Charge neutral fermionic states and current oscillation in a graphene-superconductor hybrid structure
The proximity properties of edge currents in the vicinity of the interface between the graphene and superconductor in the presence of magnetic field are investigated. It is shown that the edge states introduced by Andreev reflection at the graphene-superconductor (G=S) interface give rise to the charge neutral states in all Landau levels. We note that in a topological insulator-superconductor (TI=S) hybrid structure, only N = 0 Landau level can support this type of charge neutral states. The different interface states of a G=S hybrid and a TI=S hybrid is due to that graphene consists of two distinct sublattices. The armchair edge consists of two inequivalent atoms. This gives rise to unique electronic properties of edge states when connected to a superconductor. A direct consequence of zero charge states in all Landau levels is that the current density approaches zero at interface. The proximity effect leads to quantum magnetic oscillation of the current density in the superconductor region. The interface current density can also be tuned with a finite interface potential. For sharp δ-type interface potential, the derivative of the wavefunction is discontinuous. As a result, we found that there is current density discontinuity at the interface. The step of the current discontinuity is proportional to the strength of the interface potential.