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arXiv:2502.13960 · Physical review. B./Physical review. B

Extended s -wave pairing from an emergent Feshbach resonance in bilayer nickelate superconductors

Pietro Borchia, Hannah Lange, Fabian Grusdt

Published Oct 10, 2025• 2 citations
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Abstract

Since the discovery of unconventional superconductivity in cuprates, unraveling the pairing mechanism of charge carriers in doped antiferromagnets has been a long-standing challenge. Motivated by the discovery of high- T c superconductivity in nickelate bilayer La 3 Ni 2 O 7 (LNO), we study a minimal mixed dimensional t − J model supplemented with a repulsive Coulomb interaction V . When hole doped, previous numerical simulations revealed that the system exhibits strong binding energies, with a phenomenology resembling a BCS-to-BEC crossover accompanied by a Feshbach resonance between two distinct types of charge carriers. Here, we perform a mean-field analysis that enables a direct observation of the BCS-to-BEC crossover as well as microscopic insights into the crossover region and the pairing symmetry for two-dimensional bilayers. We benchmark our mean-field description by comparing it to density-matrix renormalization group simulations in quasi-one-dimensional settings and find remarkably good agreement. For the two-dimensional system relevant to LNO, our mean-field calculations predict a BCS pairing gap with an extended s -wave symmetry, directly resulting from the pairing mechanism's Feshbach origin. Our analysis hence gives insights into pairing in unconventional superconductors and, further, can be tested in currently available ultracold atom experiments.

DOI
10.1103/q8qm-1ttf

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Since the discovery of unconventional superconductivity in cuprates, unraveling the pairing mechanism of charge carriers in doped antiferromagnets has been a long-standing challenge. Motivated by the discovery of high- T c superconductivity in nickelate bilayer La 3 Ni 2 O 7 (LNO), we study a minimal mixed dimensional t − J model supplemented with a repulsive Coulomb interaction V . When hole doped, previous numerical simulations revealed that the system exhibits strong binding energies, with a phenomenology resembling a BCS-to-BEC crossover accompanied by a Feshbach resonance between two distinct types of charge carriers. Here, we perform a mean-field analysis that enables a direct observation of the BCS-to-BEC crossover as well as microscopic insights into the crossover region and the pairing symmetry for two-dimensional bilayers. We benchmark our mean-field description by comparing it to density-matrix renormalization group simulations in quasi-one-dimensional settings and find remarkably good agreement. For the two-dimensional system relevant to LNO, our mean-field calculations predict a BCS pairing gap with an extended s -wave symmetry, directly resulting from the pairing mechanism's Feshbach origin. Our analysis hence gives insights into pairing in unconventional superconductors and, further, can be tested in currently available ultracold atom experiments.
Since the discovery of superconductivity in cuprate materials, the minimal ingredients for high-Tc_cc​ superconductivity have been an outstanding puzzle. Motivated by the recently discovered nickelate bilayer superconductor La3_33​Ni2_22​O3_33​ under pressure, we study a minimal bilayer model, in which, as in La3_33​Ni2_22​O3_33​, inter- and intralayer magnetic interactions but no interlayer hopping are present: a mixed-dimensional (mixD) t−Jt-Jt−J model. In the setting of a mixD ladder, we show that the system exhibits a crossover associated with a Feshbach resonance: from a closed-channel dominated regime of tightly bound bosonic pairs of holes to an open-channel dominated regime of spatially more extended Cooper pairs. The crossover can be tuned by varying doping, or by a nearest-neighbor Coulomb repulsion VVV that we include in our model. Using density matrix renormalization group (DMRG) simulations and analytical descriptions of both regimes, we find that the ground state is a Luther-Emery liquid, competing with a density wave of tetraparton plaquettes at commensurate filling δ=0.5δ=0.5δ=0.5 at large repulsion, and exhibits a pairing dome where binding is facilitated by doping. Our observations can be understood in terms of pairs of correlated spinon-chargon excitations constituting the open channel, which are subject to attractive interactions mediated by the closed channel of tightly bound chargon-chargon pairs. When the closed channel is lowered in energy by doping or tuning VVV, a Feshbach resonance is realized, associated with a dome in the binding energy. Our predictions can be directly tested in state-of-the art quantum simulators, and we argue that the pairing mechanism we describe may be realized in the nickelate bilayer superconductor La3_33​Ni2_22​O3_33​.
Since the discovery of superconductivity in cuprate materials, the minimal ingredients for high-Tc{T}_{c}Tc​ superconductivity have been an outstanding puzzle. Motivated by the recently discovered nickelate bilayer superconductor La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ under pressure, we study a minimal bilayer model, in which, as in La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​, interlayer and intralayer magnetic interactions but no interlayer hopping are present: A mixed-dimensional (mixD) $t\text{\ensuremath{-}}J$ model. In the setting of a mixD ladder, we show that the system exhibits a crossover associated with a Feshbach resonance: From a closed-channel-dominated regime of tightly bound bosonic pairs of holes to an open-channel-dominated regime of spatially more extended Cooper pairs. The crossover can be tuned by varying doping, or by a nearest-neighbor Coulomb repulsion VVV that we include in our model. Using density matrix renormalization group simulations and analytical descriptions of both regimes, we find that the ground state is a Luther-Emery liquid, competing with a density wave of tetraparton plaquettes at commensurate filling $\ensuremath{\delta}=0.5$ at large repulsion, and exhibits a pairing dome where binding is facilitated by doping. Our observations can be understood in terms of pairs of correlated spinon-chargon excitations constituting the open channel, which are subject to attractive interactions mediated by the closed channel of tightly bound chargon-chargon pairs. When the closed channel is lowered in energy by doping or tuning VVV, a Feshbach resonance is realized, associated with a dome in the binding energy. Our predictions can be directly tested in state-of-the art quantum simulators, and we argue that the pairing mechanism we describe may be realized in the nickelate bilayer superconductor La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​.
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.
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