DC Josephson Effect in a Tomonaga-Luttinger Liquid

TL;DR

This paper investigates the dc Josephson effect in a one-dimensional Tomonaga-Luttinger liquid using two bosonized models, revealing that electron-electron interactions suppress the Josephson current based solely on charge correlations.

Contribution

It demonstrates that the Josephson current suppression depends only on charge correlations, contrasting previous findings involving spin degrees of freedom.

Findings

Josephson current is suppressed by repulsive interactions.

Suppression depends only on charge correlation exponent.

Results are consistent across two different models.

Abstract

The dc Josephson effect in a one-dimensional Tomonaga-Luttinger (TL) liquid is studied on the basis of two bosonized models. We first consider a TL liquid sandwiched between two superconductors with a strong barrier at each interface. Both the interfaces are assumed to be perfect if the barrier potential is absent. We next consider a TL liquid with open boundaries, weakly coupled with two superconductors. Without putting strong barriers, we instead assume that the coupling at each interface is described by a tunnel junction. We calculate the Josephson current in each model, and find that the two models yield same results. The Josephson current is suppressed by repulsive electron-electron interactions. It is shown that the suppression is characterized by only the correlation exponent for the charge degrees of freedom. This result is inconsistent with a previously reported result, where the spin degrees of freedom also affects the suppression. The reason of this inconsistency is discussed.