Upper Critical Field and the Density of States in Amorphous Strong-Coupling Superconductors

The upper critical field of the amorphous superconductors ${\mathrm{Bi}}_{0.85}$ ${\mathrm{Tl}}_{0.15}$, Ga, ${\mathrm{Sn}}_{0.86}$ ${\mathrm{Cu}}_{0.14}$, and ${\mathrm{Pb}}_{0.75}$ ${\mathrm{Bi}}_{0.25}$ is measured in the temperature range from 1.5 °K to the zero-field transition temperature. Films of the amorphous metals about 1500 Å thick are obtained by quenched condensation onto a substrate at He temperature. The initial slopes of the $B_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ curves are used to determine the electronic density of states at the Fermi surface. For all the investigated materials these values were enhanced compared with the density of states which one obtains from the free electron model. For Ga, ${\mathrm{Sn}}_{0.86}$ ${\mathrm{Cu}}_{0.14}$, and ${\mathrm{Pb}}_{0.75}$ ${\mathrm{Bi}}_{0.25}$ the experimental enhancement factor agrees well with the electron-phonon enhancement factor $1+\lambda$, where $\lambda$ is taken from superconducting-tunneling experiments. The temperature dependence of $B_{c2\mathrm{}}$ deviates from that predicted by Werthamer, Helfand, and Hohenberg, showing $B_{c2\mathrm{}}$ values too large in the low-temperature region. It is suggested that the strong-coupling behavior of the amorphous superconductors is responsible for the deviation at low temperature.