Supercurrent blockade in Josephson junctions with a Majorana wire

TL;DR

This paper investigates the Josephson effect in topologically nontrivial superconducting wires with Majorana states, revealing unique supercurrent behaviors and signatures that can identify Majorana modes.

Contribution

It provides an exact current-phase relation for Majorana-based Josephson junctions and highlights how charging effects reveal Majorana signatures.

Findings

No supercurrent in S-TS junction under general conditions

Exact CPR shows -periodic behavior with negative critical current

Charging effects induce an anomalous CPR sensitive to Majorana parity

Abstract

We study the Josephson effect for a topologically nontrivial superconducting (TS) wire with Majorana fermion end states and tunnel-coupled to s-wave BCS superconducting (S) electrodes. In an S-TS junction, no supercurrent flow is possible under fairly general conditions. For the S-TS-S junction, bulk TS quasiparticles must be accessible to have a Josephson effect. In the noninteracting case, we derive the exact current-phase relation (CPR) and find \pi-periodic behavior with negative critical current for weak tunnel couplings. Charging effects then cause the anomalous CPR $I(\varphi)=I_c \cos\varphi$, where the parity-sensitive critical current I_c provides a signature for Majorana states.