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Physical review. B./Physical review. B

Feshbach resonance in a strongly repulsive ladder of mixed dimensionality: A possible scenario for bilayer nickelate superconductors

Hannah Lange, Lukas Homeier, Eugene Demler, Ulrich Schollwöck, Fabian Grusdt, Annabelle Bohrdt

Published Jan 16, 2024• 40 citations
Publisher

Abstract

Since the discovery of superconductivity in cuprate materials, the minimal ingredients for high-${T}_{c}$ superconductivity have been an outstanding puzzle. Motivated by the recently discovered nickelate bilayer superconductor ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ under pressure, we study a minimal bilayer model, in which, as in ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$, 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 $V$ 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 $V$, 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 ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$.

DOI
10.1103/physrevb.109.045127

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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\ensuremath-Jt\text{\ensuremath{-}}Jt\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 \ensuremathδ=0.5\ensuremath{\delta}=0.5\ensuremathδ=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​.
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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.
Understanding unconventional superconductivity involves unraveling the pairing mechanism of charge carriers in doped antiferromagnets, where Cooper pairs form despite repulsive interactions. This paper examines a model relevant to bilayer nickelate superconductors, revealing a transition from tightly bound to spatially extended pairs as repulsion increases. At strong repulsion, a microscopic pairing mechanism is identified that leads to robust pairing with a peak in binding energies at around 30% doping, which can be tested using quantum simulators.
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.
Simulating superconductivity in mixed-dimensional t∥t_\parallelt∥​-J∥{J}_\parallelJ∥​-J⊥{J}_\perpJ⊥​ bilayers with neural quantum states
Motivated by the recent discovery of superconductivity in the bilayer nickelate La3_33​Ni2_22​O7_77​ (LNO) under pressure, we study a mixed-dimensional (mixD) bilayer t∥t_\parallelt∥​-J∥J_\parallelJ∥​-J⊥J_\perpJ⊥​ model, which has been proposed as an effective low-energy description of LNO. Using neural quantum states (NQS), and in particular Gutzwiller-projected Hidden Fermion Pfaffian State, we access the ground-state properties on large lattices up to 8×8×28\times 8\times 28×8×2 sites. We show that this model exhibits superconductivity across a wide range of dopings and couplings, and analyze the pairing behavior in detail. We identify a crossover from tightly bound, Bose-Einstein-condensed interlayer pairs at strong interlayer exchange to more spatially extended Bardeen-Cooper-Schrieffer-like pairs as the interlayer exchange is decreased. Furthermore, upon tuning the intralayer exchange, we observe a sharp transition from interlayer sss-wave pairing to intralayer ddd-wave pairing, consistent with a first-order change in the pairing symmetry. We verify that our simulations are accurate by comparing with matrix product state simulations on coupled ladders. Our results represent the first simulation of a fermionic multi-orbital system with NQS, and provide the first evidence for superconductivity in two-dimensonal bilayers using high-precision numerics. These findings provide insight into superconductivity in bilayer nickelates and cold atom quantum simulation platforms.
Abstract Ever since the discovery of high-temperature superconductivity in cuprates, gaining microscopic insights into the nature of pairing in strongly correlated systems has remained one of the greatest challenges in modern condensed matter physics. Following recent experiments reporting superconductivity in the bilayer nickelate La3Ni2O7 (LNO) with remarkably high critical temperatures of Tc = 80 K, it has been argued that the low-energy physics of LNO can be described by the strongly correlated, mixed-dimensional bilayer t–J model. Here we investigate this bilayer system and utilize density matrix renormalization group techniques to establish a thorough understanding of the model and the magnetically induced pairing through comparison to the perturbative limit of dominating inter-layer spin couplings. In particular, this allows us to explain appearing finite-size effects, firmly establishing the existence of long-range superconducting order in the thermodynamic limit. By analyzing binding energies, we predict a BEC–BCS crossover as a function of the Hamiltonian parameters. We find large binding energies of the order of the inter-layer coupling that suggest strikingly high critical temperatures of the Berezinskii–Kosterlitz–Thouless transition, raising the question of whether (mixD) bilayer superconductors possibly facilitate critical temperatures above room temperature.