Effects of finite superconducting coherence lengths and of phase gradients in topological SN and SNS junctions and rings

Abstract

We study the effect of a finite proximity superconducting (SC) coherence length in SN and SNS junctions consisting of a semiconducting topological insulating wire whose ends are connected to either one or two s-wave superconductors. We find that such systems behave exactly as SN and SNS junctions made from a single wire for which some regions are sitting on top of superconductors, the size of the topological SC region being determined by the SC coherence length. We also analyze the effect of a non-perfect transmission at the NS interface on the spatial extension of the Majorana fermions. Moreover, we study the effects of continuous phase gradients in both an open and closed (ring) SNS junction. We find that such phase gradients play an important role in the spatial localization of the Majorana fermions.

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• Visualising Majorana bound states in 1D and 2D using the generalized Majorana polarization
• Majorana Braiding Dynamics on Nanowires
• From Andreev bound states to Majorana fermions in topological wires on superconducting substrates : a story of mutation
• Quasiclassical Eilenberger theory of the topological proximity effect in a superconducting nanowire
• Renormalization of quantum dot $g$-factor in superconducting Rashba nanowires
• Edge states, Majorana fermions and topological order in superconducting wires with generalized boundary conditions
• Detecting a quantum critical point in topological SN junctions
• Transport across a system with three p-wave superconducting wires: effects of Majorana modes and interactions
• Unusual Superconducting Proximity Effect in Magnetically Doped Topological Josephson Junctions
• Effects of Peierls phases in open linear chains