Some classes of homeomorphisms that preserve multiplicity and tangent cones

Abstract

Taking into account microscopic properties of most usual high-Tc 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 pairing at the bottom of their spectrum, despite their space isotropy. This phenomenon appears when a 'giant electron-phonon anomaly' is present at the boundaries of the Brillouin zone ('half breathing' bond-stretching mode), as 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.