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The BCS-BE crossover phase diagram at T = 0 K for a d-wave superconductor: The importance of the Debye frequency and the tight binding band structure

Abstract:

We consider the phase diagram of the BCS (Bardeen-Cooper-Schrieffer)-BE (Bose-Einstein) crossover in the ground state (r = 0 K) of a d x2-y2-wave superconductor, with a nearest neighbour tight binding structure, when we take into account the Debye (phononic) frequency around the chemical potential, μ. This approach is a continuation of the work of den Hertog (1999 Phys. Rev. B 60 559) and that of Scares et al (2002 Phys. Rev. B 65 174506). The latter authors considered the influence of the second-nearest neighbours, but neither set of authors took into account the effect of the Debye frequency, ωD, or the influence of the next nearest neighbour matrix hopping element. We have found the following results: (1) there is not a metallic phase - that is, δ/4t → 0 when V/4t → 0, VωD/4t, ∀αε (-1/2,+1/2), and ∀ n, where n is the carrier density per site, V is the attractive interaction, t is the nearest neighbour hopping integral, and α′ is the next nearest neighbour hopping ratio; (2) the BCS-BE crossover line is strongly affected by the presence of ωD/4t and that of α′ - actually, the values of V/4t needed to achieve the Bose-Einstein regime become extremely large for small values of ωD/4t; and (3) both δ/4t and μ/4t strongly depend on the values of ωD/4t and α′. The results (1) are in agreement with the ones found by Perali et al (2003 Phys. Rev. B 68 066501 (Preprint condmat/0211132)) and Rodríguez-Nunez et al (2003 Phys. Rev. B 68 066502), and in disagreement with those of den Hertog and Soares et al.