[Paper Review] Feshbach resonance in a strongly repulsive bilayer model: a possible scenario for bilayer nickelate superconductors

Hannah Lange, Lukas Homeier+4 more|arXiv (Cornell University)|Sep 27, 2023

Physics of Superconductivity and MagnetismPhysics and Astronomy3 citations

TL;DR

This paper proposes a Feshbach resonance mechanism in a strongly repulsive bilayer $t-J$ model that enables a crossover from tightly bound chargon-chargon pairs (BEC-like) to spatially extended spinon-chargon pairs (BCS-like), driven by doping or nearest-neighbor repulsion $V$. The key result is a pairing dome with enhanced binding energy near resonance, offering a microscopic mechanism for superconductivity in bilayer nickelates like La₃Ni₂O₇.

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 La$_3$Ni$_2$O$_3$ under pressure, we study a minimal bilayer model, in which, as in La$_3$Ni$_2$O$_3$, inter- and intralayer magnetic interactions but no interlayer hopping are present: a mixed-dimensional (mixD) $t-J$ 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 (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 $δ=0.5$ 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 La$_3$Ni$_2$O$_3$.

Motivation & Objective

• To understand the pairing mechanism in bilayer nickelate superconductors, particularly La₃Ni₂O₇ under pressure, which exhibits high-$T_c$ superconductivity.
• To investigate how strong Coulomb repulsion and mixed-dimensional (mixD) hopping in a bilayer $t-J$ model can still support robust superconducting pairing.
• To explore the role of Feshbach resonance in mediating effective attraction between spinon-chargon pairs via a closed-channel of tightly bound chargon-chargon pairs.
• To determine whether the observed pairing dome and competing density wave order at $ar{\delta}=0.5$ can be explained by emergent parton excitations and effective interactions.

Proposed method

• Employing a mixed-dimensional (mixD) $t-J$ model with interlayer magnetic exchange $J_\perp$ and intralayer hopping $t_\parallel$, but no interlayer hopping.
• Using density matrix renormalization group (DMRG) simulations to study the ground state and pairing correlations across doping and $V$.
• Deriving an effective Hamiltonian via Gutzwiller projection and second-order perturbation theory, revealing an attractive interaction mediated by the closed-channel $\mathrm{cc}$ pairs.
• Analyzing the system as a BEC-BCS crossover by tuning the energy of the closed-channel $\mathrm{cc}$ pairs via doping or $V$, leading to a Feshbach resonance.
• Introducing parton decomposition into spinons and chargons to describe emergent mesonic bound states and their interactions.
• Evaluating variational energies for Heisenberg and valence-bond crystal (VBS) orders to assess competing phases at half-filling ($\delta=0.5$).

Experimental results

Research questions

• RQ1 Can a Feshbach resonance mechanism explain high-$T_c$ superconductivity in bilayer nickelates despite strong on-site and nearest-neighbor repulsion?
• RQ2 How does the crossover between BEC-like and BCS-like pairing regimes emerge in a strongly repulsive mixD $t-J$ model?
• RQ3 What role does the energy of the closed-channel $\mathrm{cc}$ pairs play in tuning the pairing strength and binding energy?
• RQ4 Does the system exhibit competing orders such as a bond-ordered density wave at $\delta=0.5$, and how do they influence superconducting pairing?
• RQ5 Can the effective attraction between spinon-chargon pairs be understood as a result of virtual recombination into tightly bound chargon-chargon pairs?

Key findings

• The system exhibits a Feshbach resonance-like crossover tuned by doping or nearest-neighbor repulsion $V$, transitioning from a BEC-like regime of tightly bound $\mathrm{cc}$ pairs to a BCS-like regime of spatially extended $\mathrm{sc}$ pairs.
• A pairing dome emerges in the binding energy as a function of doping or $V$, peaking near the resonance condition where the closed-channel $\mathrm{cc}$ pairs are near degenerate with the open-channel $\mathrm{sc}$ pairs.
• At $\delta=0.5$ and large $V$, a bond-ordered density wave (BODW) of tetraparton plaquettes competes with superconductivity, driven by a second-order term in the effective Hamiltonian favoring alternating singlet/triplet order.
• The effective Hamiltonian at half-filling reduces to a form favoring a valence-bond crystal (VBS) state, with variational energy $E_0 \approx -0.28$ per bond, lower than the Heisenberg AFM energy of $-0.196$ per bond.
• The attraction between $\mathrm{sc}$ pairs is mediated by virtual recombination into the $\mathrm{cc}$ channel, with amplitude proportional to $-t_\parallel^2 / (V - J_\perp)$, leading to finite binding energy when $V \approx J_\perp$.
• DMRG simulations confirm finite positive binding energies for $V=5J_\perp$ and $t_\parallel / J_\perp = 1.0, 3.0$, validating the resonance condition and pairing dome.