Related papers: Spectral gaps in graphene antidot lattices
We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a semi-infinite Bethe lattice of arbitrary coordination number q. In particular, we determine the pressure exerted by the polymer on the wall, as…
The propagation of a surface plasmon-polariton along a stack of doped graphene sheets is considered. This auxiliary problem is used to discuss: (i) the scattering of such a mode at an interface between the stack and the vacuum; (ii) the…
Motivated by a number of recent experimental studies, we have carried out the microscopic calculation of the quasiparticle self-energy and spectral function in a doped graphene when a symmetry breaking of the sublattices is occurred. Our…
Knabe's theorem lower bounds the spectral gap of a one dimensional frustration-free local hamiltonian in terms of the local spectral gaps of finite regions. It also provides a local spectral gap threshold for hamiltonians that are gapless…
It is proved that small periodic singular perturbation of a cylindrical waveguide surface may open a gap in the continuous spectrum of the Dirichlet problem for the Laplace operator. If the perturbation period is long and the caverns in the…
The electronic properties of graphene may be changed from semimetallic to semiconducting by introducing perforations (antidots) in a periodic pattern. The properties of such graphene antidot lattices (GALs) have previously been studied…
Graphene and few-layer graphene at high bias expose a wealth of phenomena due to the high temperatures reached. With in-situ transmission electron microscopy (TEM) we observe directly how the current modifies the structure, and vice versa.…
The adhesion of graphene on slightly lattice-mismatched surfaces, for instance of hexagonal boron nitride (hBN) or Ir(111), gives rise to a complex landscape of sublattice symmetry-breaking potentials for the Dirac fermions. Whereas a gap…
After the discovery of graphene and its many fascinating properties, there has been a growing interest for the study of "artificial graphenes". These are totally different and novel systems which bear exciting similarities with graphene.…
The following two results are shown. 1) Let $G$ be the $k$-rational points of a simple algebraic group over a local field $k$ and let $H$ be a lattice in $G.$ Then the regular representation of $G$ on $L^2(G/H)$ has a spectral gap (that is,…
Electron scattering in the monolayer graphene with short-range impurities modelled by the annular well with a band-asymmetric potential has been considered. Band-asymmetry of the potential resulted in the mass (gap) perturbation in the…
Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary conditions at the vertices to get an eigenvalue problem. A…
Lattice defects are inevitably present in two-dimensional materials, with direct implications on their physical and chemical properties. We show that the formation energy of a lattice defect in buckled two-dimensional crystals is not…
The insertion of the band gap $\Delta$ in the rippled graphene superlattice leads to new outcomes, as demonstrated. The essential thing is the appearance of opposite-spin transmissions, which increase with $\Delta$ and vanish without it.…
We report on infrared spectroscopy of bilayer graphene integrated in gated structures. We observed a significant asymmetry in the optical conductivity upon electrostatic doping of electrons and holes. We show that this finding arises from a…
Photonic crystals with a sufficiently high refractive index contrast display partial or full band gaps. However, imperfections in the metamaterial cause light scattering and extinction of the interfering propagating waves. Positive as well…
In this paper we study the spectral gap of the path graph and illustrate an interesting effect which has been described recently in the continuous setting. More explicitly, in the large-volume limit and in the presence of a certain external…
We present a formalism and numerical results for the energy loss of a charged particle scattered at an arbitrary angle from epitaxially grown multilayer graphene (MLG). It is compared with that of free-standing graphene layers.…
Signed graphs are graphs whose edges get a sign $+1$ or $-1$ (the signature). Signed graphs can be studied by means of graph matrices extended to signed graphs in a natural way. Recently, the spectra of signed graphs have attracted much…
We report on a theoretical study of the influence of electron-electron interactions on ARPES spectra in graphene that is based on the random-phase-approximation and on graphene's massless Dirac equation continuum model. We find that level…