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Graphene is a 2-dimensional (2D) carbon allotrope with the atoms arranged in a honeycomb lattice. The low-energy electronic excitations in this 2D crystal are described by massless Dirac fermions that have a linear dispersion relation…

We provide a semiclassical description of the electronic transport through graphene n-p junctions in the quantum Hall regime. A semiclassical approximation for the conductance is derived in terms of the various snake-like trajectories at…

Density functional perturbation theory is used to analyze electron-phonon interaction in bilayer graphene. The results show that phonon scattering in bilayer graphene bears more resemblance with bulk graphite than monolayer graphene. In…

The law of reflection states that smooth surfaces reflect waves specularly, thereby acting as a mirror. This law is insensitive to disorder as long as its length scale is smaller than the wavelength. Monolayer graphene exhibits a linear…

A perpendicular electric field breaks the layer symmetry of Bernal-stacked bilayer graphene, resulting in the opening of a band gap and a modification of the effective mass of the charge carriers. Using scanning tunneling microscopy and…

We analyze spin scattering in ballistic transport of electrons through a ripple at a normal incidence of an electron flow. The model of a ripple consists of a curved graphene surface in the form of an arc of a circle connected from the…

Some properties of the electron-electron collision operator in graphene are analyzed along with the evaluation of collision rate. Monte Carlo simulations complete the study and highlight the non-negligible role of the electron-electron…

We describe an angularly asymmetric interface-scattering mechanism which allows to spatially separate the electrons in the two low-energy valleys of bilayer graphene. The effect occurs at electrostatically defined interfaces separating…

We study the electronic properties of commensurate faulted bilayer graphene by diagonalizing the one-particle Hamiltonian of the bilayer system in a complete basis of Bloch states of the individual graphene layers. Our novel approach is…

Electron-electron interactions play a critical role in many condensed matter phenomena, and it is tempting to find a way to control them by changing the interactions' strength. One possible approach is to place a studied system in proximity…

Fractal scatterings in weak solitary wave interactions is analyzed for generalized nonlinear Schr\"odiger equations (GNLS). Using asymptotic methods, these weak interactions are reduced to a universal second-order map. This map gives the…

We calculate the differential, total, and transport cross-sections for scattering of two-dimensional massless Dirac electrons by a circular barrier. For scatterer of a small radius, the cross-sections are dominated by quantum effects such…

Detailed similarities between polarization states of light and ballistic charge carriers in graphene are derived. Based on these, the optical equivalent of quantum wavefunctions, Dirac equation, and the effect of an electrostatic potential…

We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy. The…

Inspired by the four-fold spin-valley symmetry of relativistic electrons in graphene, we investigate a possible SU(4) fractional quantum Hall effect, which may also arise in bilayer semiconductor quantum Hall systems with small Zeeman gap.…

Focusing of electron waves in graphene p-n junctions is a striking manifestation of fermionic negative refraction. We analyze lensing in smooth p-n junctions and find that it differs in several interesting ways from that in the previously…

Scattering problem for electrons in monolayer graphene with short-range perturbations of the types "local chemical potential" and "local gap" has been solved. Zero gap and non-zero gap kinds of graphene are considered. The determined…

A theoretical study is presented on the scattering of graphene surface plasmons by defects in the graphene sheet they propagate in. These defects can be either natural (as domain boundaries, ripples and cracks, among others) or induced by…

We propose a spectroscopic method of identifying broken symmetry states of bilayer graphene. We demonstrate theoretically that, in contrast to gapped states, a strained bilayer crystal or nematic phase of the electronic liquid are…

We present a computationally efficient method to incorporate density-functional theory into the calculation of reflectivity in low-energy electron microscopy. The reflectivity is determined by matching plane waves representing the electron…