Isotropic Bipolaron-Fermion-Exchange Theory and Unconventional Pairing in Cuprate Superconductors
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The discovery of high-temperature superconductors in 1986 represented a major experimental breakthrough (Nobel Prize 1987), but their theoretical explanation is still a subject of much debate. These materials have many exotic properties, such as $d$- and $p$-wave pairing and density waves. The appearance of unconventional pairing is examined from a microscopic model, taking into account important properties of hole-doped copper oxides. We consider an exchange interaction between fermions and dominantly inter-site bipolarons to be the mechanism which leads to the pairing. We connect its momentum dependency to the well-established fermion-phonon anomalies in cuprate superconductors. Since charge carriers in these materials are strongly correlated, we add a screened Coulomb repulsion to this exchange term. We avoid any ad hoc assumptions like anisotropy, but rather provide a microscopic explanation of unconventional pairing for coupling strengths that are in accordance with experimental facts. One important outcome is a mathematically rigorous elucidation of the role of Coulomb repulsion in unconventional pairing, which is shown to be concomitant with a strong depletion of superconducting pairs. Our theory, applied to the special case of LaSr 214, predicts at optimal doping (i) a coherence length of $21A$, which is the same as that obtained from the Ginzburg-Landau critical magnetic field measured for this material, and (ii) $d$-wave pair formation in the pseudogap regime, i.e., at temperatures much higher than the superconducting transition temperature. The understanding of pairing symmetry and the pseudogap phase are central issues in the theoretical comprehension of high-temperature superconductivity, with possible technological applications like $s$-, $d$-, and $p$-wave Josephson junctions used nowadays in quantum computers.