ISSN:
1572-9605
Keywords:
Theory of superconductivity
;
new formula forT c
;
high-T c superconductor
;
Bose-Einstein condensation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
,
Physics
Notes:
Abstract A general theory of superconductivity is developed, starting with a BCS Hamiltonian in which the interaction strengths (V 11,V 22,V 12) 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 lengthsξ 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) aboveT c are shown to move like free bosons with the energy-momentum relationɛ=1/2vFq. They undergo a Bose-Einstein condensation atT c = 0.977ħv F k b −1 n 1/2, wheren is the number density of the Cooper pairs. The relatively high value ofT c (∼100 K) arises from the fact that the densityn is high:n 1/2∼ξ−1 ∼107 cm−1. The phase transition is of the third order, and the heat capacity has a reversed lambda (λ)-like peak atT c .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00617622
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