Bound states near the interface of a distorted graphene sheet and a superconductor

[摘要] ENGLISH ABSTRACT: The goal of this thesis is to investigate the effects of distorting a graphene lattice and connect-ing this distorted graphene sheet to a superconductor. At low energies the possible excitationstates in graphene are restricted to two distinct regions in momentum space called valleys. Manyelectronic applications are possible if one can design a graphene system where excitations canbe forced to occupy a single valley in a controllable way. Investigating the spectrum of thedistorted graphene sheet reveals that, if the chemical potential is chosen to coincide with a bulkLandau level, the normal-superconductor interface always supports propagating modes in bothdirections. Excitations from opposite valleys travel in opposite directions along the interface.The spectrum of a distorted graphene sheet terminated by an armchair edge, in contrast, is dis-persionless. We verify this insulating nature of the armchair edge for finite samples by numericalmeans. Furthermore, we verify previous analytical results pertaining to a graphene sheet with NSinterface and an applied perpendicular real magnetic field numerically. In the process, it is shownthat considering graphene sheets of perfect width is not necessary, as long as the width a fewmagnetic lengths away from the interface is well-defined. By then considering a finite graphenesheet, terminated by armchair edges, that is distorted and connected to a superconductor, wefind bound states near the NS interface that can be changed by distorting the graphene latticefurther.

[发布机构] Stellenbosch University