Magnetic Field Effects on Charge and Current Density in Finite Monolayer Graphene

In this work, we study the effects of an external magnetic field on the charge and current density in finite monolayer graphene, i.e., with zig-zag and armchair edges. We use the tight-binding model to include the effects of the magnetic field and the effect of the edges. By using the transmission probability and analyzing the local density of states (charge density) ob- tained from Green’s function method, we find an energy region where the wave functions are more localized in the edges and, consequently, the current flow across the borders. On the other hand, for energies close to Landau levels, the charge and current density are localized on the bulk of the system.