On the difference between type I and type II superconductors

Abstract

Abstract It is shown that for the metals that get superconducting, the heat capacity above the transition temperature, TSC, is given by a sequence of power function of absolute temperature and not, as for the metals that get not 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 single power functions of absolute temperature result. Since the interaction details and the proportion between the heat capacities of the two boson fields change with temperature, the temperature dependence of the observed heat capacity is given by a sequence of power functions with different rational exponents. 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, BC(T), exhibits critical behaviour at T = 0 only but not at the transition temperature, TSC. The superconducting transition, therefore, is not into a long-range ordered state. For all type I superconductors the critical exponent of BC(T) at T = 0 seems to be ε = 2. The lower and upper critical fields, BC1(T) and BC2(T), of the type II superconductors exhibit critical behaviour not only at T = 0 but additionally at TSC, as it is common for lang-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 = TSC, the identified critical exponents are β = 2/3, 3/4 and 1. The large BC1 and BC2 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 of TSC. The diameter of the Cooper-pairs of the type II superconductors and, therefore, their diamagnetic moments are correspondingly small. At the critical field BC1, the diamagnetic moment of the individual Cooper-pair is no longer large enough 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 behaviour of BC1 and BC2 at TSC suggest, the flux-line lattice has the character of a long-range ordered system.