🔬 condensed matter

{\it Ab initio} prediction of $d_{x^2-y^2}$ -wave superconductivity in infinite-layer nickelates

This paper presents a fully *ab initio* theoretical study demonstrating that spin-fluctuation-mediated interactions drive $d_{x^2-y^2}$ -wave superconductivity in infinite-layer nickelates, a mechanism that successfully explains experimental observations and predicts specific properties for immediate verification.

Original authors: Guang-Yu Guo, Ren-Guo Guo, Yun-Chen Liao, Yang-hao Chan

Published 2026-08-04

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CC BY 4.0

Original authors: Guang-Yu Guo, Ren-Guo Guo, Yun-Chen Liao, Yang-hao Chan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where electricity flows without losing a single drop of energy, powering our cities, computers, and gadgets with perfect efficiency. This dream relies on a phenomenon called superconductivity, where certain materials let electric current zip through them with zero resistance. For decades, scientists have been hunting for "high-temperature" superconductors—materials that do this trick without needing to be cooled to the freezing cold of outer space. The most famous suspects in this hunt are copper-based compounds called cuprates, which have been the stars of the show since the late 1980s. But there's a mystery: we still don't fully understand how they pair up their electrons to achieve this super-state. Because nickel sits right next to copper on the periodic table, scientists thought, "Hey, maybe nickel compounds work the same way!" Recently, a new family of nickel-based materials, called infinite-layer nickelates, was discovered to be superconductors too. This has sparked a huge debate: Are they just like their copper cousins, or is there a completely new secret recipe at play? The big question is what "glue" holds the electrons together to make them superconduct. Is it the vibrations of the atoms (phonons), or is it something more exotic like magnetic wiggles (spin fluctuations)?

In this study, a team of researchers used powerful computer simulations to act as a detective, peering into the microscopic world of these nickel superconductors to solve the mystery. They focused on three specific versions of the material, where some atoms were swapped out to optimize their superconducting abilities. Using a sophisticated method called "ab initio" (which means starting from the very basic laws of physics without guessing), they built a digital model that accounted for every possible force: the shaking of atoms, the repulsion between electrons, and the magnetic interactions.

The results were a clear "aha!" moment. The simulations revealed that these nickelates are not simple superconductors; they are complex, two-band superconductors with a very specific shape to their superconducting "gap" (the energy barrier electrons must overcome). The researchers found that the electrons form pairs in a pattern shaped like a four-leaf clover, known as a $d_{x^2-y^2}$ -wave. But here's the twist: on one part of the material's electron map, the pattern points one way, and on another part, it points the opposite way. It's like a dance where partners on one side of the room spin clockwise, while partners on the other side spin counter-clockwise, yet they still move in perfect harmony.

Crucially, the study ruled out the idea that the shaking of atoms (phonons) is the main driver. When the researchers turned off the magnetic interactions in their simulation, the superconductivity almost vanished, dropping to a temperature of about 0.01 Kelvin—practically absolute zero. This proves that the "glue" holding the electrons together is not the atomic vibrations, but rather the magnetic fluctuations (spin fluctuations). The simulations showed that these magnetic wiggles are about ten times stronger than the other forces on the main electron paths, acting as the powerful engine that drives the superconductivity.

The team also compared their digital predictions with real-world experiments that have already been done. They found that their calculated temperatures, the shape of the electron surfaces, and the way energy is absorbed by the material matched up very well with what scientists have measured in the lab. For instance, their predicted "V-shaped" energy gap matches the signals seen in scanning tunneling microscope experiments, which is a strong sign that their model is correct. However, they noted that some experiments on a specific nickel compound showed confusing results, possibly because of magnetic interference from the atoms themselves. The researchers suggest that more experiments, particularly using high-resolution tools to look at the electron patterns directly, are needed to settle the remaining questions.

In short, this paper suggests that these new nickel superconductors are driven by magnetic forces, not atomic vibrations, and they dance to a complex, clover-shaped rhythm. While the computer simulations are very convincing and match existing data, the scientific community still needs to run more real-world tests to confirm every detail of this exciting new chapter in the story of superconductivity.

Technical Summary: Ab Initio Prediction of $d_{x^2-y^2}$ -Wave Superconductivity in Infinite-Layer Nickelates

Problem Statement
Infinite-layer nickelates (specifically hole-doped $Re_{1-x}Sr_xNiO_2$ , where $Re = La, Pr, Nd$) have emerged as a new family of potential unconventional high-temperature superconductors. However, fundamental aspects of their superconductivity, including the pairing mechanism and gap symmetry, remain under intense debate. While structural and electronic similarities to cuprates suggest unconventional $d$ -wave pairing, previous theoretical studies have yielded conflicting results. Some density functional theory (DFT) calculations suggest electron-phonon coupling (EPC) is too weak to explain observed critical temperatures ( $T_c$ ), while recent GW-based studies predict phonon-mediated two-gap $s$ -wave superconductivity. Crucially, the role of spin fluctuation (SF) interactions, often cited as the driver for $d$ -wave pairing in cuprates, has not been rigorously investigated in a fully ab initio framework for these materials.

Methodology
The authors present a fully ab initio theoretical study using the Density Functional Theory for Superconductors (SCDFT). This approach extends conventional DFT to account for gauge symmetry breaking in superconductors. The study focuses on optimally doped $Re_{0.8}Sr_{0.2}NiO_2$ ($Re = La, Pr, Nd$).

Key methodological features include:

Equal Footing Treatment: The SCDFT formalism treats electron-phonon coupling (EPC), dynamically screened electron-electron (e-e) Coulomb repulsion, and spin-fluctuation (SF) mediated pairing interactions simultaneously and on an equal footing.
Computational Framework: The calculations utilize the QUANTUM ESPRESSO package for normal-state DFT (LDA) and density functional perturbation theory (DFPT) for phonons and EPC matrix elements. The SCDFT gap equation is solved using the SCTK code.
Approximations: Charge and spin susceptibilities are calculated within the Adiabatic Local Density Approximation (ALDA), though the authors note that results using the Random Phase Approximation (RPA) do not differ significantly.
Controlled "Computer Experiments": To isolate the driving mechanism, the authors perform calculations by selectively turning off specific interaction terms (e.g., SF interaction or Coulomb repulsion) to observe the resulting changes in $T_c$ and gap symmetry.

Key Results

Gap Symmetry and Structure: The calculations reveal that $Re_{0.8}Sr_{0.2}NiO_2$ $R e_{0.8} S r_{0.2} N i O_{2}$ are two-band superconductors characterized by a sign-reversing $d_{x^2-y^2}(\pm)$ $d_{x^{2} - y^{2}} (\pm)$ -wave gap structure.
- The large quasi-two-dimensional Fermi surface (FS) pocket (H-band) at the Brillouin zone (BZ) center exhibits a large $d_{x^2-y^2}$ -wave gap with $B_{1g}$ symmetry.
- The small three-dimensional electron FS pockets (E-band) at the BZ corners also exhibit $d_{x^2-y^2}$ -wave gaps but with much smaller magnitudes and an opposite sign relative to the H-band.
Driving Mechanism: The study demonstrates that superconductivity is driven primarily by spin fluctuations (SF).
- When the SF interaction is turned off, the system initially behaves as a conventional phonon-mediated superconductor with a $T_c$ of $\sim 1.0$ K. However, when the screened Coulomb repulsion is subsequently included in this phonon-only scenario, the $T_c$ is suppressed to a negligible value of $\sim 0.01$ K.
- On the large H-band FS pocket, the SF interaction strength is an order of magnitude stronger than both EPC and screened Coulomb repulsion.
- Conversely, on the small E-band pockets, EPC dominates, but the overall superconductivity is dictated by the SF-mediated pairing on the larger H-band.
Critical Temperatures: The calculated $T_c$ values for La, Pr, and Nd compounds (7.3 K, 12.7 K, and 16.1 K, respectively) agree well with experimental values.
Origin of $d$ -Wave Pairing: The emergence of the nodal $d_{x^2-y^2}$ gap is traced to pronounced peaks in the calculated Lindhard response function (bare susceptibility $\chi_0(q)$ ) near the BZ corners ( $Q \approx (\pi/a, \pi/a)$ ). These peaks indicate strong antiferromagnetic nesting vectors that connect FS regions with opposite gap signs, satisfying the condition for repulsive SF-mediated pairing ( $\Delta_k = -\Delta_{k+Q}$ ).
Comparison with Experiments:
- The calculated Fermi surface topology for LaSrNiO matches Angle-Resolved Photoemission Spectroscopy (ARPES) data.
- The calculated quasiparticle density of states (QPDOS) exhibits a V-shaped gap structure, consistent with nodal superconductivity. This theoretical spectrum aligns well with Scanning Tunneling Spectroscopy (STS) data taken on flat surface regions of NdSrNiO films.
- The calculated gap-to- $T_c$ ratios ( $\Delta_{max}/k_B T_c \approx 2.3$ ) significantly exceed the BCS weak-coupling limit, further supporting unconventional nodal superconductivity.

Significance and Claims
The paper claims to provide the first fully ab initio evidence that infinite-layer nickelates are unconventional $d_{x^2-y^2}$ -wave superconductors driven by spin fluctuations, rather than phonons. By treating EPC, Coulomb repulsion, and SF interactions self-consistently, the authors resolve the ambiguity regarding the pairing mechanism, demonstrating that SF interactions are the dominant force.

The study highlights a discrepancy with previous GW-based predictions of phonon-mediated $s$ -wave superconductivity, attributing this difference to the omission of SF interactions and the semi-empirical treatment of Coulomb repulsion in those earlier works. The authors assert that their predicted properties—including the specific FS topology, nodal gap structure, and quasiparticle density of states—are consistent with most available experimental data. Furthermore, they propose that their predictions for the scanning tunneling spectra of $La_{0.8}Sr_{0.2}NiO_2$ and $Pr_{0.8}Sr_{0.2}NiO_2$ are ready for immediate experimental verification to further validate the proposed $d$ -wave mechanism.

Technical Summary: Ab Initio Prediction of dx2−y2d_{x^2-y^2}dx2−y2​-Wave Superconductivity in Infinite-Layer Nickelates

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Technical Summary: Ab Initio Prediction of $d_{x^2-y^2}$ -Wave Superconductivity in Infinite-Layer Nickelates