d-Wave Pairing Driven by Bipolaric Modes Related to Giant Electron-Phonon Anomalies in High-$T_{c}$ Superconductors

TL;DR

This paper introduces a microscopic model demonstrating d-wave pairing in high-$T_c$ superconductors driven by bipolaric modes linked to giant electron-phonon anomalies, providing insights into high-temperature superconductivity mechanisms.

Contribution

The study presents a new class of microscopic Hamiltonians showing d-wave pairing due to bipolaric modes, relevant for understanding high-$T_c$ superconductivity in cuprates.

Findings

Model Hamiltonians exhibit d-wave pairing at spectrum bottom.

Giant electron-phonon anomalies induce pairing despite isotropy.

Framework allows rigorous mathematical analysis of superconductivity mechanisms.

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.