Flux Flow in Thin Type-I Superconducting Films

Abstract

Using dc and pulsed currents of 80-nsec duration, the flux-flow resistance has been observed at temperatures $T\ge 0.9T_c$ in flat films of tin of thickness 440 to 1580 Å in a perpendicular magnetic field $H_{\perp }$. At low values of $H_{\perp }$, the reduced flow resistivity $\frac{{\rho }_f}{{\rho }_n}$ is given by $\frac{{\rho }_f}{{\rho }_n}=0.76\mathrm{}{\left[\frac{H_{\perp }}{H_{c\perp }\mathrm{}\left(T\right)\mathrm{}}\right]}^{\frac{3}{2}}$, which is in agreement with published data on bulk type-II superconductors. Flux flow is absent at temperatures $T\le 0.9T_c$, and highly nonlinear for a film of 3420 Å thickness. The flux flow starts at a current density $J_p$ where the flux tubes break free from their pinning centers. The dependence of $J_p$ on magnetic field and temperature has been investigated both experimentally and theoretically. As the sample current is increased, an instability is observed at a current density $J_I$, at which the resistance increases sharply. The dependence of $J_I$ on magnetic field, temperature, and film thickness has been determined. Close to $T_c$, the instability current $J_I$ is almost independent of thickness and is given by $J_I=3.0\mathrm{}\times {10}^6[1-{\left(\frac{T}{T_c}\right)}^2][0.9-\frac{H_{\perp }}{H_{c\perp }\mathrm{}\left(T\right)\mathrm{}}]$ A/${\mathrm{cm}}^2$. An investigation of the time dependence of the sample voltage indicates the existence of a time constant $t^{\prime }$ which, near $T_c$, decreases exponentially with current density. $J_I$ is then defined as the current density at which $t^{\prime }$ becomes shorter than the time of observation.