Hotspot temperatures reached in current-driven superconducting Niobium filaments

In a superconducting microbridge too narrow to support vortex motion, the current-induced resistance occurs non-uniformly at definite spots designated as Phase- Slip-Centres (PSC). Further, if the core of a PSC happens to heat above the critical temperature T_c, a PSC may evolve into a normal propagating zone, or hotspot. The PSC’s time of nucleation and the HS minimum current I_h are determined, which allows deriving without ambiguity the rate of heat transfer to the substrate, the latter is compatible with a phonon blackbody radiation model at the Nb/R–sapphire interface. The computation of the HS temperature is then straightforward, while the PSC case is more involved. However, the PSC core temperature can be obtained through an independent determination of the inelastic quasi-particle diffusion length Λ_qp ~ 2.8 μm. The results of these computations are consistent with all the specific cases, PSCs and HSs, measured experimentally.