Bardeen-Stephen flux flow law disobeyed in the high-$T_c$ superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$

TL;DR

This study shows that the flux flow resistance in a high-$T_c$ superconductor does not follow the classical Bardeen-Stephen law, revealing a different magnetic field dependence in the flux flow regime.

Contribution

The paper provides experimental evidence and empirical formulas demonstrating deviation from the Bardeen-Stephen flux flow law in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+ extdelta}$.

Findings

Flux flow resistance is a logarithmic function of magnetic field.

Resistivity follows $ ho_{ab} \\propto H^{3/4}$, deviating from classical law.

Resistivity along c-axis follows $ ho_{c} \\propto H^{-3/4} \\log^{2}H$.

Abstract

Pulsed high current experiments in single crystals of the high-$T_{c}$ superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ in c-axis directed magnetic field $H$ reveal that the $ab$-face resistance in the free flux flow regime is a solely logarithmic function of H, devoid of any power law component. Re-analysis of published data confirms this result and leads to empirical analytic forms for the $ab$-plane and c-axis resistivities: $\rho_{ab}\propto$ $H^{3/4}$, which does not obey the expected Bardeen-Stephen result for free flux flow, and $\rho_{c} \propto H^{-3/4} \log^{2}H$.