Functional derivatives ofHc2including Pauli paramagnetism

Abstract

We have extended some recent work on the functional derivative of the upper critical magnetic field ($H_{c2}$) to include Pauli paramagnetism. Our results are valid for any impurity concentration and any temperature. We explicitly discuss the effect on $H_{c2}$ of the imaginary part of the Matsubara gaps which is found to be very important. The functional derivatives display important changes in shape and size with temperature as well as impurity content. No general rule can be developed for the effect of different phonon energies on the critical field.