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

Van Zyl, Hendrik Jacobus Rust (2011-12)

Thesis (MSc)--Stellenbosch University, 2011.

Thesis

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 excitation states in graphene are restricted to two distinct regions in momentum space called valleys. Many electronic applications are possible if one can design a graphene system where excitations can be forced to occupy a single valley in a controllable way. Investigating the spectrum of the distorted graphene sheet reveals that, if the chemical potential is chosen to coincide with a bulk Landau level, the normal-superconductor interface always supports propagating modes in both directions. 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 numerical means. Furthermore, we verify previous analytical results pertaining to a graphene sheet with NS interface and an applied perpendicular real magnetic field numerically. In the process, it is shown that considering graphene sheets of perfect width is not necessary, as long as the width a few magnetic lengths away from the interface is well-defined. By then considering a finite graphene sheet, terminated by armchair edges, that is distorted and connected to a superconductor, we find bound states near the NS interface that can be changed by distorting the graphene lattice further.

AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om die uitwerking van die vervorming van ’n grafeenrooster te ondersoek wanneer die met ’n supergeleier verbind word. By lae energieë word die moontlike opwekkings in grafeen beperk tot twee aparte gebiede van momentumruimte — die sogenaamde valleie. Verskeie elektroniese toepassings is moontlik indien ’n grafeenstelsel ontwerp kan word waar opwekkings slegs ’n enkele vallei beset en die besetting beheer kan word. Deur die spektrum van die vervormde grafeenrooster te ondersoek word daar gevind dat, indien die chemiese potensiaal gekies word om saam te val met ’n Landauvlak, die NS-tussenvlak geleiding in beide rigtings ondersteun. Opwekkings van verskillende valleie beweeg in teenoorgestelde rigtings langs die tussenvlak. Daarteenoor is die spektrum van ’n vervormde grafeenroster met ’n leunstoelrand dispersieloos. Ons bevestig hierdie insulerende gedrag van ’n leunstoelrand vir eindige grafeen- roosters deur middel van ’n numeriese berekening. Verder word vorige analitiese resultate wat verband hou met ’n grafeenrooster met normaal-supergeleiertussenvlakstelsel en loodregte mag- neetveld op die vlak bevestig deur middel van numeriese berekeninge. In die proses word dit ook aangedui dat die grafeenrooster nie ’n perfekte wydte hoef te hˆe nie, solank die wydte goed gedefinieer is vir ’n paar magnetiese lengtes in die omgewing van die tussenvlak. Deur dan die eindige grafeenrooster met leunstoelrande te koppel aan ’n supergeleier word gebonde toe- stande naby aan die NS tussenvalk gevind. Hierdie toestande kan gemanipuleer word deur die grafeenrooster verder te vervorm.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/18039
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