Charge imbalance in superconductors in the low-temperature limit

Abstract

We explore charge imbalance in mesoscopic normal-metal/superconductor multiterminal structures at very low temperatures. The investigated samples, fabricated by e-beam lithography and shadow evaporation, consist of a superconducting aluminum bar with several copper wires forming tunnel contacts at different distances from each other. We have measured in detail the local and nonlocal conductance of these structures as a function of the applied bias voltage $V$, the applied magnetic field $B$, the temperature $T$, and the contact distance $d$. From these data the charge-imbalance relaxation length ${\ensuremath{\lambda}}_{{Q}^{\ensuremath{\ast}}}$ is derived. The bias-resolved measurements show a transition from dominant elastic scattering close to the energy gap to an inelastic two-stage relaxation at higher bias. We observe a strong suppression of charge imbalance with magnetic field, which can be directly linked to the pair-breaking parameter. In contrast, practically no temperature dependence of the charge-imbalance signal was observed below 0.5 K. These results are relevant for the investigation of other nonlocal effects such as crossed Andreev reflection and spin diffusion.