Bose-Einstein Condensation of Cooper-Pairs in the Conventional Superconductors

Abstract

Available data of the temperature dependence of the superconducting heat capacity and of the thermal conductivity of the conventional superconductors are analyzed in detail. It is shown that in contrast to the exponential function predicted by the BCS theory, the temperature dependence of the superconducting heat capacity consists of a sequence of a few analytically different universal power functions of absolute temperature. The changes from one to the next power function are typical examples of crossover events. The crossover occurring at the lowest temperature, commonly below about ~1 K, is identified as transition from Maxwell-Boltzmann to Bose-Einstein (BE) statistics of the Cooper-pairs. Because of the low mass of the Cooper pairs of 2m e (with m e as the mass of the electron) and their high density, the BE-condensation temperature, T BE , of the Cooper-pairs is about five orders of magnitude higher than for the dilute alkali atom condensates. The condensation temperature T BE turns out to be proportional to the superconducting transition temperature T SC . Since T BE is proportional to ~n 2/3 , with n as the density of the Cooper pairs at T BE , it is possible to obtain the density of the Cooper pairs at low temperatures. Assuming that for the type I superconductors the Cooper pairs form a dense gas of bosons with virtually no space between them, the diameter of the Cooper-pair orbital, calculated from n 2/3 , turns out to agree quantitatively with the experimental value of the London penetration depth. As a conclusion, due to the large orbital diamagnetism of the Cooper-pairs, only one layer of Cooper-pairs, next to the inner surface of the sample, is sufficient to shield an applied external magnetic field completely.