Pinning effects on hot-electron vortex flow instability in superconducting films

The hot-electron vortex flow instability in superconducting films in magnetic field B at substrate temperature T0 ≪ Tc is theoretically considered in the presence of pinning. The magnetic field dependences of the instability critical parameters (electric field E*, current density j*, resistivity ρ*, power density P* and vortex velocity v*) are derived for a cosine and a saw-tooth washboard pinning potential and compared with the results obtained earlier by M. Kunchur [Phys. Rev. Lett. 89 (2002) 137005] in absence of pinning. It is shown that the B-behavior of E*, j* and ρ* is monotonic, whereas the B-dependence of v* is quite different, namely dv*/dB may change its sign twice, as sometimes observed in experiments. The simplest heat balance equation for electrons in low-Tc superconducting films is considered within the framework of the two-fluid model. A theoretical analysis reveals that the instability critical temperature T* ≈ 5Tc/6 at T0 < T*/2 with T* being independent of B.