Normal part of (H,T) phase diagram of a superconductor: Possible applications to proximity systems

It is shown that for weak superconductivity in a uniform field (the Eilenberger Green’s function ‖f‖≪1) microscopic Eilenberger equations reduce to the linear equation ${\Pi }^2$F=$k^2$F, where Π→ is the gauge-invariant gradient and F is the average of the function f over the Fermi surface. This equation holds in uniform fields for any impurity concentration and applies to $H_{c2}$ and $H_{c3}$ problems, to fluctuations of superconductivity at T>$T_c$(H), as well as to various situations in proximity systems such as the superconductivity induced deep in the normal metal, the critical temperature, and the upper critical field of these systems. The parameter $k^2$ is to be determined self-consistently for each problem. The field and temperature dependence of $k^2$(H,T) is obtained for a ‘‘moderately dirty’’ case. At a certain curve which starts at the zero-field $T_c$ and is situated in the normal part of (H,T) phase diagram, $k^2$ is zero.