Pairing theory of high Tc and low Tc superconductors
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The recent discoveries of the various high-temperature oxide superconductors have given rise to many questions regarding the actual mechanism for the BCS pairing in these materials, beyond the usual phonon-exchange mechanism. In the presence of strong Coulomb correlations and spin fluctuations, there are new theoretical attempts to abandon even the concept of the BCS pairing in these materials. A recent formulation of the BCS pairing approach, suitable for the new materials with layered structures, will be used to discuss various possible phonon and electronic exchange mechanisms. It will be argued that for a quantitative comparison of experimental results with the theoretical predictions of the BCS pairing theory, one has to go beyond the so called “BCS predictions” which are valid only in the framework of an extremely simplified one is still far away from establishing the exact pairing mechanism in these new materials, there is no convincing reason at present to show that the BCS pairing theory will not be applicable to them.
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That the superconducting transition in underdoped high temperature superconductors is controlled by phase ordering, implies that pairing is a local phenomenon that occurs on an intermediate length scale, and typically at a temperature above T~.. The discovery of local stripe order in the LSCO family of high temperature superconductors, along with the theoretical suggestion that such structures are a general feature of doped antiferromagnets lead us further to propose that in fact pairing occurs in the vicinity of an individual stripe. The transition to a superconducting state then follows at lower temperature due tO Josephson coupling between stripes. In this paper we review our microscopic model of high temperature pairing on individual stripes.
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The BCS theory models electron correlations with pure zero-momentum pairs. I consider a family of pairing Hamiltonians, where the electron correlations are modelled with pure arbitrary-momentum pairs. I present exact solutions to this family. The BCS pairing, the \eta pairing and the d -wave pairing in T_c superconductivity are the family members. These models, expect for the BCS model, are legitimate only on an xy plane defined by the electron spin S_z, compatible with the two dimensionality of high temperature superconductivity. Surprisingly, all parings are on equal footing in the xy plane, suggesting a unification of the s-wave and d-wave theoretical mechanisms in high T_c superconductivity. I also give the extension that includes all members of this family.
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A theoretical study of BCS pairing in an extended Hubbard model with on-site repulsion (U) and a BCS pairing field (V) is presented. Treating the effect of U in the Gutzwiller approximation, we study the effect of increasing U in the Fermi-liquid phase, on the BCS pairing due to V. It is found that the superconducting energy gap (\ensuremath{\Delta}) is strongly enhanced in the correlated metallic phase near half-filling of the band due to the localization effects of U. Further, the ground state is found to be superconducting even when \ensuremath{\Vert}V\ensuremath{\Vert}U, contrary to the prediction in a Hartree-Fock treatment.
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