On the Difference Between Type I and Type II Superconductors

Abstract

It is shown that for the metals that get superconducting, the heat capacity above the transition temperature, T_SC, is given by a sequence of power function of absolute temperature and not, as for the metals that do not get superconducting (Au, Ag, Cu…), by a superposition of a linear and a cubic term of absolute temperature. The two heat capacities have to be attributed to the relevant bosons in the critical range at T = 0. For the metals that get superconducting, the two boson fields interact and their heat capacities do no longer superimpose. Since the interaction details change with temperature, a sequence of power functions with rational exponents, different from the parent exponents of α = 3 and α = 1 occur. Each power function holds over a finite temperature range. A change of the exponent is a typical crossover event. From analyses of available experimental heat capacity data, the exponents of α = 1/2, 1, 3/2, 2, 3 and 4 could firmly be established. As the zero-field heat capacity of all superconductors, the critical field of the type I superconductors, B_C(T), exhibits critical behavior at T = 0 only but not at the transition temperature, T_SC. The superconducting transition, therefore, is not into a long-range ordered state. For all type I superconductors the critical exponent of B_C(T) at T = 0 seems to be ε = 2. The lower and upper critical fields, B_C1(T) and B_C2(T), of the type II superconductors exhibit critical behavior not only at T = 0 but additionally at T_SC, as it is common for long-range ordered systems. The experimentally identified critical exponents at T = 0 are ε = 3/2, 4/2, 5/2, 6/2 and 8/2. At T = T_SC, the identified critical exponents are β = 2/3, 3/4 and 1. The large B_C1 and B_C2 values indicate that the two Cooper-pair electrons of the type II superconductors are much stronger coupled compared to the type I superconductors, remarkably, without a corresponding increase in T_SC. The diameter of the Cooper pairs of the type II superconductors and, therefore, their diamagnetic moments are correspondingly low. At the critical field B_C1, the diamagnetic moment of the individual Cooper-pair is no longer large enough such that only one layer of Cooper pairs next to the inner surface of the sample is sufficient to shield an applied magnetic field completely. The external field then penetrates the superconductor as an ordered flux-line lattice. As the critical behavior of B_C1 and B_C2 at T_SC suggest, the flux-line lattice has the character of a long-range ordered system.