Parity measurement in topological Josephson junctions

TL;DR

This paper investigates how fermion parity influences the Josephson effect in topological insulator-based junctions, revealing parity-dependent periodicity changes and the impact of Coulomb interactions on supercurrent behavior.

Contribution

It demonstrates the parity-dependent Josephson current periodicity and establishes a mathematical link between Andreev bound states and fermion parity anomaly in topological junctions.

Findings

Periodic Josephson current changes from 4π to 2π depending on fermion parity.

A rigorous connection between Andreev bound states and fermion parity anomaly is established.

Coulomb interactions quantitatively affect the Josephson current.

Abstract

We study the properties of a topological Josephson junction made of both edges of a 2D topological insulator. We show that, due to fermion parity pumping across the bulk, the global parity of the junction has a clear signature in the periodicity and critical value of the Josephson current. In particular, we find that the periodicity with the flux changes from $4\pi$ in a junction with an even number of quasi-particles to $2\pi$ in the odd sector. In the case of long junctions, we exhibit a rigorous mathematical connection between the spectrum of Andreev bound-states and the fermion parity anomaly, through bosonization. Additionally, we discuss the rather quantitative effects of Coulomb interactions on the Josephson current.