Origin of superconductivity in bilayer nickelates: a Quantum Monte Carlo study for a sign-problem-free effective model

Summary

This paper employs determinant quantum Monte Carlo to study a two-orbital model of the bilayer nickelate La₃Ni₂O₇. With realistic dispersion and specific interaction parameters, the auxiliary-field-decoupled fermionic Hamiltonian possesses Kramers antiunitary symmetry and is therefore sign-problem-free. By tuning doping, interlayer tunneling, and Hund's coupling, the authors find that the system can form spin-singlet layer-triplet superconductivity, whose transition temperature is affected by doping and Hund's coupling; lower doping favors superconductivity, whereas excessive doping suppresses or even eliminates it. Interlayer tunneling plays a decisive role in the competition between superconductivity and (π,π) interlayer bond order: in the strong-interaction limit, the same symmetry also leads to a bond-order instability, which may be related to the mysterious density wave observed experimentally and is accompanied by spin-density-wave fluctuations near (π,π). The conclusion suggests that enhancing superconductivity can be achieved by strongly breaking particle-hole symmetry and weakening interlayer/subspace tunneling, the latter being consistent with the role of apical oxygen vacancies in stabilizing superconductivity.

Materials

• La₃Ni₂O₇

Methods

• determinant Quantum Monte Carlo (DQMC)
• Hubbard-Stratonovich transformation
• stochastic analytical continuation (SAC)
• finite-size crossing analysis
• Kramers anti-unitary symmetry analysis
• two-orbital bilayer model Hamiltonian

Keywords

• superconductivity
• inter layer tunneling
• hund's coupling
• inter layer bond order
• spin density wave
• spin singlet layer triplet superconductivity
• sign problem free
• density wave state
• particle hole symmetry
• apical oxygen vacancies
• phase diagram

Highlights

• The authors identify a sign-problem-free limit of the two-orbital bilayer nickelate model due to Kramers anti-unitary symmetries, enabling efficient determinant QMC simulations.
• The same anti-unitary symmetries imply that the leading superconducting instability is in the spin-singlet layer-triplet channel and that there is a competing inter-layer bond order at momentum (π,π).
• The fluctuating inter-layer bond order is accompanied by fluctuating spin-density-wave order near (π,π), providing a promising candidate for the unknown density wave observed in experiments.
• The results suggest that a tunneling-independent antiferromagnetic interaction, such as RKKY, could be a promising direction for finding new high-temperature superconductors.
• Reducing inter-subspace tunneling avoids the bond-order instability and is closely related to the role of apical oxygen vacancies in stabilizing superconductivity.

Conclusions

• The two-orbital bilayer nickelate model supports a spin-singlet layer-triplet superconducting instability, with a transition temperature that depends on doping and Hund's coupling; lower doping favors superconductivity, while excessive doping suppresses or eliminates it.
• Inter-layer tunneling plays a decisive role in the competition between superconductivity and (π,π) inter-layer bond order, and the bond-order instability in the strong-interaction limit may be related to the enigmatic density wave state observed experimentally.
• When inter-layer tunneling is reduced, the hole density in the d_3z²-r² orbital increases and superconductivity emerges from both orbitals, making the superconducting transition insensitive to Hund's coupling.
• Enhancing superconductivity can be achieved by strongly breaking particle-hole symmetry and weakening inter-layer/subspace tunneling, the latter being consistent with the role of apical oxygen vacancies in stabilizing superconductivity in bilayer nickelates.

Main claims

• The two-orbital bilayer nickelate model has a sign-problem-free limit when the auxiliary-field-decoupled Hamiltonian preserves Kramers anti-unitary symmetries.
  • Evidence: The auxiliary-field-decoupled fermion Hamiltonian has Kramers anti-unitary symmetries which guarantee the absence of a sign problem.,The trace over fermionic degrees of freedom is positive definite for any auxiliary field configuration and gives a well-defined probability weight for Monte Carlo sampling.
• The leading superconducting instability is in the spin-singlet layer-triplet channel, with T_c affected by doping and Hund's coupling.
  • Evidence: The same anti-unitary symmetries imply that the SC pairing is maximal in the appropriate channel.,Finite-size crossing of the pair correlation function is used to identify the SC transition.,Lower doping favors superconductivity, whereas large doping in an orbital suppresses or eliminates it.
• There is a competing (π,π) inter-layer bond-order instability in the strong-interaction limit, accompanied by spin-density-wave fluctuations near (π,π).
  • Evidence: The same anti-unitary symmetries show a second instability towards (π,π) inter-layer bond order in the strong interaction limit.,The BO structure factor is maximal at (π,π), and the static spin structure factor peaks near (π,π).
• Inter-layer tunneling plays a decisive role in the competition between superconductivity and bond order.
  • Evidence: When inter-layer tunneling is added, layer charge conservation is broken, introducing a direct contribution and enabling a transition from zero-momentum order to order at momentum (π,π).,Setting inter-layer tunneling to zero changes hole densities and yields a similar SC transition temperature with SC from both orbitals.
• The (π,π) bond order is a promising candidate for the unknown density wave observed in experiment.
  • Evidence: The BO instability at (π,π) found in this work is a promising candidate for the unknown density wave observed in experiment [64,13].,The fluctuating BO is accompanied by fluctuating SDW order near (π,π).
• Superconductivity can be enhanced by strongly breaking particle-hole symmetry and weakening interlayer/subspace tunneling, consistent with the role of apical oxygen vacancies.
  • Evidence: The findings suggest two avenues for enhancing superconductivity: strongly breaking particle-hole symmetry and reducing inter-subspace tunneling to avoid a BO instability.,This is closely related to the important role of apical oxygen vacancies in stabilizing superconductivity in bilayer nickelates.

Workflow

• model_construction — A sign-problem-free limit exists for the two-orbital bilayer nickelate model under certain interaction parameters.
  • Materials: two-orbital bilayer nickelate La₃Ni₂O₇ effective model; DFT-derived parameters [19]
  • Methods: two-orbital bilayer Hamiltonian; onsite interactions and Hund's coupling; inter-layer tunneling; Hubbard-Stratonovich transformation
  • Observations: auxiliary-field-decoupled fermion Hamiltonian has Kramers anti-unitary symmetries; trace over fermions is positive definite and sign-problem-free
• symmetry_analysis — The anti-unitary symmetries imply a leading spin-singlet layer-triplet SC instability and a competing (π,π) inter-layer bond-order instability.
  • Materials: interacting Hamiltonian; fermion bilinear order parameters
  • Methods: Majorana basis; Kramers anti-unitary symmetry classification; bilinear correlation functions; Fierz identity
  • Observations: exchange contribution maximal for spin-singlet layer-triplet SC; competing inter-layer bond order at (π,π); layer charge conservation and direct contributions considered
• quantum_monte_carlo_simulation — Finite-temperature determinant QMC can simulate the sign-problem-free model and reveals gapped single-particle excitations and low double occupancy.
  • Materials: two-orbital model; auxiliary fields
  • Methods: determinant Quantum Monte Carlo; Trotter decomposition; discrete Hubbard-Stratonovich transformation; finite-temperature simulations
  • Observations: single-particle gap develops and is minimal around points; low double occupancy; spectral function and imaginary-time Green's function measured
• measurement_analysis — The model hosts superconductivity whose T_c depends on doping and Hund's coupling, with a competing (π,π) bond order and SDW fluctuations.
  • Materials: QMC correlation functions; pair correlation function; structure factors
  • Methods: finite-size crossing of order parameter with BKT exponent; stochastic analytic continuation; static structure factor calculations for SC, BO, SDW
  • Observations: SC transition temperature identified from finite-size crossing; gapless excitation branch from SAC; SC prefers small doping and is suppressed by large doping; BO structure factor maximal at (π,π); SDW fluctuations near (π,π)
• interpretation — Inter-layer tunneling is decisive for the SC/BO competition, and the (π,π) bond order is a candidate for the experimentally observed density wave; SC may be enhanced by breaking particle-hole symmetry and weakening interlayer/subspace tunneling.
  • Materials: numerical phase diagram; experimental context
  • Methods: comparison with experiment; symmetry-based phase-diagram reasoning
  • Observations: inter-layer tunneling controls SC versus BO competition; BO at (π,π) may correspond to enigmatic density wave; reducing inter-subspace tunneling and breaking particle-hole symmetry can enhance SC