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The magneto-conductivity of a single graphene layer where the electrons are described by the Dirac Hamiltonian weakly modulated by a periodic potential is calculated. It is shown that Weiss oscillations periodic in the inverse magnetic…
We study the influence of a perpendicular magnetic field with the asymptotics $B(r\to \infty)= B_0$ in a electrons in graphene. It is shown that the zero-energy solutions can exist only for one pseudospin direction, depending on the sign of…
The Dirac equation, in the field of a traveling circularly polarized electromagnetic wave and a constant magnetic field, has singular solutions, corresponding the expansion of energy in vicinity of some singular point. These solutions…
The energy spectra of spin-1/2 electrons under two-dimensional magnetic field modulations are calculated beyond the one-band approximation. Our formulation is generally applicable to a modulation field with a rectangular lattice symmetry.…
We theoretically study electronic properties of a graphene sheet on xy plane in a spatially nonuniform magnetic field, $B = B_0 \hat{z}$ in one domain and $B = B_1 \hat{z}$ in the other domain, in the quantum Hall regime and in the…
We have experimentally studied the non-equilibrium transport in low-density clean 2D electron systems at mesoscopic length scales. At zero magnetic field (B), a double-peak structure in the non-linear conductance was observed close to the…
We report on exact-diagonalization studies of correlated many-electron states in the half-filled Landau levels of graphene, including pseudospin (valley) degeneracy. We demonstrate that the polarized Fermi sea of non-interacting composite…
Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall…
Spin-polarized two-dimensional materials with large and tunable spin-splitting energy promise the field of 2D spintronics. While graphene has been a canonical 2D material, its spin properties and tunability are limited. Here, we demonstrate…
We provide a systematic quantitative description of spin polarization in armchair and zigzag graphene nanoribbons in a perpendicular magnetic field. We first address spinless electrons within the Hartree approximation studying the evolution…
Two-dimensional electrons in graphene are known to behave as massless fermions with Dirac-Weyl type linear dispersion near the Dirac crossing points. We have investigated the collective excitations of this system in the presence or absence…
The modified Dirac-Pauli equations, which are introduced by means of ${\gamma_5}$-mass factorization of the ordinary Klein-Gordon operator, are considered. We also take into account the interaction of fermions with the intensive homogenous…
The electronic behavior in graphene under arbitrary uniaxial deformations, such as foldings or flexural fields is studied by including in the Dirac equation pseudoelectromagnetic fields. General foldings are thus studied by showing that…
Introducing quantum confinement has uncovered a rich set of interesting quantum phenomena and allows one to directly probe the physics of confined (quasi-)particles. In most experiments, however, electrostatic potential is the only…
We discuss the novel electronic properties of graphene under an external periodic scalar or vector potential, and the analytical and numerical methods used to investigate them. When graphene is subjected to a one-dimensional periodic scalar…
We propose a mechanism to construct the eigenvalues and eigenfunctions of the massless Dirac-Weyl equation in the presences of magnetic flux $\Phi$ localized in a restricted region of the plane. Using this mechanism we analyze the…
The conductivity of the system magnetic dielectric (EuO) - graphene channel - ferroelectric substrate was considered. The magnetic dielectric locally transforms the band spectrum of graphene by inducing an energy gap in it and making it…
We predict that spin-waves in an easy-plane ferromagnet have a finite lifetime at zero temperature due to spontaneous decays. In zero field the damping is determined by three-magnon decay processes, whereas decays in the two-particle…
The behavior of electrons in strained graphene is usually described using effective pseudomagnetic fields in a Dirac equation. Here we consider the particular case of a spatially constant strain. Our results indicate that lattice…
We investigate the combined influence of a magnetic field and a harmonic interparticle interaction on the thermodynamic properties of a finite number of spin polarized fermions in a confiment potential. This study is an extension using our…