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arXiv:2312.02978 · Physical review. B./Physical review. B

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

Lukas Homeier, Pit Bermes, Fabian Grusdt

Published Mar 20, 2024• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.109.125135

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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 dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ 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\ensuremath-t\ensuremath′\ensuremath-Jt\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}Jt\ensuremath-t\ensuremath′\ensuremath-J model using a truncated basis method. After integrating out the closed channel constituted by bipolaronic pairs, we find dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ 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.
Abstract Resonant interactions associated with the emergence of a bound state constitute one of the cornerstones of modern many-body physics. Here we present a Feshbach perspective on the origin of strong pairing in Fermi-Hubbard type models. We perform a theoretical analysis of interactions between spin-polaron charge carriers in doped Mott insulators, modeled by a near-resonant two-channel scattering problem, and report evidence for Feshbach-type interactions in the dx2−y2{d}_{{x}^{2}-{y}^{2}}dx2−y2​ d x 2 − y 2 channel, consistent with the established phenomenology of cuprates. Existing experimental and numerical results on hole-doped cuprates lead us to conjecture the existence of a light, long-lived, low-energy excited state of two holes, which enables near-resonant interactions. To put our theory to a test we suggest to use coincidence angle-resolved photoemission spectroscopy (cARPES), pair-tunneling measurements or pump-probe experiments. The emergent Feshbach resonance among spin-polarons could also underlie superconductivity in other doped antiferromagnetic Mott insulators highlighting its potential as a unifying strong-coupling pairing mechanism rooted in quantum magnetism.
Resonant interactions associated with the emergence of a bound state constitute one of the cornerstones of modern many-body physics, ranging from Kondo physics, BEC-BCS crossover, to tunable interactions at Feshbach resonances in ultracold atoms or 2D semiconductors. Here we present a Feshbach perspective on the origin of strong pairing in Fermi-Hubbard type models. We perform a theoretical analysis of interactions between charge carriers in doped Mott insulators, modeled by a near-resonant two-channel scattering problem, and find strong evidence for Feshbach-type interactions in the dx2−y2d_{x^2-y^2}dx2−y2​ channel that can support strong pairing, consistent with the established phenomenology of cuprates. Existing experimental and numerical results on hole-doped cuprates lead us to conjecture the existence of a light, long-lived, low-energy excited state of two holes with bipolaron character in these systems, which enables near-resonant interactions and can thus provide a microscopic foundation for theories of high-temperature superconductivity involving strong attraction, as assumed e.g. in BEC-BCS crossover scenarios. To put our theory to a direct test we suggest to use coincidence angle-resolved photoemission spectroscopy (cARPES), pair-tunneling measurements or less direct pump-probe experiments. The emergent Feshbach resonance we propose could also underlie superconductivity in other doped antiferromagnetic Mott insulators, as recently proposed for bilayer nickelates, highlighting its potential as a unifying strong-coupling pairing mechanism rooted in quantum magnetism.
Understanding pairing in the strong-coupling regime of doped Mott insulators remains an open problem in the context of cuprate superconductors. We perform ultra-high resolution numerical simulations of spectral functions in the highly underdoped t−Jt-Jt−J model and discover two coupled branches of hole pairs emerging at low energies in the largely unexplored two-particle spectrum. As spin anisotropy is tuned from the Ising limit to the SU(2)SU(2)SU(2)-symmetric Heisenberg regime, the lowest ddd-wave pair evolves from a single bipolaronic branch into two hybridized branches separated by an avoided crossing. We explain this behaviour using an effective two-channel model involving a tightly bound bipolaronic state and a second channel associated with two magnetic polarons. The model reproduces the qualitative low-energy spectra and implies near-resonant ddd-wave interactions in the SU(2)SU(2)SU(2)-symmetric t−Jt-Jt−J model, consistent with proximity to an emergent Feshbach-type resonance. To probe these predictions experimentally, we propose a Raman spectroscopy scheme for the attractive Hubbard model that can be directly implemented using ultracold atoms in optical lattices. Our work establishes two-particle spectroscopy, beyond single-particle Green's functions, as a powerful tool for revealing the microscopic origins of unconventional superconductivity.
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