B.S. Kandemir

Zone-boundary phonon induced mini band gap formation in graphene

Abstract We investigate the effect of electron– A 1 g phonon coupling on the gapless electronic band dispersion of the pristine graphene. The electron–phonon interaction is introduced through a Kekule-type distortion giving rise to inter-valley scattering between K and K ′ points in graphene. We develop a Frohlich type Hamiltonian within the continuum model in the long-wave length limit. By presenting a fully theoretical analysis, we show that the interaction of charge carriers with the highest frequency zone-boundary phonon mode of A 1 g - symmetry induces a mini band gap at the corners of the two-dimensional Brillouin zone of the graphene in the THz region. Since electron–electron interactions favor this type of lattice distortion, it is expected to be enhanced, and thus its quantitative implications might be measurable in graphene.

Boundaries of Subcritical Coulomb Impurity Region in Gapped Graphene

AbstractThe electronic energy spectrum of graphene electron subjected to a homogeneous magnetic field in the presence of a charged Coulomb impurity is studied analytically within two-dimensional Dirac-Weyl picture by using variational approach. The variational scheme we used is just based on utilizing the exact eigenstates of two-dimensional Dirac fermion in the presence of a uniform magnetic field as a basis for determining analytical energy eigenvalues in the presence of an attractive/repulsive charged Coulomb impurity. This approach allows us to determine under which conditions bound state solutions can or can not exist in gapped graphene in the presence of magnetic field. In addition, the effects of uniform magnetic field on the boundaries of subcritical Coulomb impurity region in the massless limit are also analyzed. Our analytical results show that the critical impurity strength decreases with increasing gap/mass parameter, and also that it increases with increasing magnetic field strength. In the massless limit, we investigate that the critical Coulomb coupling strength is independent of magnetic field, and its upper value for the ground-state energy is 0.752.

Variational approach for the effects of periodic modulations on the spectrum of massless Dirac fermion

AbstractIn the variational framework, we study the electronic energy spectrum of massless Dirac fermions of graphene subjected to one-dimensional oscillating magnetic and electrostatic fields centered around a constant uniform static magnetic field. We analyze the influence of the lateral periodic modulations in one direction, created by these oscillating electric and magnetic fields, on Dirac like Landau levels depending on amplitudes and periods of the field modulations. We compare our theoretical results with those found within the framework of non-degenerate perturbation theory. We found that the technique presented here yields energies lower than that obtained by the perturbation calculation, and thus gives more stable solutions for the electronic spectrum of massless Dirac fermion subjected to a magnetic field perpendicular to graphene layer under the influence of additional periodic potentials.

Cyclotron mass of a polaron in a quantum dot

Abstract The cyclotron mass of a polaron confined in an anisotropic quantum dot is calculated by taking into account the electron–bulk LO phonon interaction. Whilst some approximated results for the cyclotron mass are obtained, their analytical expressions are considered in three different limiting cases and their dependence on the magnetic field strength, the electron–phonon coupling strength and the confinement length is investigated, as well.

WIGNER FUNCTIONS OF AN ELECTRON MOVING IN A ONE-DIMENSIONAL PERIODIC POTENTIAL

Abstract Wigner pseudo-density functions of an electron moving in a one-dimensional sinusoidal potential in phase-space have been obtained. By an appropriate choice of the parameters related to the periodic potential the localized and free electron Wigner functions are separately constructed and they are interpreted in terms of band structure. It is observed that the negatively weighted regions in the Wigner phase-space distribution functions correspond to the forbidden zones, in which finding the particle is improbable.