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

Understand

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.