M. R. Setare

The effect of an inhomogeneous magnetic field which varies inversely as distance on the ground state energy level of graphene is studied. In this work, we analytically show that graphene under the influence of a magnetic field arising from a straight long current-carrying wire ( proportional to the magnetic field from carbon nanotubes and nanowires) exhibits zero energy solutions. We find that contrary to the case of a uniform magnetic field for which the zero energy modes show the localization of electrons entirely on just one sublattice corresponding to single valley Hamiltonian, zero energy solutions in this case reveal that the probability for the electrons to be on the both sublattices, say A and B, are the same.

The effect of a mass gap on the conductance of graphene double-barrier heterojunctions is studied. By obtaining the 2D expression for the electronic transport of the low energy excitations of pure graphene through double-barrier systems, it is found that the conductivity of these structures does not depend on the type of charge carriers in the zones of the electric field. However, a finite induced gap in the graphene spectrum makes conductivity dependent on the energy band index. We also discuss a few controversies concerning double-barrier systems stemming from an improper choice of the scattering angle. Then it is observed that, for some special values of the incident energy and potential's height, graphene junctions behave like left-handed materials, resulting in a maximum value for the conductivity.

In this paper, we first evaluate the electronic transmission of Dirac fermions into a p-n junction of gapped graphene and show that the final result depends on the sign of the refractive index, n. We also, by considering the appropriate wavefunctions in the region of the electrostatic potential, show that both transmission and the reflection probability turn out to be positive and less than unity instead of the negative transmission and higher than unity reflection coefficient commonly referred to as the Klein paradox. We then obtain the transmission probability corresponding to a special p-n junction for which there exists a region in which the low energy excitations of graphene acquire a finite mass and, interestingly, find that in this case the transmission is independent of the index of refraction, in contrast with the corresponding result for gapped graphene. We then discuss the validity of the solutions reported in some of the papers cited in this work which, considering the Buttiker formula, turn out to lead to the wrong results for conductivity.