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日本物理學會誌

Crossover Between Cooper-Pair Condensation and Bose Condensation

Kazumasa Miyake

Published Jun 5, 1992• 0 citations
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On Bose condensation

M. Fannes, Jv Pule, André F. Verbeure

Helvetica Physica Acta (Switzerland)•Mar 10, 1983•31 citations
We extend our previous investigations of fermionic condensation in broad Feshbach resonances by using the two-channel model developed for narrow Feshbach resonances. We investigate two crossovers: the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover by changing the sss-wave scattering length and the crossover from a narrow to a broad resonance by changing the atom-molecule coupling. At zero temperature we analyze, as a function of both atom-molecule coupling and sss-wave scattering length, the chemical potential, the energy gap, and the condensate fraction of atoms. In particular, we predict the contribution of Cooper pairs and preformed molecules to the total condensate density along the two crossovers.
Observed crossover events between different power functions of absolute temperature occurring below about ~1 K in the temperature dependence of the heat capacity or the thermal conductivity of the conventional superconductors are identified as transitions from Maxwell-Boltzmann to Bose-Einstein (BE) statistics of the Cooper-pairs. Because of the low mass of the Cooper pairs of 2me (with me as mass of the electron) and their high density, the BE-condensation temperature, TBE, of the Cooper-pairs is about five orders of magnitude higher than for the dilute alkali atom condensates. The condensation temperature TBE turns out to be proportional to the superconducting transition temperature TSC. From the observed TBE-values it is possible to calculate the density of the Cooper pairs. Assuming that the Cooper pairs form a dense gas of bosons, the diameter of the Cooper-pair orbitals turns out to be equal to the London penetration depth. As a conclusion, due to the large orbital diamagnetism of the Cooper-pairs 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.