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

## TL;DR

This paper theoretically investigates how vortex pinning influences the self-heating and flux-flow instability in superconducting films near their critical temperature, using a generalized LO theory that includes heat removal effects.

## Contribution

It introduces a theoretical analysis of pinning effects on flux-flow instability parameters in superconductors near Tc, extending the LO theory with heat removal considerations.

## Key findings

- Increasing pinning strength decreases the critical electric field E*
- Increasing pinning strength increases the critical current density j*
- The critical power density P* and temperature T* remain nearly constant with pinning

## 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.