A First-principles Study of Weyl Nodal Loop and Multiple Sets of Weyl Points in Trigonal PtBi 2

arXiv:2601.05123 · cond-mat.mtrl-sci, cond-mat.supr-con · Submitted 2026-01-08 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "A First-principles Study of Weyl Nodal Loop and Multiple Sets of Weyl Points in Trigonal PtBi 2".

Mira: Coexistence of surface superconductivity and Fermi arcs in trigonal PtBi2 has recently attracted attention for possible realization of topological superconductivity.

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So we're diving into this paper now, "A First-principles Study of Weyl Nodal Loop and Multiple Sets of Weyl Points in Trigonal PtBi two <ref:2601.05123#pg0,A First-principles Study of Weyl Nodal Loop and Multiple Sets of>." We've got the band structure calculations here, and it seems like they're mapping out some really interesting topological features.

Mira: Exactly. The main thesis centers on the coexistence of surface superconductivity and Fermi arcs in trigonal PtBi2, and how this might connect to realizing topological superconductivity. It claims that their first-principles exploration reveals a Weyl nodal loop and multiple sets of Weyl points that are sensitive to structural parameters like Bi-layer buckling.

Lev: From my side, I'm interested in what these findings mean for actual experimental realization; if we were trying to build something based on this, how robust would those features be under real hardware conditions?

Kai: Right, Lev. The paper is really focusing on those structural sensitivities; they found that while the Weyl nodal loop and Set one Weyl points are pretty solid across different buckling magnitudes, the other sets of Weyl points change their number and location depending on that buckling <ref:2601.05123#pg0>.

Mira: That sensitivity is crucial because it shows how subtle structural variations directly influence the topological landscape, which is what we need to understand for practical applications. They found that switching from a "more" buckled structure to a "less" buckled one changed the count of Weyl points from five sets down to just two sets.

Lev: That level of sensitivity tells us that controlling the fabrication process precisely enough to hit a specific structural configuration is going to be incredibly challenging if those other Weyl point sets are what we're aiming for. What does that imply for error correction schemes?

Kai: It suggests that any device relying on those more sensitive Weyl points would need extremely tight control over the Bi-layer buckling, which brings us to the experimental verification part of this study. They used DFT calculations with PBE31 functionals and an mBJ exchange potential to get these band structures.

Mira: And their computational methodology seems pretty rigorous, utilizing a Monkhorst-Pack mesh of eight times eight times eight k-points and a kinetic energy cutoff of two hundred thirty point three eV for the bulk calculations, plus tight-binding models for the surface spectral function and QPI analysis using WannierTools.

Lev: The computational setup sounds like it's pushing the limits to capture both the bulk electronic structure with SOC and the surface features simultaneously; how does that help us predict what we might see in a real experiment?

Kai: It helps them bridge the gap between theory and what ARPES can measure; they calculated the 2D Fermi surface with Fermi arcs on both (one) terminations and showed good agreement with experimental ARPES data, particularly when using averaged structural parameters <ref:2601.05123#pg0>.

Mira: That agreement is significant because it confirms that their theoretical model of Weyl nodal loops and Fermi arcs aligns well with what experiments are observing in trigonal PtBi2, which was previously a topic attracting attention due to the coexistence of surface superconductivity and Fermi arcs.

Lev: If the QPI patterns match up so well with experimental data at the Fermi energy, that gives us some confidence that the topological features they've mapped out are physically real manifestations of those surface states.

Kai: They also made a prediction regarding what we should look for next; they suggest additional Fermi arc features on the other side of WP projection at higher energies above the Fermi energy, which is something experimentalists need to verify.

Mira: And that prediction is important because it points toward higher-energy topological features that might be accessible in future spectroscopy experiments, opening up new avenues for investigation beyond what's currently seen near the Fermi level.

Lev: So, to summarize this paper on "A First-principles Study of Weyl Nodal Loop and Multiple Sets of Weyl Points in Trigonal PtBi two" it maps out how structural variations affect the number and location of Weyl points while confirming that key features like the WNL and Set one WPs are robust <ref:2601.05123#pg0,A First-principles Study of Weyl Nodal Loop and Multiple Sets of>.

Kai: And they conclude by showing good agreement between their calculated Fermi arcs and QPI data with experimental results, even finding that averaged structural parameters gave them the best match so far.

Mira: The title itself really captures the essence of what they've mapped out: the existence of a Weyl nodal loop and multiple sets of Weyl points within this material system.

Lev: The implication here is that we have a detailed theoretical framework to predict which specific structural configurations might yield which topological states, which is vital for designing materials.

Kai: It gives us a much clearer picture of how those surface superconductivity and Fermi arcs might be linked to the underlying electronic topology in PtBi2.

Mira: Ultimately, this work provides a detailed map of the Weyl features, confirming their coexistence and providing predictions for new high-energy topological features that need experimental validation.

Conclusion: Kai: So, we've been deep in the weeds of those band structures in trigonal PtBi2, and now it’s time to talk about what this whole paper actually means for us out there in the lab and on a bigger scale.

Mira: This study by the authors is essentially mapping out a complex electronic landscape inside PtBi2, specifically identifying how different structural tweaks—like varying the Bi-layer buckling—directly dictate where these topological features show up.

Lev: From my angle, it's fascinating because if we were trying to engineer a system for error correction, knowing that some points are robust and others are super sensitive to geometry tells us exactly where our fabrication tolerances need to be tightest.

Kai: Exactly, Lev. The authors have found that while the main Weyl nodal loop stays put, those other sets of Weyl points shift around quite dramatically based on the buckling parameter; that’s a lot of control for a material system.

Mira: That sensitivity is what makes this work so compelling for condensed matter theory; it shows us that even small structural variations can completely alter the topological phase space we're looking at.

Lev: It gives us a roadmap for synthesis, which is key because running any kind of quantum hardware on top of such a material requires knowing exactly what features are stable and what might vanish under real-world stresses.

Kai: And I’m really excited about the experimental side, Mira; if these calculated Fermi arcs and nodal loops match what ARPES can actually see, it gives us a concrete target for our next cooling and measurement setup.

Mira: That's where the excitement builds; connecting these theoretical predictions to measurable surface states is the bridge we need to cross for realizing topological superconductivity.

Lev: I think the real impact here is on how we approach material design for quantum devices; if we can reliably tune these Weyl points, it opens up new ways to create stable topological qubits or detectors.

Kai: So, basically, this paper gives us a detailed blueprint of the electronic topology in PtBi2 and shows that controlling its structure is the key to unlocking those exotic surface states.

Mira: It’s a powerful demonstration of how fundamental symmetry and physical structure interact to produce these specific nodal features we’ve been hunting for.

Lev: And it sets up a clear challenge for us: we need to design experiments that can probe these highly sensitive regions accurately to verify the structural dependence they found.

Ames National Laboratory · Department of Physics and Astronomy, Iowa State University

cond-mat.mtrl-sci, cond-mat.supr-con

Submitted: 2026-01-08

Updated: 2026-10-02

Comments: 24 pages, 7 figures

Journal ref: Phys. Rev. B 114, 235101 (2026)

DOI: 10.1103/l1ft-gzyd

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 83/100

The gist: Coexistence of surface superconductivity and Fermi arcs in trigonal PtBi2 has recently attracted attention for possible realization of topological superconductivity.

Key concepts

Weyl Nodal Loop (WNL)
A WNL is a specific loop in the band structure that is protected by mirror symmetry. It acts as a topological feature, indicating the presence of Weyl physics in the material's electronic structure. This loop is stable even when certain structural parameters are varied.
Weyl Points (WPs)
These are isolated points in momentum space where the conduction and valence bands touch, acting as sources or sinks of Berry curvature. The study identified six sets of WPs, some robust and others highly dependent on the Bi-layer buckling parameter.
Fermi Arcs (FAs)
Fermi arcs are segments of the Fermi surface observed in surface electronic structure measurements. They are directly associated with inversion-breaking Weyl points located just above the Fermi energy. Their presence confirms the coexistence of superconductivity and topological states on the material's surface.

Terminology

Summary

Coexistence of surface superconductivity and Fermi arcs in trigonal PtBi2 has recently attracted attention for possible realization of topological superconductivity.

The gist

First-principles calculations exploring band crossings in trigonal PtBi2 reveal a Weyl nodal loop (WNL) and multiple sets of Weyl points (WPs), where the number and location of these WPs depend sensitively on structural parameters, specifically the magnitude of Bi-layer buckling.

Computational Methodology

The study employs Density Functional Theory (DFT) calculations using PBE31 exchange-correlation functionals with a modified Becke-Johnson (mBJ) exchange potential, a plane-wave basis set, and the projected augmented wave method implemented in VASP. A Monkhorst-Pack (8×8×8) k-point mesh with a Gaussian smearing of 0.05 eV and a kinetic energy cutoff of 230.3 eV were utilized for band structure calculations. Furthermore, tight-binding models based on maximally localized Wannier functions were constructed to reproduce the bulk band structure including SOC in the range of EF±2eV, involving Pt sd and Bi p orbitals. The surface spectral function, 2D Fermi surface with Fermi arcs of the semi-infinite surface, and quasi-particle interference (QPI) as a joint density of states were calculated using surface Green’s function methods implemented in WannierTools.

Structural Parameter Sensitivity

The primary structural difference between two experimentally reported parameters is the magnitude of Bi-layer buckling. The researchers investigated this by calculating band structures for both the more and less Bi-layer buckling structures as well as the averaged one. They found that while the WNL, bulk gap region, and Set 1 WPs along the -K-A plane are robust, the number and location of the other sets of WPs are sensitive to the Bi-layer buckling. For instance, switching input structural parameters to Ref.12 (more Bi-buckling) reduced the number of WP sets to two, whereas switching to Ref.1 (less Bi-buckling) resulted in five sets of WPs. The Set 1 WPs just above the EF and close to the -M direction are very robust, while the extra sets of WPs at higher energy and close to the -K direction are more susceptible to the change in structural parameters."

Identification of Weyl Features

The study identifies several key topological features:

  1. A Weyl nodal loop (WNL) protected by the Mx mirror symmetry on the ky-kz plane.

  2. Six sets of Weyl points (WPs), which are related by time-reversal, rotation, and mirror symmetries with corresponding chirality. Set 1 WPs are located halfway along the -M-% direction; the other five sets are near the -K-% direction and close to the WNL.

  3. The bulk gap region, identified as the signature from the main band inversion along the -M and A-L directions."

  4. Fermi arcs (FAs) on both (0001) surface terminations, which are associated with inversion-breaking Weyl points (WPs) just above the Fermi energy (EF).

Experimental Agreement and Predictions

The calculated 2D Fermi surface with FAs and QPI showed good agreements with ARPES and experimental QPI. Specifically, the results from the averaged structural parameters provided the best match to these experiments so far. The study also predicts additional FAs on the other side of WP projection at higher energy above the EF, which need to be verified in future experiments. The predicted QPI patterns at EF+100 meV for both terminations are described as new FA features that require further investigation.

Conclusion

The research successfully mapped the WNL, multiple sets of WPs, and Fermi arcs in trigonal PtBi2 across different structural configurations. The findings demonstrate that while certain topological features like the WNL and Set 1 WPs are robust against structural variations, other WP sets are highly sensitive to Bi-layer buckling. This detailed mapping provides a better understanding of experimental observations, confirming the coexistence of surface superconductivity and Fermi arcs and offering predictions for new high-energy topological features. The results from averaged structural parameters were found to be the most consistent with existing ARPES data and experimental QPI spectra.

The data that support the findings of this study are openly available at doi:10.7910/DVN/EWA2OA.

How it works

The investigation begins by calculating band structures in space group P31m (157) using DFT with PBE31 exchange-correlation functionals and mBJ exchange potentials.

Improvements for AI systems

Based on the provided scientific paper, here are specific improvements that can be made to AI systems, categorized by the type of capability they would gain:

)AI System Improvement: Materials Discovery & Topological Material Screening"

  1. [Improvement] Implement a machine learning (ML) model trained on DFT-derived structural parameters and their relationship to Weyl Point (WP) configurations.

  2. [Capability] The improved AI system can predict the specific number and location of Weyl points in novel trigonal PtBi2 variants based solely on input structural descriptors (e.g., Bi-layer buckling magnitude, lattice constants). This allows for rapid, high-throughput screening of hypothetical materials to identify candidates exhibiting topological features like Weyl Nodal Loops (WNL) or specific sets of WPs.

)AI System Improvement: Surface State Characterization & Spectroscopy Simulation"

  1. [Improvement] Develop a deep learning model that maps DFT band structures (especially near the Fermi energy, EF) and Projected Density of States (PDOS) to simulated experimental spectroscopic signatures (ARPES, STS).

  2. [Capability] The improved AI system can analyze raw ARPES or STS data from experiments on PtBi2 surfaces and determine the underlying electronic structure topology—specifically identifying whether observed Fermi arcs correspond to a Weyl Node or a specific set of Weyl Points (e.g., Set 1 WPs vs. higher-energy sets). This moves beyond simple band mapping to direct topological feature classification.

)AI System Improvement: Structural Parameter Sensitivity Analysis"

  1. [Improvement] Create an AI framework that quantitatively assesses the sensitivity of topological features (like the existence or location of WP sets) to subtle structural perturbations, such as small changes in Bi-layer buckling distance (e.g., comparing Ref. 1 vs. Ref. 12).

  2. [Capability] The improved AI system can predict which structural parameters are robust (e.g., the WNL protected by mirror symmetry) and which are sensitive to changes in strain or growth conditions (e.g., the extra WP sets at higher energies). This provides a predictive tool for designing materials with stable topological properties under varying experimental conditions.

)AI System Improvement: Predictive Modeling of Novel Fermi Arc Features"

  1. [Improvement] Utilize the paper's prediction regarding new Fermi arc features at higher energy and their associated QPI patterns as a feature in a generative model.

  2. [Capability] The improved AI system can predict the existence and spatial distribution of novel, high-energy Fermi arcs in PtBi2 surfaces that are not captured by current experimental data or simpler models. This allows researchers to guide future experimental efforts toward specific energy regimes where new topological phenomena might manifest.

)AI System Improvement: Data Interpretation and Model Selection"

  1. [Improvement] Implement a comparative analysis module using the paper's findings on the best match between theoretical calculations (DFT/Wannier functions) and experimental data (ARPES/QPI).

  2. [Capability] The improved AI system can automatically compare different theoretical methodologies (e.g., PBE vs. D3 vs. r2SCAN+rVV10) against a dataset of experimental QPI patterns to recommend the most physically accurate functional or structural parameter set for a given sample, significantly reducing the guesswork in interpreting complex experimental results.

Abstract

Coexistence of surface superconductivity and Fermi arcs in trigonal γ-PtBi 2 has recently attracted attention for possible realization of topological superconductivity. The Fermi arcs on the two different (0001) surface terminations have been associated with the set of Weyl points just above the Fermi energy (E F). Here using first-principles calculations to explore the band crossings over the full Brillouin zone between the nominally highest valence and lowest conduction bands in γ-PtBi 2, we study the Weyl nodal loop (WNL) and multiple sets of Weyl points (WPs). The main difference between the two reported experimental structural parameters is the magnitude of Bi-layer buckling. While the WNL, bulk gap region and the set of Weyl points just above the E F are robust, the number and location of the other sets of WPs depend sensitively on the structural parameters with different magnitude of Bi-layer buckling. Besides calculating the 2D Fermi surface with Fermi arcs and quasi-particle interference (QPI) around the E F in good agreements with ARPES and experimental QPI, we also predict new Fermi arc features at higher energy.

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