Temperature dependence of the superconductor energy gap

Abstract

For a superconductor to be able to receive an external magnetic field, there must be a vacant energy state in the superconductor to receive the energy associated with the field. For a small range of energies near that of the critical magnetic field, Hc, these energy states lie within the superconductor temperature dependent energy gap. This paper uses thermodynamic analysis of the energy balance in the loss of dissipative electron scattering and the change in entropy of the conducting phase that occur in the phase transition between the normal metal and the superconducting state to suggest that changes in electron Gibbs free energy at T, from these sources are the basis for the temperature dependent energy gap. The critical magnetic field for a superconductor at temperature, T, Hc(T) occurs when the energy of the magnetic field is equal to the magnitude of the superconductor energy gap at T. When the superconductor energy gap is occupied with the energy of the external magnetic field, the normal metal conducting bands that became inaccessible at the superconductor - normal conductor phase transition are once again available for conduction, and the superconductor quenches. Experimental data from the literature suggests that the ratio of the superconductor energy gap to the superconductor critical temperature depends upon the chemical structure of superconductor. We anticipate that the superconducting energy gaps for mercury, and lead will show small maxima near 0.21, and 0.11 K, respectively.