Fractional Josephson Effect in Number-Conserving Systems

TL;DR

This paper investigates the fractional Josephson effect in a number-conserving system with topological ground-state degeneracy, proposing a method to detect topological phases via supercurrent measurements in a flux loop.

Contribution

It introduces a microscopic model and effective low-energy theory for a topological superconductor-nanowire system, analyzing the effect of quantum phase fluctuations on the fractional Josephson effect.

Findings

Supercurrent periodicity reveals topological phases.

Quantum phase slips affect the stability of the fractional Josephson effect.

Effective low-energy theory accounts for quantum phase fluctuations.

Abstract

We study fractional Josephson effect in a particle-number conserving system consisting of a quasi-one-dimensional superconductor coupled to a nanowire or an edge carrying $e/m$ fractional charge excitations with $m$ being an odd integer. We show that, due to the topological ground-state degeneracy in the system, the periodicity of the supercurrent on magnetic flux through the superconducting loop is non-trivial which provides a possibility to detect topological phases of matter by the $dc$ supercurrent measurement. Using a microscopic model for the nanowire and quasi-one-dimensional superconductor, we derived an effective low-energy theory for the system which takes into account effects of quantum phase fluctuations. We discuss the stability of the fractional Josephson effect with respect to the quantum phase slips in a mesoscopic superconducting ring with a finite charging energy.