Scattering theory of mesons in doped antiferromagnetic Mott insulators: Multichannel perspective and Feshbach resonance

Modeling the underlying pairing mechanism of charge carriers in strongly correlated electrons, starting from a microscopic theory, is among the central challenges of condensed-matter physics. Hereby, the key task is to understand what causes the appearance of superconductivity at comparatively high temperatures upon hole doping an antiferromagnetic (AFM) Mott insulator. Recently, it has been proposed that at strong coupling and low doping, the fundamental one- and two-hole meson-type constituents---magnetic polarons and bipolaronic pairs---likely realize an emergent Feshbach resonance producing near-resonant ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ interactions between charge carriers. Here, we provide detailed calculations of the proposed scenario by describing the open and closed meson scattering channels in the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model using a truncated basis method. After integrating out the closed channel constituted by bipolaronic pairs, we find ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ attractive interactions between open channel magnetic polarons. The closed form of the derived interactions allows us analyze the resonant pairing interactions and we find enhanced (suppressed) attraction for hole (electron) doping in our model. The formalism we introduce provides a framework to analyze the implications of a possible Feshbach scenario, e.g., in the context of BEC-BCS crossover, and establishes a foundation to test quantitative aspects of the proposed Feshbach pairing mechanisms in doped antiferromagnets.