Parity-controlled $2\pi$ Josephson effect mediated by Majorana Kramers pairs

TL;DR

This paper predicts a parity-controlled Josephson effect mediated by Majorana Kramers pairs in a topological superconductor island, offering a potential method for qubit read-out in quantum computing.

Contribution

It introduces a novel parity-controlled Josephson effect involving Majorana Kramers pairs in a Coulomb blockade regime, advancing topological quantum computation.

Findings

Josephson current is mediated by Majorana Kramers pairs.

The current's sign depends on the joint parity of Majorana states.

Potential application in qubit read-out for Majorana-based quantum computers.

Abstract

We study a time-reversal-invariant topological superconductor island hosting spatially separated Majorana Kramers pairs, with weak tunnel couplings to two s-wave superconducting leads. When the topological superconductor island is in the Coulomb blockade regime, we predict that a Josephson current flows between the two leads due to a non-local transfer of Cooper pairs mediated by the Majorana Kramers pairs. Interestingly, we find that the sign of the Josephson current is controlled by the joint parity of all four Majorana bound states on the island. Consequently, this parity-controlled Josephson effect can be used for qubit read-out in Majorana-based quantum computing.