PaperlayerView exact revision on arXiv

Source-linked AI summary

Agentic Fusion of Large Atomic and Language Models to Accelerate Superconductor Discovery

Mingze Li, Yu Rong, Songyou Li, Lihong Wang, Jiacheng Cen, Liming Wu, Anyi Li, Zongzhao Li, Qiuliang Liu, Rui Jiao, Tian Bian, Pengju Wang, Hao Sun, Jianfeng Zhang, Ji-Rong Wen, Deli Zhao, Shifeng Jin, Tingyang Xu, Wenbing Huang

arXiv:2604.23758v3cs.LGcond-mat.mtrl-sci

TL;DR

Materials discovery still requires difficult decisions about experimentally viable targets that combine atomic-scale numerical computation with high-level semantic reasoning. ElementsClaw addresses this gap by orchestrating specialized Large Atomic Models derived from Elements with Large Language Model reasoning. Applied to superconductors, it reconstructs missing knowledge, screens 2.4 million crystals to identify 68,000 high-confidence candidates, and experimentally validates four novel superconductors.

  • Problem

    Choosing viable experimental targets remains difficult because materials discovery requires both atomic-scale numerical computation and high-level semantic reasoning.

  • Method

    ElementsClaw coordinates specialized Large Atomic Model tools derived from Elements with Large Language Model reasoning, literature synthesis, and human oversight.

  • Results

    ElementsClaw identified 68,000 high-confidence candidates from 2.4 million crystals, rediscovered 66 database-absent superconductors, and experimentally validated four novel superconductors.

  • Takeaways & Limitations

    The study demonstrates an experimentally grounded agentic workflow that integrates numerical modeling, semantic reasoning, literature reconstruction, and candidate discovery for superconductors.

  • Takeaways & Limitations

    Standard DFT training data limit predictive fidelity for strongly correlated unconventional superconductors, while literature extraction remains vulnerable to hallucinations and corpus bias.

Abstract

from arXiv · show

Artificial intelligence has accelerated materials discovery through high-throughput prediction and generation, yet the decision problem remains a formidable bottleneck. While current AI systems readily propose millions of candidates, navigating the decision regarding a viable experimental target requires resolving multi-dimensional judgments across atomic-scale numerical computation and high-level semantic reasoning. Here we present ElementsClaw, an agentic framework for materials discovery that orchestrates a suite of Large Atomic Model (LAM) tools finetuned from our proposed 1-billion-parameter model Elements for numerical computation, while leveraging Large Language Models (LLMs) for semantic reasoning. Applied to superconductors, ElementsClaw rediscovers 66 experimentally verified superconductors that are absent from the standard SuperCon3D database. Scaling to 2.4 million equilibrium crystals, ElementsClaw identifies 68,000 high-confidence candidates in just 28 GPU hours (https://developer.damo-academy.com/material), expanding known superconducting space by orders of magnitude compared to datasets curated over decades. Guided by the agent's reasoning, we experimentally synthesize and verify four novel superconductors: the motif-guided Zr$_3$ScRe$_8$ ($T_c$ = 6.5 K), the de novo generated HfZrRe$_4$ ($T_c$ = 5.9 K), the structurally reinterpreted Zr$_4$VRe$_7$ ($T_c$ = 3.5 K), and the database-latent Hf$_{21}$Re$_{25}$ ($T_c$ = 2.5 K). Together, our results establish a knowledge integrated, autonomously orchestrated, and experimentally grounded paradigm for materials discovery.

1 Introduction

Materials discovery is bottlenecked not only by candidate generation but by selecting experimentally viable targets across numerical computation and semantic reasoning. ElementsClaw addresses this challenge by coordinating specialized atomic models with language-model reasoning, then applies the framework to reconstruct and expand superconducting knowledge.

  • Motivation: Selecting viable experimental targets requires reconciling atomic-scale numerical computation with high-level semantic reasoning.The relevant judgments include structure generation, property prediction, stability evaluation, novelty, and synthetic feasibility.
  • Framework: The framework autonomously coordinates prediction, literature synthesis, hypothesis formulation, and candidate rejection instead of treating discovery as isolated processes.The agent can decide what to predict, where to retrieve literature, when to generate structures, and when to reject unstable or synthetically inaccessible candidates.
  • Framework: ElementsClaw coordinates specialized Large Atomic Models with Large Language Models to combine numerical computation and semantic reasoning under human oversight.Its Elements foundation is pretrained on 125 million structures and supports specialized tools for property and structure prediction.
  • Superconductor application: 66 experimentally verified superconductors absent from the standard SuperCon3D database were rediscovered through literature reasoning.This result addresses incompleteness in existing superconductivity databases.
  • Superconductor application: 68,000 high-confidence candidates were identified by screening 2.4 million crystals, alongside four experimentally validated novel superconductors.The reported validated compounds are Zr3ScRe8, HfZrRe4, Zr4VRe7, and Hf21Re25.

2 Results

ElementsClaw combines pretrained atomic modeling, language-based literature reasoning, and agentic orchestration to screen, refine, and experimentally validate superconducting candidates. Across retrospective and prospective discovery, it recovers missing superconductors, supports accurate property prediction, and identifies experimentally verified phases while exposing limitations from magnetic interactions.

  • 2 Results: ElementsClaw orchestrates specialized atomic tools and language-model reasoning across multi-stage materials discovery.Its tool base includes Elements-T for superconducting properties, Elements-C for classification, Elements-E for stability, and Elements-G for structure generation.
  • 2 Results: Elements achieves state-of-the-art or leading performance across property prediction, interatomic potential estimation, and crystal structure prediction tasks.It outperforms the prior leading method by approximately 30% on QM9 HOMO and LUMO prediction, achieves the highest force-prediction accuracy across evaluated DPA-2 categories, and more than doubles DiffCSP’s MPTS-52 Match Rate.
  • 2 Results: Elements-T predicts superconductivity-related properties with a Tc MAE of 0.992 and R2 of 0.816 on a DFT-derived dataset.High-Tc structures cluster in the learned embedding space, while the model performs best for higher-symmetry crystal lattices.
  • 2 Results: ElementsClaw recovered 66 literature-verified superconductors absent from SuperCon3D, representing 41.8% of the 158 verified positives.Some recovered entries have experimental Tc values above 10 K, showing that the missing records include more than marginal low-temperature cases.
  • 2 Results: Superconductor-identification precision rose from 15.9% at low predicted Tc to 72.4% for candidates with predicted Tc > 15 K.The authors characterize Elements-T as a ranking model that enriches superconducting candidates, despite larger absolute Tc errors among high-Tc outliers.
  • 2 Results: ElementsClaw identified and experimentally validated superconducting phases in the Hf–Zr–Re system, including database-latent Hf21Re25 and generated candidates.Hf21Re25 showed a superconducting transition near 2.0 K, while generated HfZrRe4 and related phases exhibited magnetic onsets near 5.9 K or 5.7 K; the excluded HfZrRe formed by phase separation.

3 Discussion

ElementsClaw combines Large Atomic Models, Large Language Models, and human oversight into an agentic discovery framework that autonomously builds specialized tools and navigates superconducting chemical spaces. Its reported capabilities include large-scale candidate screening, experimental validation, structural reinterpretation, instability exclusion, and prospective extension to other materials domains.

  • Discussion: ElementsClaw combines Elements-based Large Atomic Models with LLM reasoning and human oversight to coordinate materials-discovery workflows.Elements supplies specialized numerical tools, while LLMs handle literature-derived insights and heuristic design judgments.
  • Discussion: The framework autonomously refines task-specific capabilities by using empirically extracted data to specialize tools such as the Elements-C classifier.This self-evolution is presented as a transferable approach for exploring uncharted chemical spaces.
  • Discussion: 66 literature-reported superconductors absent from the standard SuperCon database were identified, while experiments validated unverified phases and novel candidates reaching transition temperatures of 6 K.The validation covered the Hf–Zr–Re and V–Zr–Re systems and included structural reinterpretation and motif-preserving substitution searches.
  • Discussion: 68,000 high-confidence candidates emerged from screening over 2.4 million stable crystals, expanding the known superconducting space.The framework links this broad screening landscape to focused experimental selection.
  • Discussion: The framework remains limited by standard DFT data for strongly correlated superconductors, LLM hallucinations and corpus biases, and ambient-pressure synthesis assumptions.These boundaries affect unconventional superconductors, literature coverage, and extreme-condition phases such as high-pressure hydrides.
  • Discussion: ElementsClaw is proposed as adaptable beyond superconductors to battery electrolytes, heterogeneous catalysts, and thermoelectric materials.The paper anticipates increasingly autonomous discovery loops when such systems are integrated with self-driving laboratories.

4 Methods

Elements represents molecules and crystals as geometric graphs, incorporates periodic interactions and lattice information, and is pretrained on balanced stable and unstable atomic configurations. Elements then uses equivariant message passing and human-guided screening rules to support superconductivity discovery and experimental synthesis.

  • Unified geometric representation: Elements represents molecules and periodic crystals as geometric graphs using atomic numbers, coordinates, edges, and lattice matrices.For periodic systems, atom positions in translated cells are given by x_i + Lz.
  • Periodic graph construction: Crystal graphs use cutoff-based multi-edges across periodic boundaries plus three self-loops per atom to encode lattice information efficiently.The complete crystal edge set merges periodic cutoff edges with self-loop edges associated with the three lattice directions.
  • MCDB pretraining dataset: 125.21 million atomic configurations form MCDB, including 106.55 million crystals and 18.66 million molecular geometries.The dataset combines stable structural states with unstable configurations annotated to provide gradient information for learning non-equilibrium behavior.
  • Dataset curation: MCDB aggregates public repositories and applies filters of forces ≤20 meV/Å and energy above hull ≤0.08 eV atom−1 for equilibrated subsets.The resulting dataset covers nearly all chemically relevant elements except heavy radioactive elements and actinides.
  • Elements architecture: Elements uses graph construction, embedding, stacked equivariant message passing, and task-specific output heads for molecular and crystalline modeling.Atomic embeddings derive from one-hot atomic numbers, while edge embeddings encode local geometry through interatomic distances and atomic numbers.
  • Screening and synthesis: The screening prompt requires exact structural matching and manual verification, while Hf21Re25 synthesis requires varying starting composition to suppress HfRe2 formation.A starting Hf:Re ratio of 1.2:1 yields the optimal phase purity for Hf21Re25.

5 Author Contributions Statement

The authors divide responsibility across model and agent development, experimentation, engineering, computation, and manuscript preparation under senior supervision.

  • M.L., Y.R., and S.L. conceived ElementsClaw, trained and tested it, developed the software, and drafted the manuscript under W.H.’s supervision.
  • L.Wa. conducted materials synthesis and experimental validation under S.J.’s supervision.
  • T.B. engineered the agentic system under T.X.’s supervision, while D.Z. provided computational resources and technical guidance.
  • J.C., L.Wu., and A.L. contributed to exploration of the model architecture.

Contents of Supplementary Information

The supplementary information details Elements’ symmetry-aware geometric modeling, architectural choices, crystal-structure generation, and supporting dataset distributions.

  • A.1 Geometric Graphs and Symmetry: Atomic systems are represented as geometric graphs G = (A, X, E), with Euclidean transformations acting on coordinates while preserving atomic identities.
  • A.1 Geometric Graphs and Symmetry: E(3)-invariant mappings predict frame-independent scalar properties, whereas E(3)-equivariant mappings predict vector or tensor fields such as forces.
  • A.2 Architectural Background: Elements adopts EquiformerV2 as its backbone for scalable equivariant attention and efficient tensor-product computation, adding Long-Range Residual Connections for models up to 1B parameters.
  • A.3 Crystal Structure Prediction: Crystal structure prediction jointly generates lattice matrices, atomic types, and fractional coordinates through diffusion-based modeling.
  • A.3 Crystal Structure Prediction: DiffCSP denoises in fractional-coordinate space, while MatterGen computes interactions in Cartesian space to use physically valid distances and angles.
  • B.1 Pretrained Datasets: Supplementary Figure B.1 summarizes dataset proportions, unstable-structure energy and force distributions, and elemental coverage across the periodic table.

B.1.1 Non-equilibrium Datasets

The supplementary datasets span perturbed molecular and crystal configurations, equilibrium structures, and large curated sources designed to represent potential-energy surfaces and stable materials.

  • Non-equilibrium datasets: Non-equilibrium datasets sample high-energy, high-force configurations so models learn restoring forces away from equilibrium.
  • Crystal Datasets (Non-Equilibrium): OMAT-24 generates crystal perturbations with Gaussian noise and includes relaxation trajectories spanning high- to low-energy states.
  • Crystal Datasets (Non-Equilibrium): OMAT-24 is described as a premier source for universal force-field and energy-prediction training, supporting generalization across unseen compositions.
  • Molecular Datasets (Non-Equilibrium): ANI-1x targets vibrational modes and near-equilibrium distortions in organic molecules through active-learning-based dataset construction.
  • Crystal Datasets (Equilibrium): Equilibrium crystal data combine approximately 5.75 million structures from multiple high-confidence databases and curated sources.
  • Crystal Datasets (Equilibrium): ALEXANDRIA-S applies Ehull ≤0.08 eV/atom filtering to retain 1.4 million equilibrium or near-equilibrium structures.
  • Crystal Datasets (Equilibrium): Additional equilibrium collections include OQMD-S, JARVIS-QETB-S, MPF-S, and NOMAD, with NOMAD screening 3.3 million equilibrium structures.
  • Molecular Datasets (Equilibrium): Equilibrium molecular data provide accurate three-dimensional conformers for denoising tasks.

B.2 Downstream Datasets

The downstream datasets evaluate molecular and crystal properties, unstable-state modeling, crystal generation, transport, superconductivity, and leakage-controlled classification.

  • Molecular datasets: QM9 contains approximately 134,000 stable organic molecules used to evaluate molecular electronic-property prediction.
  • Crystalline materials: Matbench subsets cover metallicity, dielectric response, band gaps, and perovskite formation energies relevant to electronic and superconducting behavior.
  • Potential-energy surfaces: DPA-2 datasets assess unstable states and potential-energy surfaces across crystals, molecules, adsorbates, and mixtures.
  • Generative tasks: MP-20 contains 45,231 stable crystals with at most 20 atoms per unit cell, while MPTS-52 contains 40,476 larger-unit-cell structures.
  • Transport properties: JARVIS-DFT transport tasks predict the Seebeck coefficient, thermal conductivity, and electrical conductivity.
  • Superconductivity datasets: The superconductivity resources combine DFT-based Tc data, SuperCon3D structural mappings, and agent-derived positive and negative structural instances.
  • Superconductivity datasets: The agent-derived dataset contains 1,138 positive and 2,026 negative structural entries after retaining distinct literature-reported structures.
  • Dataset partitioning: Splitting occurs by unique unaugmented structures, assigning all augmented variants together to training or validation to prevent leakage.

C Training Strategies

Elements combines denoising, energy, force, property, and generative objectives through task-specific heads and physically matched processing choices.

  • Denoising: Gaussian noise perturbs atomic coordinates and lattice vectors to train separate denoising heads.The perturbations use position and cell noise scales σpos and σcell.
  • Energy and force prediction: Energy prediction uses separate molecular and crystal heads, with per-dataset standardization to accommodate differing energy scales.The total energy is obtained by sum pooling over atoms.
  • Energy and force prediction: A unified force head predicts atom-wise forces across molecular and crystalline modalities using an SO(3)-equivariant graph-attention architecture.The force head has independent learned parameters from the coordinate denoising head.
  • Multi-task objective: The total pretraining loss weights position and cell denoising equally, energy fivefold, and force twentyfold.The objective is a weighted sum of coordinate, lattice, molecular-energy, crystal-energy, and force MAEs.
  • Downstream adaptation: For macroscopic properties such as Tc, Elements replaces the final projection head and uses mean pooling to preserve intensive scaling.The modified output maps intermediate features to the target-property channels.
  • Crystal structure prediction: Crystal structure generation jointly diffuses lattice matrices and Cartesian coordinates with a prior-informed process that avoids near-zero lattice volumes.The approach is designed to prevent severe atomic overlap and neighbor-graph edge explosion.

D.1 Model Architecture

Elements uses a geometric Transformer architecture whose capacity, optimization, and finetuning schedules vary across model sizes and downstream datasets.

  • Architecture: The 1B-parameter Elements architecture uses 12 Transformer blocks, 24 attention heads, a 12 Å cutoff, and 512 radial bases.Its feature configuration includes mixed-degree embeddings and a point-sample resolution R = 2.
  • Architecture scaling: Scaling experiments vary model capacity from 28M to 544M parameters through compound changes in depth, width, and geometric expressivity.The model family supports evaluation of performance scaling across parameter counts.
  • Pretraining: Pretraining uses AdamW with cosine scheduling, a maximum learning rate of 2 × 10^-4, batch size 4096, and 2 epochs.Training uses 64 NVIDIA H100 GPUs for 286 hours.
  • Pretraining: The pretraining objective combines energy, force, and coordinate/lattice denoising losses with coefficients λE = 5, λF = 20, and λpos = λcell = 1.The loss is applied to molecular and crystal energy terms separately.

E.1 Architecture Ablations and Scaling Laws

Ablations show that model connectivity, mixed-domain data, and larger training sets improve Elements’ predictive or denoising performance, while finer grids are not necessary for accuracy.

  • Data scaling: Training on 1M structures achieves a potential-energy MAE of 0.01825 eV, compared with 0.03697 eV on 0.25M structures.The comparison uses a fixed 28M-parameter model and 15 training epochs.
  • Grid-resolution ablation: Reducing grid resolution improves efficiency while lowering MAE from 0.02224 eV to 0.02161 eV.The result indicates that finer grid resolution is not strictly necessary for essential geometric features.
  • Architecture ablations: Long-range connections marginally reduce potential-energy MAE from 0.02197 eV to 0.02161 eV.The change is described as a consistent improvement in model expressivity.
  • Architecture ablations: Self-loops reduce position denoising loss from 0.07721 to 0.06865 and cell loss from 0.1412 to 0.1263.The result highlights the role of self-referential message passing in structural generation.
  • Data ablation: Mixed-domain training lowers potential-energy MAE from 0.02161 eV on unstable crystals alone to 0.01900 eV with molecules and stable crystals.Molecular data alone yields 0.02112 eV, while stable crystals alone yields 0.01930 eV.

E.2 Property Prediction of Stable Systems

Elements performs strongly across stable-property prediction, atomic energy and force estimation, and crystal structure generation, with particularly strong results on QM9 and MPTS-52.

  • QM9: Elements reaches 10 meV HOMO MAE and 8.9 meV LUMO MAE on QM9.These results improve on GotenNet’s 13.4 meV and 12.2 meV errors, respectively.
  • Matbench: Elements ranks first or second across all four Matbench tasks and achieves state-of-the-art results on MP_is_metal and Mp_gap.It remains competitive on Perovskites and Dielectric while maintaining broader cross-property consistency.
  • Crystal structure prediction: On MPTS-52, Elements raises crystal-structure Match Rate from DiffCSP’s 12.19% to 24.95%.The reported result is more than a two-fold improvement on the challenging dataset.

E.5 Superconductivity Validation

Elements evaluates superconductivity prediction under scaling and pretraining, finding that pretraining is decisive across critical-temperature and bandgap benchmarks while Elements-C achieves strong classification performance.

  • DFT-calculated Tc benchmark: Pretraining reduces M.A.D. Tc error from 1.62 K to 1.39 K with capacity scaling, then to 1.16 K for pretrained Elements.For direct Tc, the pretrained model reaches 0.98 K error.
  • Jarvis bandgap benchmark: 0.09 eV MAE makes pretrained Elements the best bandgap predictor, outperforming PotNet at 0.127 eV on the Jarvis dataset.Models trained from scratch do not surpass ALIGNN or PotNet.
  • Superconductivity classification: Elements-C achieves 95.6% precision, 98.7% recall, and a 0.971 F1 score on held-out positive and negative instances.The validation set contains only 2 false negatives among 155 actual positive instances.
  • Superconductivity classification: The classification results indicate that Elements-C can identify nearly all genuine superconductors while limiting the number of false leads.The authors characterize positive predictions as high-probability candidates for prioritization.

F.1 The Dialogue with ElementsClaw for Superconductor Recommendation

ElementsClaw combines interactive classification, visualization, compositional analysis, and feasibility filtering to move from unverified structures toward experimentally actionable superconductivity candidates.

  • Initial screening: 314 of 981 unverified structures receive positive Elements-C logits during initial screening.The screened results are saved for subsequent analysis.
  • Composition analysis: t-SNE analysis identifies a high-scoring region enriched in Zr, B, Si, Re, Ru, and Nb, guiding compositional exploration.The region is defined by y < x + 5 and is enriched with Class 1 candidates.
  • Composition analysis: Re has the highest mean SC_logit among partners paired with Zr, at +4.176 across three Zr–Re candidates.The two cited Zr–Re examples are Zr2VRe3 and Zr21Re25.
  • Feasibility filtering: Sequential filtering reduces 314 positive samples to a final database-screened set after removing known, duplicated, toxic, mismatched, unstable, and impractical entries.The intermediate counts include 273 after removing known materials and 139 after excluding theoretical or hard-to-synthesize structures.
  • Candidate recommendation: The dialogue ranks Hf21Re25, Zr2VRe3, and Zr21Re25 highest, with superconducting probabilities of 0.986, 0.986, and 0.984.Their predicted Tc values are 6.91, 11.07, and 8.22, respectively.
  • Candidate recommendation: The workflow initially recommends 53 candidates and selects Zr2VRe3, Zr21Re25, and Hf21Re25 for synthesis in the Zr–Re-focused search.The pipeline includes deduplication, toxicity removal, exclusion of known materials, and phase-stability verification.

F.3 Superconductivity Validation on Experimental Dataset

On experimental Tc prediction, Elements is evaluated with ten-fold cross-validation and candidate screening, while auxiliary DFT supervision improves prediction performance and the generated list includes high-Tc proposals.

  • Training setup: The experimental-Tc training setup uses 1000 epochs, batch size 256, and hybrid-loss coefficients of 5 for λ and 1 for ωlog.These settings adapt training to sparse and noisy experimental data.
  • Experimental Tc prediction: Elements reaches 0.732 MAE on log(Tc), surpassing the reproduced competing baselines without auxiliary guidance.Evaluation uses the SuperCon3D dataset and a rigorous 10-fold cross-validation scheme.
  • Experimental Tc prediction: 0.703 MAE on log(Tc) and 0.548 R2 are achieved when DFT-calculated Tc is added as auxiliary supervision.The base Elements model achieves 0.732 MAE on log(Tc) without auxiliary guidance.

F.4 First-Principles Analysis and Computational Efficiency

The paper compares data-driven experimental prediction with first-principles analysis, reports detailed DFT and electron–phonon calculations for Zr2VRe3, and validates six synthesized compounds experimentally.

  • DFT methodology: DFT calculations use VASP with GGA, PAW interactions, a 600 eV cutoff, and convergence thresholds for forces and total energy.Brillouin-zone integration uses Monkhorst-Pack meshes with maximum spacing 2π × 0.03 Å.
  • Electron–phonon analysis: DFPT calculations in Quantum ESPRESSO evaluate phonons and electron–phonon coupling for Zr2VRe3 before estimating theoretical Tc.The Allen-Dynes modified McMillan formula uses λ, ωlog, and µ* = 0.1.
  • First-principles versus experiment: Zr2VRe3 lacks bulk superconductivity experimentally despite a theoretical transition signal attributed to a trace impurity phase.The discrepancy is linked by the authors to phase stability, defects, impurities, and non-ideal stoichiometry.
  • Computational efficiency: The Elements workflow is presented as substantially faster than traditional DFT for high-throughput screening, using Zr2VRe3 as the example system.The passage states that standard DFT calculations typically require approximately 2 days.
  • Experimental validation: Six synthesized compounds show superconducting transitions with Tc values of approximately 6.5, 5.9, 5.9, 5.7, 3.5, and 2.5 K.The compounds are characterized using refined crystal structures, PXRD with Rietveld refinement, and magnetic susceptibility.

F.5 Structural Validation, Magnetic, and Electrical Transport Characterization

Structural, magnetic, and electrical measurements validate bulk superconductivity in several synthesized compounds, while also revealing a model limitation for magnetic-element systems. Demagnetization corrections and complementary transport measurements help interpret the superconducting transitions.

  • Magnetic characterization: Demagnetization correction uses the cylindrical sample geometry, with N determined from the measured height and diameter before obtaining intrinsic susceptibility.The corrected susceptibility is derived from the apparent measured susceptibility and the equivalent demagnetization factor.
  • Structural validation: Six compounds show structurally validated bulk superconductivity through refined crystal structures, PXRD with Rietveld refinement, and temperature-dependent magnetic susceptibility.The compounds are Zr3ScRe8, HfZrRe4, HfZr3Re8, Hf3ZrRe8, Zr4VRe7, and Hf21Re25.
  • Electrical transport: Electrical transport measurements find transitions near 6.8 K for Zr3ScRe8 and 3 K for Hf21Re25, slightly above magnetic-susceptibility values of approximately 6.5 K and 2.5 K.The measurements use a standard four-probe method on polished bulk metallic ingots.
  • Caveat: Zr2VRe3 lacks bulk superconductivity despite an approximately 8.5 K diamagnetic transition, because its shielding fraction is extremely small and magnetic V introduces uncaptured pair-breaking effects.The response is attributed to a trace impurity phase rather than the target material, highlighting a limitation of the underlying density-functional-theory-based training data.
  • Electrical transport: The transport–magnetic transition offset is consistent with zero resistance requiring a continuous superconducting percolation path, which forms above the onset of bulk diamagnetism.This interpretation is stated as physically reasonable for the observed difference between measurement modalities.
Loading 2604.23758v3…