Enhancement of the upper critical field by nonmagnetic impurities in dirty two-gap superconductors

Quasiclassic Uzadel equations for two-band superconductors in the dirty limit with the account of both intraband and interband scattering by nonmagnetic impurities are derived for any anisotropic Fermi surface. From these equations the Ginzburg-Landau equations, and the critical temperature $T_c$ are obtained. An equation for the upper critical field, which determines both the temperature dependence of $H_{c2}(T)$ and the orientational dependence of $H_{c2}(\theta)$ as a function of the angle $\theta$ between ${\bf H}$ and the c-axis is obtained. It is shown that the shape of the $H_{c2}(T)$ curve essentially depends on the ratio of the intraband electron diffusivities $D_1$ and $D_1$, and can be very different from the standard one-gap dirty limit theory. In particular, the value $H_{c2}(0)$ can considerably exceed $0.7T_cdH_{c2}/dT_c$, which can have important consequences for applications of $MgB_2$. A scaling relation is proposed which enables one to obtain the angular dependence of $H_{c2}(\theta)$ from the equation for $H_{c2}$ at ${\bf H}\| c$. It is shown that, depending on the relation between $D_1$ and $D_2$, the ratio of the upper critical field $H_{c2}^\|/H_{c2}^\perp$ for ${\bf H}\| ab$ and ${\bf H}\perp ab$ can both increase and decrease as the temperature decreases. Implications of the obtained results for $MgB_2$ are discussed

Limits of the upper critical field in dirty two-gap superconductors

An overview of the theory of the upper critical field in dirty two-gap superconductors, with a particular emphasis on MgB$_2$ is given. We focus here on the maximum $H_{c2}$ which may be achieved by increasing intraband scattering, and on the limitations imposed by weak interband scattering and paramagnetic effects. In particular, we discuss recent experiments which have recently demonstrated ten-fold increase of $H_{c2}$ in dirty carbon-doped films as compared to single crystals, so that the $H_{c2}(0)$ parallel to the ab planes may approach the BCS paramagnetic limit, $H_p[T] = 1.84T_c[K] \simeq 60-70T$. New effects produced by weak interband scattering in the two-gap Ginzburg-Landau equations and $H_{c2}(T)$ in ultrathin MgB$_2$ films are addressed.Comment: Submitted to the special issue of Physica C on MgB$_2$ on Dec. 3, 200

Manganese nodule geochemistry from the Challenger Expedition

C. W. Gümbel received nodules from J. Murray which were collected at a depth of 2740 fathoms, between Japan and the Sandwich Islands, by the "Challenger" Expedition. They were either round or long in shape, with a dull, dirty-brown coloured surface, and enclosed fragments of pumice-stone, and more rarely teeth of sharks or fragments of mussels. They were analysed by A. Schwager