Related papers: Zero-energy states in graphene quantum dots and ri…
Using the tight-binding approximation we calculated the magnetic susceptibility of graphene quantum dots (GQD) of different geometrical shapes and sizes, smaller than the magnetic length, when the magnetic properties are governed by the…
We study quantum dots defined by external potentials within finite flakes of bilayer graphene using the tight-binding approach. We find that in the limit of large flakes containing zigzag edges the dot-localized energy levels appear within…
When an electron is confined to a triangular atomic thick layer of graphene [1-5] with zig-zag edges, its energy spectrum collapses to a shell of degenerate states at the Fermi level (Dirac point) [6-9]. The degeneracy is proportional to…
It is shown that for monolayer graphene electrons are confined on a perfect two dimensional surface. The implications for the electronic properties of corrugated graphene are discussed in view of a derivation of the constrained relativistic…
When sweeping the carrier concentration in monolayer graphene through the charge neutrality point, the experimentally measured Hall resistivity shows a smooth zero crossing. Using a two- component model of coexisting electrons and holes…
The quantum behavior of electrons in bilayer graphene with applied magnetic fields is addressed. By using second-order supersymmetric quantum mechanics the problem is transformed into two intertwined one dimensional stationary Schr\"odinger…
Recent observation of a metal-insulator phase transition in the $\nu=0$ Hall state of graphene has inspired the idea that charge carriers in the metallic state could be fractionally charged vortices. We examine the question of whether…
We propose a new method to use gapped graphene as barrier to confine electrons in gapless graphene and form a good quantum dot, which can be realized on an oxygen-terminated $SiO_{2}$ substrate partly H-passivated. In particular, we use…
We find the exact solution of graphene s carriers under electromagnetic radiation. To obtain such solution, we combine Floquet theory with a trial solution. Then the energy spectrum is obtained without using any approximation. Using such…
We present a quantum analysis of the massless excitations in graphene with a charge impurity. When the effective charge exceeds a certain critical value, the spectrum is quantized and is unbounded from below. The corresponding eigenstates…
The quantum Hall effect near the charge neutrality point in bilayer graphene is investigated in high magnetic fields of up to 35 T using electronic transport measurements. In the high field regime, the eight-fold degeneracy in the zero…
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…
Adopting a purely two dimensional relativistic equation for graphene's carriers contradicts the Heisenberg uncertainty principle since it requires setting off-the-surface coordinate of a three-dimensional wavefunction to zero. Here we…
We present theoretical results based on mean-field and exact many-body approaches showing that in bilayer triangular graphene quantum dots with zigzag edges the magnetism can be controlled by an external vertical electric-field. We…
We demonstrate the existence of a new type of zero energy state associated to vacancies in multilayer graphene that has a finite amplitude over the layer with a vacancy and adjacent layers, and the peculiarity of being quasi-localized in…
Quasi-exactly solvable rational potentials with known zero-energy solutions of the Schro\" odinger equation are constructed by starting from exactly solvable potentials for which the Schr\" odinger equation admits an so(2,1) potential…
The electronic energy gap and total dipole moment of chemically functionalized hexagonal and triangular graphene quantum dots are investigated by the density functional theory. It has been found that the energy gap can be efficiently tuned…
The problem of a spin-free electron with mass $m$, charge $e$ confined onto a ring of radius $R_0$ and with an attractive Dirac delta potential with scaling factor (depth) $\kappa$ in non-relativistic theory has closed form analytical…
The perfect transmission of charge carriers through potential barriers in graphene (Klein tunneling) is a direct consequence of the Dirac equation that governs the low-energy carrier dynamics. As a result, localized states do not exist in…
We compare the conductance of an undoped graphene sheet with a small region subject to an electrostatic gate potential for the cases that the dynamics in the gated region is regular (disc-shaped region) and classically chaotic (stadium).…