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Reply to "comment on 'BCS to Bose-Einstein crossover phase diagram at zero temperature for a d<inf>x</inf>2-<inf>y</inf>2 order parameter superconductor: Dependence on the tight-binding structure'"

Abstract:

In a recent Comment, Perali, Pieri, and Strinati [Phys. Rev. B 68, 066501 (2003)] came forward with a correction to the work of Soares et al. [Phys. Rev. B 65, 174506 (2002)], in the sense that they correctly found no nonpairing region in the density vs coupling diagram of the two-dimensional attractive Hubbard model for a d-wave symmetry for the order parameter. But, the BCS-Bose-Einstein crossover diagram also changes, a point missed by Perali, Pieri, and Strinati in their Comment. Furthermore, they use an analytical treatment of the gap equation to find the order parameter as C function of interaction strength, namely, Δ/4t vs V/4t. We point out that this treatment is not completely correct for the evaluation of the chemical potential, μ/4t vs V/4t, when we include the Debye frequency, ω D/4t, and their cutoff frequency, ωo. As a consequence, the phase diagram, namely, n vs V/4t, strongly depends on the value of ωD/4t, i.e., for small values of ω D/4t the phase diagram moves to higher values of V/4t.