Non-relativistic Josephson Junction from Holography

TL;DR

This paper constructs a non-relativistic Josephson junction using holography with Lifshitz geometry, analyzing how Lifshitz scaling influences the junction's properties compared to relativistic cases.

Contribution

It introduces a holographic model of a non-relativistic Josephson junction with Lifshitz scaling and studies its current-phase relation and coherence lengths.

Findings

Sinusoidal current-phase relation persists for various Lifshitz scalings.

Exponential decay of condensate and critical current with barrier width observed.

Discrepancies in coherence lengths derived from different exponential relations for non-relativistic case.

Abstract

We construct a Josephson junction in non-relativistic case with a Lifshitz geometry as the dual gravity. We investigate the effect of the Lifshitz scaling in comparison with its relativistic counterpart. The standard sinusoidal relation between the current and the phase difference is found for various Lifshitz scalings characterised by the dynamical critical exponent. We also find the exponential decreasing relation between the condensate of the scalar operator within the barrier at zero current and the width of the weak link, as well as the relation between the critical current and the width. Nevertheless, the coherence lengths obtained from two exponential decreasing relations generically have discrepancies for non-relativistic dual.