The Hall Conductivity of a Doped Graphene in a Quantizing Magnetic Field

Abstract

In this paper we study the electron energy spectrum corresponding to Landau levels in doped graphene when an external magnetic field is applied in the direction normal to the graphene planar sheet. The derived dispersion relation for the electrons in the doped graphene allows us to determine the dependence of the electrical conductivity on the applied magnetic field. This relationship between electrical conductivity and applied magnetic field is further analyzed for different characteristics of the impurities; specifically the potential of hybridization and the energy of the adsorbed atom.

Landau level transitions in doped graphene in a time dependent magnetic field

“…Doped graphene shows remarkable high field-effect mobilities, even at room temperatures ( [22], [23]). Also it is possible the appearance of negative conductivity in graphene with impurities in magnetic fields (see [24] and [25]). …”

“…This Hamiltonian acts on the electron wavefunctions localized on sublattice A and B respectively. Using the tight binding approximation, is not difficult to show that if we place an impurity near the atom of the sublattice A and B, the corresponding Hamiltonian can be written as (see [25])…”

“…However, Landau level transitions in graphene with impurities placed in a time-dependent magnetic field has not been theoretically studied, therefore in this work we address this problem using time-dependent perturbation theory, where the free Hamiltonian is defined on eq. ( 2) of [25], and the interacting Hamiltonian is defined in eq. ( 6) of this work.…”

“…Some of the arguments of this section are based on the work[25], which will be used as a starting point for the subsequent development.…”

Influence of multi-level impurities on the dynamics of ultrashort electromagnetic pulses in carbon nanotubes

“…-Consider the propagation of extremely short electromagnetic pulses in an array of carbon nanotubes with impurities, where we suppose the electric field to be directed along the nanotubes axes. The matrix form of the Hamiltonian can be constructed as [12][13][14]…”