Thermoelectric response of Josephson junction: from ballistic to disordered

TL;DR

This paper demonstrates that ballistic Josephson junctions can exhibit finite thermoelectric response due to broken symmetry, with disorder affecting the phase dependence and sign fluctuations of the thermoelectric coefficient.

Contribution

It reveals that even in ballistic JJs, symmetry breaking leads to thermoelectric effects and analyzes how disorder influences phase dependence and sign fluctuations of the thermoelectric response.

Findings

Ballistic JJs show non-zero thermoelectric response due to symmetry breaking.

Disorder causes the even-in-phase thermoelectric component to fluctuate and average out.

The odd-in-phase component approaches a universal sinusoidal dependence with increasing disorder.

Abstract

It is known that Josephson junction (JJ) hosting scattering centers with energy-dependent scattering amplitudes which breaks the $\omega\rightarrow-\omega$ symmetry (where $\omega$ is the excitation energy of electron about the Fermi level) exhibits finite thermoelectric response. In contrast, here we show that even in a ballistic JJ this symmetry is broken and it leads to a non-zero thermoelectric response when the junction length is of the order of coherence length of the superconductor and the corresponding thermoelectric coefficient confirms to the universal sinusoidal dependence on $\phi_{12}$, where $\phi_{12}$ is the superconducting phase bias. In presence of multiple scatterers in the junction region, we have numerically shown that the sign of the even-in-$\phi_{12}$ part of the thermoelectric coefficient fluctuates violently from one disorder configuration to another hence averaging to vanishingly small values while the odd part tends towards the universal sinusoidal dependence on $\phi_{12}$ as we approach the large disorder limit under disorder averaging.