Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions

TL;DR

This paper demonstrates how multi-terminal Josephson junctions with phase differences can manipulate fermion parity and break time-reversal symmetry, enabling new quantum states and potential applications in Majorana states and spin control.

Contribution

It introduces a method to use phase differences in multi-terminal junctions to control fermion parity and break Kramers degeneracy, overcoming limitations of two-terminal junctions.

Findings

Phase differences can split Kramers degeneracy in multi-terminal junctions.

Fermion parity can switch from even to odd with phase winding.

Presence of a 'discrete vortex' enables fermion parity change.

Abstract

We show how the superconducting phase difference in a Josephson junction may be used to split the Kramers degeneracy of its energy levels and to remove all the properties associated with time reversal symmetry. The superconducting phase difference is known to be ineffective in two-terminal short Josephson junctions, where irrespective of the junction structure the induced Kramers degeneracy splitting is suppressed and the ground state fermion parity must stay even, so that a protected zero-energy Andreev level crossing may never appear. Our main result is that these limitations can be completely avoided by using multi-terminal Josephson junctions. There the Kramers degeneracy breaking becomes comparable to the superconducting gap, and applying phase differences may cause the change of the ground state fermion parity from even to odd. We prove that the necessary condition for the appearance of a fermion parity switch is the presence of a "discrete vortex" in the junction: the situation when the phases of the superconducting leads wind by $2\pi$. Our approach offers new strategies for creation of Majorana bound states as well as spin manipulation. Our proposal can be implemented using any low density, high spin-orbit material such as InAs quantum wells, and can be detected using standard tools.