Paraconductivity and upper critical field in inhomogeneous amorphous superconductors

Correlation between enhanced paraconductivity ${\sigma }^{\prime }$ near the superconducting transition temperature $T_{c0\mathrm{}}$ and enhanced upper critical field $H_{c2\mathrm{}}$ at low temperature is observed in bulk amorphous superconductors. It is pointed out that the presence of inhomogeneities is responsible for this observation. Phase inhomogeneity causes ${\sigma }^{\prime }$ to diverge as ${\epsilon }^{-\frac{5}{2}}$ near $T_{c0\mathrm{}}$ where $\epsilon =\frac{(T-T_{c0\mathrm{}})}{T_{c0\mathrm{}}}$; while statistical fluctuation in alloy composition yields the usual result ${\sigma }^{\prime }\propto {\epsilon }^{-\frac{1}{2}}$. Various models of enhanced $H_{c2\mathrm{}}$ are discussed. Comparison with new data on both homogeneous and inhomogeneous amorphous ${\mathrm{Zr}}_3$Pd samples is made.