Josephson effect in superconducting wires supporting multiple Majorana edge states

TL;DR

This paper investigates the Josephson effect in one-dimensional topological superconductors with multiple Majorana edge states, revealing preserved fractional periodicity, doubled conductance, and phase gradient effects.

Contribution

It provides a detailed analysis of the Josephson effect in systems supporting multiple Majorana modes, highlighting new conductance properties and phase stability considerations.

Findings

Four pi-periodicity of the fractional Josephson effect is preserved.

Conductance doubles in topological superconductors with two Majorana modes.

Superconducting phase gradients can destabilize Majorana-supporting phases.

Abstract

We study superconducting-normal-superconducting (SNS) Josephson junctions in one-dimensional topological superconductors which support more than one Majorana end mode. The variation of the energy spectrum with the superconducting phase is investigated by combining numerical diagonalizations of tight-binding models describing the SNS junction together with an analysis of appropriate low-energy effective Hamiltonians. We show that the four pi-periodicity characteristic of the fractional dc Josephson effect is preserved. Additionally, the ideal conductance of a NS junction with a topological supraconductor, hosting two Majorana modes at its ends, is doubled compared to the single Majorana case. Last, we illustrate how a nonzero superconducting phase gradient can potentially destroy the phases supporting multiple Majorana end states.