Flux-Flow Resistance in Type-II Superconductors

Electrical resistance of type-II superconductors measured by a dc method is related to the motion of Abrikosov vortices. Flux lines in the mixed state are driven into a viscous-flow state by increasing the Lorentz force J×H beyond the depinning threshold; the voltage observed under this condition is linear in current and the slope $\frac{\Delta V}{\Delta I}$ is interpreted to represent the flow rate. At low temperatures, the flow resistivity ${\rho }_f$ so measured follows an empirical relation $\frac{{\rho }_f}{{\rho }_n}=\frac{H}{H_{c2\mathrm{}}}$, where ${\rho }_n$ is the normal-state resistivity and $H_{c2\mathrm{}}$ the upper critical field predicted by the Ginsburg-Landau-Abrikosov-Gor'kov (GLAG) theory. In high-field superconductors the GLAG upper critical fields are not accessible for conventional measurements since the paramagnetic spin alignment quenches superconductivity at much lower fields, but the above empirical rule still holds and makes it possible to determine the GLAG upper critical fields from the flow-resistivity measurements. The empirical relation also suggests that the frictional drag on a moving flux line arises from normal currents flowing in the core of the vortex line. The observed damping is, however, much larger than can be accounted for by eddy currents induced by the moving magnetic field of the vortex line. Two new mechanisms, one proposed by Tinkham and another by Stephen and Bardeen, appear to correct this difficulty and they are discussed in the text. Also reported is a new type of resistance-minimum phenomenon: if the temperature $T$ is increased from zero at a fixed field $H$, the resistance $R\left(T\right)\mathrm{}$ of a type-II specimen decreases initially and goes through a minimum before it reaches the normal resistance at $T_c\mathrm{}\left(H\right)\mathrm{}$. This behavior is qualitatively accounted for by including the dissipation outside of the vortex core.