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The quantum density of states of the H\'enon-Heiles potential displays a pronounced beating pattern. This has been explained by the interference of three isolated classical periodic orbits with nearby actions and periods. A singular…
We predict unusual (for non-relativistic quantum mechanics) electron states in graphene, which are localized within a finite-width potential barrier. The density of localized states in the sufficiently high and/or wide graphene barrier…
The quantum Hall effect in graphene p-n junctions is studied numerically with emphasis on the effect of disorder at the interface of two adjacent regions. Conductance plateaus are found to be attached to the intensity of the disorder, and…
Ferromagnetism and superconductivity are most fundamental phenomena in condensed matter physics. Entailing opposite spin orders, they share an important conceptual similarity: Disturbances in magnetic ordering in magnetic materials can…
We study transport properties of graphene-based p-n junctions irradiated by an electromagnetic field (EF). The resonant interaction of propagating quasiparticles with an external monochromatic radiation opens dynamical gaps in their…
We consider electron transport in ferromagnets or antiferromagnets sandwiched between metals. When spins in the magnetic materials precess, they emit currents into the surrounding conductors. Generally, adiabatic pumping in mesoscopic…
The stationary Josephson effect in a system of ballistic graphene is studied in the framework of quasiclassical Green's function theory. Reflecting the ultimate two-dimensionality of graphene, a Josephson junction involving a graphene sheet…
We predict and analyze {\it radiation-induced quantum interference effect} in low-dimensional $n$-$p$ junctions. This phenomenon manifests itself by large oscillations of the photocurrent as a function of the gate voltage or the frequency…
In contrast to graphene which is a gapless semiconductor, graphane, the hydrogenated graphene, is a semiconductor with an energy gap. Together with the two-dimensional geometry, unique transport features of graphene, and possibility of…
We study quasi-particle transmission through an $n $-$p$ junction in a graphene irradiated by an electromagnetic field (EF). In the absence of EF the electronic spectrum of undoped graphene is gapless, and one may expect the perfect…
In normal mesoscopic metals of a ring topology persistent currents can be induced by threading the center of the ring with a magnetic flux. This phenomenon is an example of the famous Aharonov-Bohm effect. In the paper we study the current…
Graphene-like materials can be effectively described by Quantum Electrodynamics in (2+1)-dimensions. In a pristine state, these systems exhibit a symmetry between the nonequivalent Dirac points in the honeycomb lattice. Realistic samples…
The kinetic transport of electrons through graphene magnetic barriers is studied theoretically in presence of an external time harmonic scalar potential. The transmission coefficients are calculated in the framework of the non-perturbative…
We study the scattering of graphene quasiparticles by topological defects, represented by holes, pentagons and heptagons. For the case of holes, we obtain the phase shift and found that at low concentration they appear to be irrelevant for…
We present a theory presenting new quantum oscillations in the magnetoresistance that are revealed as fine structures superimposed to the Schubnikov-de-Haas oscillations. They may be observed in experiments on graphene layers as fine…
The optical conductivity of graphene, bilayer graphene, and graphite in quantizing magnetic fields is studied. Both dynamical conductivities, longitudinal and Hall's, are analytically evaluated. The conductivity peaks are explained in terms…
We study the Josephson current in long ballistic superconductor-monolayer graphene-superconductor junctions. As a first step, we have developed an efficient computational approach to calculate the Josephson current in tight-binding systems.…
Revivals of electric current in graphene in the presence of an external magnetic field are described. It is shown that when the electrons are prepared in the form of wave packets assuming a Gaussian population of only positive (or negative)…
We describe a nonlinear interaction between charge currents and spin currents which arises from the energy dependence of the conductivity. This allows nonmagnetic contacts to be used for measuring and controlling spin signals. We choose…
We demonstrate the possibility of a turbulent flow of electrons in graphene in the hydrodynamic region, by calculating the corresponding turbulent probability density function. This is used to calculate the contribution of the turbulent…