Theory of superconductivity. 3. 2D conduction bands for high Tc. Bose-Einstein condensation transition of the third order |
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Authors: | S. Fujita and S. Watanabe |
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Affiliation: | (1) Department of Physics and Astronomy, State University of New York at Buffalo, 14260 Buffalo, New York;(2) Metals Research Institute, Hokkaido University, 060 Sapporo, Japan |
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Abstract: | A general theory of superconductivity is developed, starting with a BCS Hamiltonian in which the interaction strengths (V11,V22,V12) among and between electron (1) and hole (2) Cooper pairs are differentiated, and identifying electrons (holes) with positive (negative) masses as those Bloch electrons moving on the empty (filled) side of the Fermi surface. The supercondensate is shown to be composed of equal numbers of electron and hole ground (zero-momentum) Cooper pairs with charges ±2e and different masses. This picture of a neutral supercondensate naturally explains the London rigidity and the meta-stability of the supercurrent ring. It is proposed that for a compound conductor the supercondensate is formed between electron and hole Fermi energy sheets with the aid of optical phonons having momenta greater than the minimum distance (momentum) between the two sheets. The proposed model can account for the relatively short coherence lengths observed for the compound superconductors including intermetallic compound, organic, and cuprous superconductors. In particular, the model can explain why these compounds are type II superconductors in contrast with type I elemental superconductors whose condensate is mediated by acoustic phonons. A cuprous superconductor has 2D conduction bands due to its layered perovskite lattice structure. Excited (nonzero momentum) Cooper pairs (bound by the exchange of optical phonons) aboveTc are shown to move like free bosons with the energy-momentum relation=1/2vFq. They undergo a Bose-Einstein condensation atTc = 0.977vFkb–1n1/2, wheren is the number density of the Cooper pairs. The relatively high value ofTc (100 K) arises from the fact that the densityn is high:n1/2–1 107 cm–1. The phase transition is of the third order, and the heat capacity has a reversed lambda ()-like peak atTc. |
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Keywords: | Theory of superconductivity new formula forTc high-Tc superconductor Bose-Einstein condensation |
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