Current-phase relation and flux-dependent thermoelectricity in Andreev interferometers

TL;DR

This paper predicts a new type of Josephson junction state in multi-terminal Andreev interferometers, where quantum coherence and non-equilibrium effects lead to unique current-phase relations and flux-dependent thermoelectric properties.

Contribution

It introduces the concept of a $(I_0,\,\phi_0)$-junction state arising from quantum coherence and non-equilibrium effects in Andreev interferometers, expanding understanding of their phase relations.

Findings

The system exhibits a flux-dependent thermopower with features similar to a $(I_0,\phi_0)$-junction.

The current-phase relation can resemble a $\,\phi_0$-junction with a non-zero average current.

In certain limits, the thermopower becomes an odd or even function of flux, matching experimental observations.

Abstract

We predict a novel $(I_0,\phi_0)$-junction state of multi-terminal Andreev interferometers that emerges from an interplay between long-range quantum coherence and non-equilibrium effects. Under non-zero bias $V$ the current-phase relation $I_S(\phi)$ resembles that of a $\phi_0$-junction differing from the latter due to a non-zero average $I_0(V) = \left< I_S(\phi)\right>_{\phi}$. The flux-dependent thermopower ${\mathcal S}(\Phi)$ of the system exhibits features similar to those of a $(I_0,\phi_0)$-junction and in certain limits it can reduce to either odd or even function of $\Phi$ in the agreement with a number of experimental observations.