Summary
Based on a bilayer two-orbital Hubbard model, this study employs the ground-state constrained path integral quantum Monte Carlo method to investigate the regulatory mechanisms of vertical electric fields (interlayer potential differences) and electron correlations on the competition between interlayer s± and intralayer d-wave pairing in bilayer nickelates. The results indicate that increasing the interlayer potential difference typically enhances the d-wave pairing vertex contribution and suppresses s± pairing, thereby shifting the pairing preference toward the d-wave channel; conversely, increasing the crystal field splitting enhances the relative competitiveness of s± pairing, while increasing the Hund coupling favors s± pairing under weak bias but enhances d-wave pairing under large bias. Microscopic analysis reveals that the electric field primarily induces interlayer charge redistribution within each orbital sector, accompanied by enhancements in the antiferromagnetic spin structure factor and local interorbital parallel spin correlations induced by Hund coupling. These findings elucidate the potential connections among charge redistribution, magnetic correlations, and pairing competition, providing a theoretical basis for understanding how layer polarization and multi-orbital interactions influence the relative pairing tendencies in bilayer nickelates.
Materials
Methods
- constrained-path quantum Monte Carlo
- ground-state constrained-path quantum Monte Carlo
- bare static Lindhard susceptibility
Keywords
- pairing competition
- layer polarization
- interlayer s± pairing
- intralayer d wave pairing
- charge redistribution
- antiferromagnetic spin structure factor
- hund's coupling
- crystal field splitting
- orbital occupations
Highlights
- The study identifies layer polarization as a means of tuning the competition between interlayer and intralayer pairing in bilayer nickelates without changing chemical composition.
- Step-like enhancements in the antiferromagnetic spin structure factor and lower-layer orbital occupation are observed in similar field intervals, suggesting a connection between charge redistribution and magnetic response.
- The bare static susceptibility exhibits similar step-like variations to the interacting observables, indicating that finite-size electronic structure may play a role in the observed magnetic response.
Conclusions
- Increasing the effective layer potential difference generally enhances the finite-size pairing vertex contribution for d-wave pairing and reduces the s± pairing vertex, shifting the relative pairing preference toward the d-wave channel.
- Increasing the onsite repulsion enhances both vertex contributions, more strongly in the d-wave channel, whereas increasing the crystal-field splitting reduces both and makes s± pairing relatively more competitive.
- Hund's coupling increases the relative competitiveness of s± pairing at weak bias, while enhancing the relative strength of d-wave pairing at large bias.
- The electric-field potential difference primarily redistributes charge between layers within each orbital sector, accompanied by an increase in the antiferromagnetic spin structure factor.
- Hund's coupling enhances local interorbital parallel-spin correlations, suggesting a connection between charge redistribution, magnetic correlations, and pairing competition.
Main claims
- Increasing the layer potential difference (\varepsilon) shifts the pairing preference toward the d-wave channel by enhancing Vd and reducing Vs±.
- Evidence: Figure 2 shows Vd increases and Vs± decreases with \varepsilon.,Text states: 'increasing \varepsilon generally enhances the finite-size pairing vertex contribution Vd and reduces Vs±, shifting the relative pairing preference toward the d-wave channel.'
- Onsite repulsion (U) enhances both pairing vertex contributions, with a stronger effect on the d-wave channel.
- Evidence: Figure 3 shows Vd increases more than Vs± as U increases from 2 to 3.,Text states: 'Increasing the onsite repulsion enhances both vertex contributions, more strongly in the d-wave channel.'
- Crystal-field splitting reduces both pairing vertex contributions, making s± pairing relatively more competitive.
- Evidence: Figure 3(c) and (d) show the crossover boundary shifts as crystal-field splitting increases.,Text states: 'increasing the crystal-field splitting reduces both and makes s± pairing relatively more competitive.'
- Hund's coupling increases the relative competitiveness of s± pairing at weak bias but enhances d-wave pairing at large bias.
- Evidence: Figure 4 shows the crossover field changes with Hund's coupling.,Text states: 'Hund's coupling increases the relative competitiveness of s± pairing at weak bias, while enhancing the relative strength of d-wave pairing at large bias.'
- The electric field primarily redistributes charge between layers within each orbital sector, accompanied by increased antiferromagnetic spin correlations.
- Evidence: Figure 5 shows layer-resolved orbital occupations change with \varepsilon while total orbital occupations remain nearly constant.,Figure 6(a) shows the antiferromagnetic spin structure factor increases with \varepsilon.,Text states: 'The bias primarily redistributes charge between layers within each orbital sector, accompanied by an increase in the antiferromagnetic spin structure factor.'
Workflow
- model_definition — The model captures the essential multiorbital physics and external field tuning of bilayer nickelates.
- Materials: Bilayer two-orbital Hubbard model; Layer potential-energy difference (effective perpendicular electric field); Onsite repulsion; Crystal-field splitting; Hund's coupling
- Methods: Hamiltonian construction with density-density Hund interaction; Parameter selection based on first-principles Wannier downfolding
- numerical_simulation — CPMC provides accurate ground-state properties for the interacting multiorbital system.
- Materials: Ground-state constrained-path quantum Monte Carlo (CPMC); Slater determinant walkers; Trial wave function from noninteracting Hamiltonian
- Methods: Importance-sampled branching random walk in imaginary time; Hubbard-Stratonovich transformation; Constrained-path approximation to control fermion sign problem; Back propagation for equal-time observables
- Observations: Systematic error typically within a few percent; Statistical error bars smaller than symbol size
- observable_analysis — The interplay of electric field and electronic correlations shifts the pairing preference between interlayer s± and intralayer d-wave channels.
- Materials: Pairing vertex contributions (Vd, Vs±); Orbital occupations; Antiferromagnetic spin structure factor; Local interorbital parallel-spin correlations; Bare static Lindhard susceptibility
- Methods: Calculation of equal-time correlation functions; Subtraction of disconnected single-particle contributions; Evaluation of layer- and orbital-resolved densities; Comparison of interacting and noninteracting susceptibilities
- Observations: Increasing \varepsilon enhances Vd and reduces Vs±; Increasing U enhances both vertices, more strongly in d-wave; Increasing crystal-field splitting reduces both vertices, making s± more competitive; Hund's coupling increases s± competitiveness at weak bias and d-wave at large bias; Charge redistribution occurs primarily between layers within each orbital sector; Antiferromagnetic spin structure factor increases with \varepsilon
- interpretation — Layer polarization and multiorbital interactions influence relative pairing tendencies through charge redistribution and magnetic correlations.
- Materials: Charge redistribution patterns; Magnetic correlation enhancements; Pairing vertex trends
- Methods: Correlation analysis between charge, spin, and pairing observables; Comparison with noninteracting reference
- Observations: Layer imbalance reduces relative advantage of interlayer pairing at large bias; Hund's coupling links magnetic responses of orbitals, promoting interlayer pairing at weak bias