Emergence of Charge-Imbalanced BCS State and Suppression of Nonequilibrium FFLO State in Asymmetric NSN Junctions

TL;DR

This paper develops a theoretical framework to understand how asymmetry and impurities affect nonequilibrium superconducting states in NSN junctions, revealing the suppression of the FFLO state and the emergence of distinct BCS regimes.

Contribution

It extends equilibrium BCS theory to nonequilibrium conditions in NSN junctions, analyzing the effects of lead asymmetry and impurities on superconducting phases.

Findings

Impurity scattering suppresses the nonequilibrium FFLO state.

Lead asymmetry splits the BCS phase into two regimes.

Identifies phase transitions and bistability in nonequilibrium states.

Abstract

We theoretically study nonequilibrium superconductivity in voltage-biased normal metal-superconductor-normal metal (NSN) junctions, focusing on effects of lead-coupling asymmetry and impurity scattering. Using the Keldysh Green's function technique, we extend the thermal-equilibrium mean-field BCS theory to the case where the system is out of equilibrium, to analyze superconducting properties in the nonequilibrium steady state. We find that, in close analogy with the thermal-equilibrium case, the inhomogeneous nonequilibrium Fulde-Ferrell-Larkin-Ovchinnikov (NFFLO) state induced by nonequilibrium electron distributions is highly sensitive to impurity scattering, whereas the uniform nonequilibrium BCS (NBCS) state remains robust against nonmagnetic impurities. Moreover, lead-coupling asymmetry is also found to suppress the NFFLO phase and to split the NBCS phase into two distinct regimes, characterized by the presence or absence of a chemical-potential imbalance between quasiparticles and the condensate. We identify a phase transition or a crossover between these two NBCS states, as well as parameter regimes exhibiting bistability. Our results provide a unified microscopic understanding of nonequilibrium superconductivity in NSN junctions under experimentally relevant conditions and are expected to provide a theoretical framework applicable to a broad class of nonequilibrium superconducting hybrid structures.