Superconductivity Simulated in Layered Material, Edging Closer to Room Temperature Applications

Researchers are increasingly focused on understanding the mechanisms behind superconductivity in layered materials, particularly following the recent observation of this phenomenon in bilayer nickelate LaNiO under pressure. Hannah Lange, Ao Chen, and Antoine Georges, alongside colleagues from Ludwig-Maximilians-Universität München, Collège de France, and the Flatiron Institute, present a detailed investigation of a mixed-dimensional bilayer model thought to capture the essential physics of this material. Their work, utilising advanced neural quantum state techniques, demonstrates robust superconductivity across a broad parameter space and reveals a fascinating interplay between interlayer and intralayer pairing symmetries. This represents a significant advance as the first application of neural states to a fermionic multi-orbital system and offers crucial insights into both bilayer nickelates and potential implementations in cold atom platforms.

Scientists have achieved a breakthrough in simulating superconductivity within complex materials using a novel computational approach. This work details the first evidence of superconductivity in two-dimensional bilayers using high-precision numerical methods, representing a significant advancement in the field of condensed matter physics.
Researchers employed neural quantum states, specifically a Gutzwiller-projected Hidden Fermion Pfaffian State, to model the ground-state properties of a mixed-dimensional bilayer system up to lattices of 8 × 8 × 2 sites. The study, motivated by the recent discovery of superconductivity in the bilayer nickelate La3Ni2O7 under pressure, explores similar phenomena in theoretically modelled systems.

Gutzwiller projection of Hidden Fermion Pfaffian States for mixD bilayer systems

A Gutzwiller-projected Hidden Fermion Pfaffian State forms the core of this study’s methodology for investigating the ground-state properties of a mixed-dimensional (mixD) bilayer model. This approach enables access to large lattices of up to 8 × 8 × 2 sites, facilitating the exploration of superconductivity across a range of dopings and couplings.

The research addresses a gap in fully two-dimensional numerical studies of strongly correlated mixD systems beyond mean-field treatments. Specifically, the work employs a variational wave function conceptually similar to a mean-field pairing function, but incorporates correlation effects via neural networks and Gutzwiller projection.

The physical Hilbert space, consisting of N orbitals and Nv visible fermions, is expanded by adding Nh hidden fermions, resulting in a total of Ntot = Nv + Nh fermions. A Hidden Fermion Pfaffian State, ψ(n), is then constructed, incorporating couplings between visible and hidden fermions represented by matrices Fvv, Fvh θ (n), and Fhh, where θ denotes the neural network parameters.

To enhance symmetry and stability, a Group Convolutional Neural Network is used to represent the configuration-dependent orbitals, incorporating translation, rotation, reflection, and spin-parity symmetries within a single forward pass. This yields a symmetric state, ψsym, which is then subjected to Gutzwiller projection to obtain the final wave function.

The researchers demonstrate that this combination of techniques allows for the investigation of pairing physics in the mixD model on fully two-dimensional bilayers, explicitly accounting for strong local correlations. Comparisons with matrix product state calculations on coupled ladders were performed to verify the accuracy of the neural network results.

Superconductivity and Pairing Symmetry in Bilayer Nickelate Models

Researchers have demonstrated superconductivity in a mixed-dimensional bilayer model, simulating systems up to 8x8x2 sites using neural quantum states. The study reveals a crossover from Bose-Einstein-condensed interlayer pairs at strong interlayer exchange to more spatially extended Bardeen-Cooper-Schrieffer-like pairs as interlayer exchange decreases.

Tuning the intralayer exchange reveals a sharp transition from interlayer s-wave pairing to intralayer d-wave pairing, indicative of a first-order change in pairing symmetry. Simulations were performed with parameters relevant to the bilayer nickelate La3Ni2O7, specifically considering J⊥/t∥ = 0.6, J∥/t∥ = 0.4, and a doping level of δ = 0.5.

These calculations represent the first simulation of a fermionic multi-orbital system using neural quantum states and establish the first evidence for superconductivity in two-dimensional bilayers using high-precision numerics. The work employed a Gutzwiller-projected Hidden Fermion Pfaffian State ansatz, enabling investigation of pairing physics on fully two-dimensional bilayers while explicitly accounting for strong local correlations.

Analysis of the mixD bilayer model shows a theoretically anticipated Bose-Einstein condensation to Bardeen-Cooper-Schrieffer crossover as a function of t∥/J⊥. Furthermore, the research identifies a change in pairing symmetry from interlayer s-wave to intralayer d-wave pairing as a function of J∥/t∥. The accuracy of these simulations was verified through comparison with matrix product state simulations on coupled ladders, confirming the reliability of the numerical approach. This research provides insight into superconductivity in both bilayer nickelates and cold atom quantum simulation platforms.

Pairing symmetry and interlayer exchange in bilayer nickelates

Researchers have demonstrated superconductivity within a mixed-dimensional bilayer model, offering insights into the behaviour of bilayer nickelates like La₃Ni₂O₇ and potentially informing the design of cold atom platforms. Employing neural quantum states, specifically a Gutzwiller-projected Hidden Fermion Pfaffian State, they performed large-scale simulations on lattices containing up to 512 sites to investigate the ground-state properties of this model.

The simulations reveal a transition in pairing behaviour, shifting from tightly bound interlayer pairs at strong interlayer exchange to more extended pairs resembling Bardeen-Cooper-Schrieffer theory as the interlayer exchange weakens. Furthermore, a sharp transition was observed between interlayer s-wave pairing and intralayer d-wave pairing when adjusting the intralayer exchange, indicating a change in pairing symmetry.

This work represents the first application of neural quantum states to a fully two-dimensional, multi-orbital fermionic system, successfully capturing both ground-state energies and subtle pairing phenomena. The authors acknowledge limitations inherent in the numerical methods used, particularly the computational cost associated with simulating strongly correlated systems. Future research will likely focus on applying this neural quantum state framework to more complex systems relevant to real materials and quantum simulation platforms, extending the capabilities of numerical simulation beyond conventional methods.