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 Π²F=k²F, 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 Hc2 and Hc3 problems, to fluctuations of superconductivity at T>Tc(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 k² is to be determined self-consistently for each problem. The field and temperature dependence of k²(H,T) is obtained for a ``moderately dirty'' case. At a certain curve which starts at the zero-field Tc and is situated in the normal part of (H,T) phase diagram, k² is zero.