gaps in the length spectrum of negatively curved manifolds. For manifolds with algebraic generators for the fundamental group, we establish the existence of exponential lower bounds for the…
We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we show that the S-matrix for all energies in any given open set…
The electron scattering by the short-range defects in the monolayer graphene is considered in the framework of the flatland model. We analyze the effect of this scattering on the electronic resistivity of the monolayer graphene (direct…
We present exact analytical and numerical results for the electronic spectra and the Friedel oscillations around a substitutional impurity atom in a graphene lattice. A chemical dopant in graphene introduces changes in the on-site potential…
The spectral problem on a periodic domain with cracks is studied. An asymptotic form of dispersion relations is calculated under assumption that the opening of the cracks is small.
We consider the gapped graphene superlattice (SL) constructed in accordance with the Fibonacci rule. Quasi-periodic modulation is due to the difference in the values of the energy gap in different SL elements. It is shown that the effective…
A graphene-based superlattice formed due to the periodic modulation of the band gap has been investigated. Such a modulation is possible in graphene deposited on a strip substrate made of silicon oxide and hexagonal boron nitride. The…
The present manuscript summarizes the modern view on the problem of the graphene-metal interaction. Presently, the close-packed surfaces of d metals are used as templates for the preparation of highly-ordered graphene layers. Different…