Modification of the Upper Critical Field in a Two-Band Superconductor

Abstract

The upper critical field $H_{c2\mathrm{}}$ for a Type-II two-band superconductor is investigated in the pure limit. Near $T_c$, $H_{c2\mathrm{}}$ is dominated by the $s$ band, whereas the thermodynamic properties are determined by the $d$ band. A modification to the Gor'kov theory is found for the ratio of $K_1\mathrm{}\left(T\right)\mathrm{}$ at $T=0\mathrm{}$ and $T=T_c$. This result may explain the discrepancy between the one-band theory and experimental data.