Investigation of Nonequilibrium Phenomena in Superconducting Hybrid Structures

Superconducting hybrid structures have found ubiquitous application in the different spheres of modern technology and science: from simple on-chip coolers to peculiar quantum logic devices, just to name a few. An academic interest primarily revolves around quasiparticle current from normal metal to superconductor because almost all interesting phenomena in these structures are usually triggered by it. In this paper, we investigate the influence of nonequilibrium processes on a quasiparticle electric current and on distribution functions in tunnel junctions normal metal (Al) - insulator ($\text{Al}_2 \text{O}_3$) - nonequilibrium superconductor (Al) - superconductor (Al) (NI$\text{S}^\prime$S). For the temperatures in this paper $0.2 T_C \le T \le 0.7 T_C$, Andreev current is negligible. Our approach relies on the one-dimensional Keldysh-Usadel equations for the nonequilibrium superconductor, from which we yield expressions for electric, heat currents and distribution functions. For numerical calculations, the Python program is developed. The results show that in absence of strong relaxation electric and heat current are suppressed for voltage biases $e V < \Delta$. To that end, plots of quasiparticle current and distribution functions for different temperatures are plotted. From our perspective, the backtunneling of quasiparticles is account for the suppression.