$8\pi$-periodic dissipationless ac Josephson effect on a quantum spin-Hall edge via a Quantum magnetic impurity

TL;DR

This paper demonstrates that interactions and spin-conservation breaking enable a dissipationless, fractional ac Josephson effect on quantum spin Hall edges, which is fundamentally $8 extpi$-periodic, contrasting with the typical dissipative behavior.

Contribution

The authors introduce a quantum impurity model that achieves a dissipationless fractional Josephson effect and prove its fundamental $8 extpi$-periodicity.

Findings

Dissipationless fractional Josephson effect is possible with interactions and spin-breaking.

The effect is inherently $8 extpi$-periodic, not reducible to lower periodicities.

A simple impurity model supports the theoretical argument.

Abstract

Time-reversal invariance places strong constraints on the properties of the quantum spin Hall edge. One such restriction is the inevitability of dissipation in a Josephson junction between two superconductors formed on such an edge without the presence of interaction. Interactions and spin-conservation breaking are key ingredients for the realization of dissipationless ac Josephson effect on such quantum spin Hall edges. We present a simple quantum impurity model that allows to create a dissipationless fractional Josephson effect on a quantum spin Hall edge. We then use this model to substantiate a general argument that shows that any such non-dissipative Josephson effect must necessarily by $8\pi$-periodic.