Theory of Flux-Flow Resistivity near $H_{c2}$ for s-wave Type-II Superconductors

TL;DR

This paper provides a microscopic theory for flux-flow resistivity in s-wave type-II superconductors near the upper critical field, showing how impurity levels influence resistivity behavior and deviation from classical models.

Contribution

It introduces a detailed microscopic calculation of flux-flow resistivity near $H_{c2}$ for various impurity concentrations, extending previous models.

Findings

Resistivity $ ho_f$ increases with mean free path $l$.

Behavior of $ ho_f(H)$ can change from convex to concave as $l$ increases.

Deviates from the linear Bardeen-Stephen prediction at low temperatures.

Abstract

This paper presents a microscopic calculation of the flux-flow resistivity $\rho_{f}$ for s-wave type-II superconductors with arbitrary impurity concentrations near the upper critical field $H_{c2}$. It is found that, as the mean free path $l$ becomes longer, $\rho_{f}$ increases gradually from the dirty-limit result of Thompson [Phys. Rev. B{\bf 1}, 327 (1970)] and Takayama and Ebisawa [Prog. Theor. Phys. {\bf 44}, 1450 (1970)]. The limiting behaviors suggest that $\rho_{f}(H)$ at low temperatures may change from convex downward to upward as $l$ increases, thus deviating substantially from the linear dependence $\rho_{f}\propto H/H_{c2}$ predicted by the Bardeen-Stephen theory [Phys. Rev. {\bf 140}, A1197 (1965)].