Bilayer Nickelate Pairing-Symmetry Crossover Driven by Hund’s Coupling and Crystal-Field Splitting is Mapped

The search for unconventional superconductivity in layered nickelates continues to drive exciting developments in condensed matter physics, with the precise nature of electron pairing remaining a key question. Yicheng Xiong, Yanmei Cai, and Tianxing Ma, from the School of Physics and Astronomy at Beijing Normal University, investigate the pairing symmetry within bilayer nickelates using advanced computational modelling. Their work addresses a critical gap in understanding how interactions between electrons, specifically Hund’s coupling and crystal field splitting, influence the emergence of superconductivity. The team demonstrates that increasing Hund’s coupling and crystal field splitting favour a particular pairing state, shifting the system from one dominated by in-layer pairing to one where pairing occurs between layers, and ultimately suggesting that a -wave pairing symmetry is the most likely scenario within realistic conditions for these materials. This research provides crucial insight into the complex interplay between electronic correlations and orbital physics, bringing scientists closer to realising the full potential of nickelate superconductors.

Nickelate Superconductivity, Pairing Symmetry and Correlations

A comprehensive review of recent research reveals a dynamic and complex field focused on the newly discovered superconductivity in La3Ni2O7 and related nickelate materials. Investigations center on understanding the fundamental mechanisms driving this phenomenon, with a particular emphasis on the nature of electron pairing and the role of electronic interactions. A central debate revolves around the symmetry of the superconducting gap, with studies exploring both s±-wave and d-wave possibilities. Many findings initially suggest s±-wave superconductivity, characterized by a change in the superconducting gap’s sign across the Fermi surface.

However, research continues to investigate d-wave pairing, particularly in related materials or under altered conditions. Strong electronic correlations, arising from interactions between electrons, are considered crucial in driving the pairing mechanism, and researchers are actively investigating how these correlations operate. The interplay between the two Eg orbitals, d3z2-r2 and dxy, is a recurring theme, as understanding their contribution to the Fermi surface and pairing is vital. Some studies propose that magnetic fluctuations mediate the pairing, similar to the mechanism observed in cuprate superconductors.

Research also explores how applying pressure or doping, such as with neodymium, affects the pairing symmetry and superconducting properties. Theoretical modeling plays a significant role, with the Hubbard model and its extensions frequently employed to describe the electronic structure and interactions within these materials. Density Functional Theory calculations help understand the electronic band structure, while Density Functional Theory combined with the U parameter attempts to account for strong correlations. Dynamical Mean-Field Theory, a more sophisticated method for treating strong correlations, is often combined with Density Functional Theory.

Quantum Monte Carlo, a powerful numerical technique, is used to benchmark theoretical models and explore the ground state properties. Studies focus on La3Ni2O7 thin films, as they are easier to synthesize and study, and researchers investigate the superconducting properties of different Ruddlesden-Popper phases to understand how the number of layers affects superconductivity. The impact of doping with elements like neodymium and applying pressure to tune the electronic structure are also key areas of investigation. Key research questions and challenges remain, including definitively establishing the pairing symmetry and understanding the role of orbital selectivity. Overcoming computational challenges remains a key priority. In conclusion, research on La3Ni2O7 and related nickelates is rapidly evolving, with the combination of theoretical modeling, computational simulations, and experimental studies driving progress towards understanding the mechanism of superconductivity and potentially discovering new superconducting materials with even higher transition temperatures.

Nickelate Superconductivity, Pairing Symmetry via Quantum Monte Carlo

Scientists investigated the pairing symmetry within the bilayer nickelate superconductor La₃Ni₂O₇, a material where the nature of superconductivity remains a topic of intense debate. To explore its ground-state properties in a realistic setting, the team constructed a two-orbital bilayer Hubbard model, a theoretical framework capturing the essential electronic interactions within the material. They then employed the constrained-path quantum Monte Carlo method, a powerful computational technique, for large-scale simulations, effectively mitigating computational challenges associated with strongly correlated electron systems. The study systematically calculated ground-state pairing correlation functions, allowing researchers to map the phase diagram of pairing symmetry across a range of parameters.

Simulations involved scanning key variables including the on-site Coulomb interaction U, varying it from weak to intermediate coupling, and exploring the influence of the Hund’s coupling ratio JH/U and crystal field splitting ∆E. Interlayer hopping, represented by t⊥, was also included as a crucial parameter in the simulations. This comprehensive parameter sweep enabled the team to identify how different electronic interactions influence the dominant pairing symmetry. Further analysis revealed that increasing the Hund’s coupling selectively enhances interlayer s±-wave pairing while suppressing intralayer d-wave pairing.

Similarly, a larger crystal field splitting drives a transition from d-wave- to s±-wave-dominant states, demonstrating a clear link between electronic structure and pairing symmetry. Notably, the region where the dominant pairing symmetry transitions closely overlaps with the inversion of orbital occupancy in response to the Hubbard U, suggesting a fundamental connection between pairing competition and orbital physics. The results indicate that, within the parameter regime relevant to the actual material, the s±-wave is the most probable pairing symmetry, providing crucial insights into the nature of superconductivity in this novel nickelate material. The team’s innovative application of the constrained-path quantum Monte Carlo method, combined with a systematic exploration of key parameters, has advanced understanding of pairing mechanisms in strongly correlated materials.

Pairing Symmetry Governed by Electron Interactions

Scientists have achieved a detailed understanding of the pairing symmetry within the bilayer nickelate superconductor La3Ni2O7, a material garnering significant attention due to its potential for high-temperature superconductivity. This work addresses a long-standing debate regarding the nature of electron pairing, specifically, whether it follows a d-wave or s±-wave pattern, by employing advanced computational methods to model the material’s behavior. The team constructed a two-orbital Hubbard model and utilized the constrained-path quantum Monte Carlo method, enabling large-scale simulations that accurately capture the complex interplay of electron interactions. Results demonstrate a strong sensitivity of pairing symmetry to both Hund’s coupling (JH) and crystal field splitting (∆E).

Increasing either of these parameters selectively enhances interlayer s±-wave pairing while simultaneously suppressing intralayer d-wave pairing. Specifically, calculations reveal that only under conditions of weak JH and strong electron correlation does the system favor d-wave pairing. Within parameter regimes relevant to the actual material, the s±-wave pairing symmetry is the most probable, aligning with experimental observations hinting at sign-changing pairing characteristics. Further analysis shows that a larger crystal field splitting effectively weakens the d-wave pairing channel by suppressing antiferromagnetic spin fluctuations.

This suppression allows the d3z2−r2 orbital to dominate the s±-wave pairing. Notably, the transition region between pairing symmetries closely overlaps with the inversion of orbital occupancy response to the on-site Coulomb interaction (U), suggesting a fundamental link between pairing competition and orbital physics. These findings resolve conflicting theoretical predictions and provide quantitative guidance for tuning the superconducting state through external pressure or strain, paving the way for advancements in high-temperature superconductivity research.