Thermoelectric response of Josephson junction: from ballistic to disordered

Abstract

It is known that Josephson junction (JJ) hosting scattering centers with energy-dependent scattering amplitudes which breaks the $\omega \to -\omega$ 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 ${\varphi }_{12}$, where ${\varphi }_{12}$ 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-${\varphi }_{12}$ 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 ${\varphi }_{12}$ as we approach the large disorder limit under disorder averaging.

11 pages, 6 figures

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