Doping dependence and multichannel mediators of superconductivity: calculations for a cuprate model

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We study two aspects of the superconductivity in a cuprate model system, its doping dependence and the influence of competing pairing mediators. We first include electron–phonon interactions beyond Migdal’s approximation and solve self-consistently, as a function of doping and for an isotropic electron–phonon coupling, the full-bandwidth, anisotropic vertex-corrected Eliashberg equations under a non-interacting state approximation for the vertex correction. Our results show that such pairing interaction supports the experimentally observed dx2−y2 -wave symmetry of the superconducting gap, but only in a narrow doping interval of the hole-doped system. Depending on the coupling strength, we obtain realistic values for the gap magnitude and superconducting critical temperature Tc close to optimal doping, rendering the electron–phonon mechanism an important candidate for mediating superconductivity in this model system. Second, for a doping near optimal hole doping, we study multichannel superconductivity, by including both vertex-corrected electron–phonon interaction and spin and charge fluctuations as pairing mechanisms. We find that both mechanisms cooperate to support an unconventional d-wave symmetry of the order parameter, yet the electron–phonon interaction is mainly responsible for the Cooper pairing and high critical temperature Tc . Spin fluctuations are found to have a suppressing effect on the gap magnitude and critical temperature due to their repulsive interaction at small coupling wave vectors.