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We study the energy levels of graphene magnetic circular quantum dot surrounded by an infinite graphene sheet in the presence of an electrostatic potential. We solve Dirac equation to derive the solutions of energy spectrum associated with…
In neutral graphene dots the Fermi level coincides with the Dirac points. We have investigated in the presence of a magnetic field several unusual properties of single electron states near the Fermi level of such a rectangular-shaped…
We investigate the superconducting proximity effect through graphene in the long diffusive junction limit, at low and high magnetic field. The interface quality and sample phase coherence lead to a zero resistance state at low temperature,…
Free electron like image potential states are observed in scanning tunneling spectroscopy on graphene quantum dots on Ir(111) acting as potential wells. The spectrum strongly depends on the size of the nanostructure as well as on the…
We present exact analytical zero-energy solutions for a class of smooth decaying potentials, showing that the full confinement of charge carriers in electrostatic potentials in graphene quantum dots and rings is indeed possible without…
We analyze the concept of causality for the conductivity of graphene described by the Dirac model. It is recalled that the condition of causality leads to the analyticity of conductivity in the upper half-plane of complex frequencies and to…
We use both continuum and lattice models to study the energy-momentum dispersion and the dynamics of a wave packet for an electron moving in graphene in the presence of spin-orbit couplings and either a single potential barrier or a…
We study the effect of band gap on the ground-state properties of Dirac electrons in a doped graphene within the random phase approximation at zero temperature. Band gap dependence of the exchange, correlation and ground-state energies and…
Solutions of the one dimensional Dirac equation with piece-wise constant potentials are presented using standard methods. These solutions show that the Klein Paradox is non-existent and represents a failure to correctly match solutions…
We analyze the dissipative conductance of the zero-plateau quantum Hall state appearing in undoped graphene in strong magnetic fields. Charge transport in this state is assumed to be carried by a magnetic domain wall, which forms by…
Magnetic confinement in graphene has been of recent and growing interest because its potential applications in nanotechnology. In particular, the observation of the so called magnetic edge states in graphene has opened the possibility to…
We report on the unusual nature of nu=0 state in the integer quantum Hall effect (QHE) in graphene and show that electron transport in this regime is dominated by counter-propagating edge states. Such states, intrinsic to massless Dirac…
The computational research that will be presented compares the coherent states of multiple layer graphene versus the coherent states of lithium ions diffused within this multilayer graphene. Unlike the prevailing research on graphene…
We consider the low-energy electronic properties of graphene cones in the presence of a global Fries-Kekul\'e Peierls distortion. Such cones occur in fullerenes as the geometric response to the disclination associated with pentagon rings.…
We investigate the effects of wedge disclination on charge carriers in circular graphene quantum dots subjected to a magnetic flux. Using the asymptotic solutions of the energy spectrum for large arguments, we approximate the scattering…
Graphene on a substrate has been shown to exhibit a transition, depending on the substrate material, from a zero-gap semiconductor state to a semimetallic state. The ground-state energy of the electron (hole) gas has been calculated within…
One intriguing finding in graphene is the vacancy-induced magnetism that highlights the interesting interaction between local magnetic moments and conduction electrons. Within density functional theory, the current understanding of the…
We report on several unusual properties of a graphene antidot created by a piecewise constant potential in a magnetic field. We find that the total probability of finding the electron in the barrier can be nearly one while it is almost zero…
We carry out a comparative study of electronic properties of 2D electron gas (2DEG) in a magnetic field of an infinitesimally thin solenoid with relativistic dispersion as in graphene and quadratic dispersion as in semiconducting…
We consider the problem of electron energy states related to strongly localized potential of a single impurity in graphene. Our model simulates the effect of impurity atom substituting the atom of carbon, on the energy spectrum of electrons…