Pinning effects on self-heating and flux-flow instability in superconducting films near $T_{c}$

Abstract: The effect of pinning on self-heating triggering the Larkin-Ovchinnikov (LO) flux-flow instability (FFI) in superconducting thin films is theoretically investigated. The problem is considered relying upon the Bezuglyj-Shklovskij (BS) generalization of the LO theory, accounting for a finite heat removal from the quasiparticles at temperature $T^\ast$ to the bath at temperature $T_0$. The FFI critical parameters, namely the current density $j^{\ast}$, the electric field $E^{\ast}$, the power density $P^{\ast}$, and the vortex velocity $v^{\ast}$ are calculated and graphically analyzed as functions of the magnetic field and the pinning strength. With increasing pinning strength at a fixed magnetic field value $E^{\ast}$ \emph{decreases}, $j^{\ast}$ \emph{increases}, while $P^{\ast}$ and $T^{\ast}$ \emph{remain practically constant}. Vortex pinning may hence be the cause for eventual discrepancies between experiments on superconductors with \emph{strong pinning} and the generalized LO and BS results.