Transmission and Goos-H\"anchen like Shifts through a Graphene Double Barrier in an Inhomogeneous Magnetic Field

We studied the transport properties of electrons in graphene as they are scattered by a double barrier potential in the presence of an inhomogeneous magnetic field. We computed the transmission coefficient and Goos-H\"anchen like shifts for our system and noticed that transmission is not allowed for certain range of energies. In particular, we found that, in contrast to the electrostatic barriers, the magnetic barriers are able to confine Dirac fermions. We also established some correlation between the electronic transmission properties of Dirac fermions with the Goos-H\"anchen like shifts, as reflected in the numerical data.Comment: 18 pages, 6 figure

Confined Dirac Particles in Constant and Tilted Magnetic Field

We study the confinement of charged Dirac particles in 3+1 space-time due to the presence of a constant and tilted magnetic field. We focus on the nature of the solutions of the Dirac equation and on how they depend on the choice of vector potential that gives rise to the magnetic field. In particular, we select a "Landau gauge" such that the momentum is conserved along the direction of the vector potential yielding spinor wavefunctions, which are localized in the plane containing the magnetic field and normal to the vector potential. These wave functions are expressed in terms of the Hermite polynomials. We point out the relevance of these findings to the relativistic quantum Hall effect and compare with the results obtained for a constant magnetic field normal to the plane in 2+1 dimensions.Comment: 10 page

Tunneling of Massive Dirac Fermions in Graphene through Time-periodic Potential

The energy spectrum of graphene sheet with a single barrier structure having a time periodic oscillating height and subjected to magnetic field is analyzed. The corresponding transmission is studied as function of the obtained energy and the potential parameters. Quantum interference within the oscillating barrier has an important effect on quasiparticles tunneling. In particular the time-periodic electromagnetic field generates additional sidebands at energies \epsilon + l\hbar \omega (l=0,\pm 1, \cdots) in the transmission probability originating from the photon absorption or emission within the oscillating barrier. Due to numerical difficulties in truncating the resulting coupled channel equations we limited ourselves to low quantum channels, i.e. l=0,\pm 1.Comment: 20 pages, 13 figures, references added. Version to appear in EPJ