Hot spots in superconducting tantalum

Abstract

We discuss experimental results on nonequilibrium superconductivity in Ag-Ta point contacts. From a hysteretic dc characteristics we conclude a normal bubble suddenly to form in the superconductor below the contact at a critical bias, its radius $R(U)$ monotonically increasing with bias voltage U. The observed radii are unexpectedly large compared with what is expected from existing models. The investigation is intended to describe this behavior in physical terms and theoretically to calculate the function $R(U)$ for varying values of contact resistance. We calculate mean values over the bubble volume of the electron and phonon distribution functions using simplified Boltzmann equations which describe the effects of electron injection into the bubble, electron-phonon scattering, and electron and phonon escape from the bubble to the surrounding superconductor. Downscattering of high-energy injected quasiparticles into subgap states $0lEl\ensuremath{\Delta}$ leads to strong occupation of subgap states because escape is prevented for these energies by Andreev reflection from the N-S interface. This explains the large bubble size. In contrast with this, occupation of states $Eg\ensuremath{\Delta}$ is typically two orders of magnitude smaller. The function $R(U)$ is determined by a self-consistency condition postulating that the calculated nonequilibrium distribution function $f(E)$ satisfies the BCS gap equation in the limit of vanishing gap parameter. Agreement of the calculated and the experimentally determined $R(U)$ functions is satisfactory.