Electron-hole imbalance in superconductor-normal metal mesoscopic structures

TL;DR

This paper investigates electron-hole imbalance and associated voltages in mesoscopic superconductor-normal metal structures under non-equilibrium conditions, revealing phase-dependent oscillations and effects on the transition to the π-state.

Contribution

It provides a detailed analysis of branch imbalance and voltage oscillations in S/N structures, highlighting their influence on the π-state transition under non-equilibrium conditions.

Findings

Voltage V_imb oscillates with phase difference φ.

Branch imbalance affects transition to π-state.

Non-equilibrium conditions induce measurable voltages.

Abstract

We analysed the electron-hole or, in another words, branch imbalance (BI) and the related electric potential $V_{imb}$ which may arise in a mesoscopic superconductor/normal metal (S/N) structure under non-equilibrium conditions in the presence of a supercurrent. Non-equilibrium conditions can be created in different ways: a) a quasiparticle current flowing between the N reservoirs; b) a temperature gradient between the N reservoirs and no quasiparticle current. It is shown that the voltage $V_{imb}$ oscillates with the phase difference $\phi$. In a cross-geometry structure the voltage $V_{imb}$ arises in the vertical branch and affects the conditions for a transition into the $\pi$-state.