Gorter-Casimir two fluid model revisited and possible applications to superconductivity

Abstract

In this paper, Gorter-Casimir (GC) two fluid model for low temperature normal superconductors is modified introducing phononic term along with electronic term in the normal phase free energy. The exponent corresponding to the normal phase fraction is changed from 1/2 to a general value n which can be different for different materials. n is a parameter which tunes how much portion of normal phase free energy will be reduced to form superconducting phase by condensation of normal electrons into super-electrons at some finite temperatures below superconducting transition temperature (T C) and the electron-phonon interaction is the controlling factor which calibrate the values of n. This present model describes the idea of different jump ratios of specific heat of different materials at T = T C , which GC model cannot predict. We have adopted a new concept of "Phase diagram" from which an idea of a new temperature T * has been obtained. Modified GC model explains well the resistivity behavior near T C. Moreover, for some high temperature superconductors along with the electronic and phononic contribution, a low temperature Schottky contribution is added to the free energy density. However, the contribution is negligible near T C .