d-Wave Pairing Driven by Bipolaric Modes Related to Giant Electron-Phonon Anomalies in High-$T_c$ Superconductors

Abstract

Taking into account microscopic properties of most usual high-$T_c$ superconductors, like cuprates, we define a class of microscopic model Hamiltonians for two fermions (electrons or holes) and one boson (bipolaron) on the two-dimensional square lattice. We establish that these model Hamiltonians can show d-wave paring at the bottom of their spectrum, despite their space isotropy. This phenomenon appear when a "giant electron-phonon anomaly" is present at the boundaries of the Brillouin zone ("half breathing" bond-stretching mode), like in doped cuprates. Our results can be used to derive effective electron-electron interactions mediated by bipolarons and we discuss regimes where the corresponding model is relevant for the physics of high-temperature superconductivity and can be mathematically rigorously studied.

Keywords: High Tc, Superconductivity, Hubbard model, BCS model, d-wave, s-wave, Bipolaron

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