Dependence of the NS conductance on the valley polarization of edge states in graphene

Abstract

The edge states in finite quantum Hall graphene have previously been shown to be valley polarised for zigzag and armchair edges. Assuming that the valley isospin is also conserved at a smooth normal-superconducting (NS) interface, theoretical research has previously predicted that plateaus in the longitudinal conductance are expected to occur in the lowest Landau level of the incoming edge modes, which depends on the angle difference between the isospins entering and leaving the superconductor. In this thesis, this prediction is verified with a tight-binding simulation of six different NS junctions: for both zigzag and armchair edge nanoribbons, the superconductor can cover a single edge, two adjacent edges or two opposite edges. The theoretical prediction could be confirmed successfully, suggesting that the edge states are valley polarised along a smooth NS interface. Some deviations from the theory could be observed for the armchair edge ribbon with opposite edges when the width of the ribbon is not a multiple of three hexagons. Two consecutive widths show a complementary behaviour in the conductance such that their average corresponds to the predicted value with a remarkable robustness. The reason for this complementarity was briefly conjectured by using the special Andreev reflection in graphene and the coupling between sublattice and valley degree of freedom for zigzag edges. The parameter regimes allowing for the existence of conductance plateaus were established, confirming that the plateaus emerge for a system size much larger than the magnetic length and the superconducting coherence length, and that a smooth chemical potential, magnetic field strength and superconducting order parameter are necessary at the NS interface. The robustness of the NS edge states was furthermore investigated with three methods: a Fermi energy mismatch between the bulk and the superconductor, and random normally distributed variation in the onsite electrostatic potential and a random potential landscape. All results could confirm that intervalley scattering is the reason for deviations from the plateaus predicted by the theory.