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arxiv: 2605.31501 · v1 · pith:KCGBFCQQnew · submitted 2026-05-29 · ❄️ cond-mat.supr-con

Kohn-Luttinger Superconductivity of Weyl Fermi Arcs in PtBi₂

Reuel Dsouza , Nikolaos Parthenios , Brian M. Andersen , Morten H. Christensen This is my paper

Pith reviewed 2026-06-28 19:59 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords Kohn-Luttinger superconductivityWeyl Fermi arcsPtBi2i-wave symmetrytopological superconductivitysurface statesunconventional pairing
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0 comments X

The pith

Electronically mediated pairing on Weyl Fermi arcs in PtBi₂ selects an i-wave superconducting state with an intra-arc node.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies the Kohn-Luttinger method to compute the pairing interaction arising from repulsive electron-electron interactions on the surface states of the Weyl semimetal PtBi₂. It shows that an i-wave symmetry emerges as the leading instability over a broad region of parameter space and places a node precisely at the center of each Fermi arc. This symmetry matches the node structure reported in recent experiments on the material's topological surface states. The result holds across changes in interaction strength and chemical potential, indicating that the surface arcs themselves can host unconventional superconductivity without bulk or phonon assistance.

Core claim

In a model of the surface states of the Weyl semimetal PtBi₂, the Kohn-Luttinger pairing interaction leads to a leading superconducting instability with i-wave symmetry that features a node at the center of each Fermi arc, and this state remains the leading one over a wide range of interaction parameters and chemical potentials.

What carries the argument

Kohn-Luttinger calculation of the momentum-dependent pairing interaction restricted to the Weyl Fermi arc surface states.

If this is right

  • The i-wave state remains the leading instability across a wide range of electronic interaction parameters and chemical potentials.
  • The mechanism supplies a possible explanation for the observed topological superconductivity with intra-arc nodes on the PtBi₂ surface.
  • Repulsive interactions on the surfaces of other Weyl semimetals can generate analogous arc-hosted superconducting instabilities.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same surface-state approach could be used to predict pairing symmetries on the arcs of related noncentrosymmetric Weyl materials.
  • Tunneling or thermal transport experiments that resolve the gap along individual arcs would directly test the intra-arc node location.
  • If phonon contributions prove comparable in magnitude, the competition between channels would shift the phase diagram boundaries.

Load-bearing premise

The electronically mediated pairing interaction on the Fermi arcs is accurately captured by the Kohn-Luttinger approach applied to a model of the surface states, with no dominant contributions from phonons, disorder, or bulk states.

What would settle it

Surface-sensitive measurements on PtBi₂ that find either a nodeless gap at the arc center or a leading pairing symmetry other than i-wave.

Figures

Figures reproduced from arXiv: 2605.31501 by Brian M. Andersen, Morten H. Christensen, Nikolaos Parthenios, Reuel Dsouza.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Recent experimental observations in the noncentrosymmetric Weyl semimetal PtBi$_2$ indicate unconventional superconductivity hosted by topological surface states -- Weyl Fermi arcs -- with a node at the center of each arc. Focusing on these Fermi arcs, we calculate the electronically mediated pairing interaction using a Kohn-Luttinger approach and find that, in a large region of the phase diagram, the leading superconducting instability has an $i$-wave symmetry featuring precisely such an intra-arc node. We study the dependence of the leading superconducting instabilities on electronic interaction parameters and chemical potential and show that the $i$-wave state is robust to changes in the model parameters. Our results provide a possible mechanism for the observation of topological $i$-wave superconductivity on the surface of PtBi$_2$ and may have implications for the broader landscape of superconducting instabilities arising from repulsive interactions on the surfaces of Weyl semimetals.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript applies the Kohn-Luttinger formalism to an effective model of the Weyl Fermi arcs in the noncentrosymmetric Weyl semimetal PtBi₂. It reports that, over a substantial region of interaction-parameter and chemical-potential space, the leading superconducting instability is an i-wave state whose gap function exhibits a node at the center of each arc, thereby providing a possible electronic mechanism for the nodal surface superconductivity observed in experiment.

Significance. If the surface-only approximation is justified, the work supplies a concrete, parameter-robust microscopic route to higher-angular-momentum pairing on topological Fermi arcs and thereby enlarges the set of known instabilities that can arise from repulsive interactions on the surfaces of Weyl semimetals. The explicit mapping of the phase diagram with respect to interaction strength and doping constitutes a falsifiable prediction that can be tested by future surface-sensitive probes.

major comments (1)
  1. [§3, Appendix A] §3 and Appendix A: The effective 2D Hamiltonian for the arcs is derived and the Kohn-Luttinger bubble diagram is evaluated with a momentum-independent or short-range repulsion, yielding an i-wave eigenvector. No quantitative estimate, cutoff, or scaling argument is supplied for the relative magnitude of pairing mediated by bulk Weyl cones or by acoustic/optical phonons. Because the reported i-wave state is claimed to be the leading instability, an explicit comparison showing that these additional channels remain sub-dominant is required; without it the central claim rests on an unverified assumption.
minor comments (1)
  1. The notation for the arc-centered node in the gap function could be made more explicit in the figure captions to facilitate direct comparison with the experimental reports cited in the introduction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the positive evaluation of its significance. We address the single major comment below.

read point-by-point responses

  1. Referee: [§3, Appendix A] §3 and Appendix A: The effective 2D Hamiltonian for the arcs is derived and the Kohn-Luttinger bubble diagram is evaluated with a momentum-independent or short-range repulsion, yielding an i-wave eigenvector. No quantitative estimate, cutoff, or scaling argument is supplied for the relative magnitude of pairing mediated by bulk Weyl cones or by acoustic/optical phonons. Because the reported i-wave state is claimed to be the leading instability, an explicit comparison showing that these additional channels remain sub-dominant is required; without it the central claim rests on an unverified assumption.

    Authors: We agree that the surface-only approximation underlying the central claim merits explicit justification. The manuscript calculates the leading instability strictly within the effective 2D model of the Weyl Fermi arcs; the i-wave state is shown to be leading over a substantial region of interaction and doping parameters inside that model. The experimental reports of surface superconductivity with the matching nodal structure provide phenomenological support for focusing on arc-mediated pairing. In the revised manuscript we will insert a new paragraph (in §3) that supplies scaling arguments: (i) the bulk Weyl cones project to a gapped continuum on the surface and their contribution to arc pairing is suppressed by the finite penetration depth of the arc wavefunctions; (ii) long-wavelength acoustic phonons generate an essentially momentum-independent attraction that would favor s-wave pairing, inconsistent with the observed intra-arc nodes. While a fully quantitative comparison would require a microscopic 3D calculation including specific electron-phonon matrix elements (outside the present scope), the added discussion will make the assumptions and their justification transparent. We view this as a partial revision that strengthens the presentation without changing the reported results. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is model-driven calculation

full rationale

The paper constructs an effective surface Hamiltonian for the Weyl arcs, computes the pairing interaction via the standard Kohn-Luttinger bubble diagram (second-order perturbation in the interaction), and solves the resulting eigenvalue problem for the leading instability. The i-wave eigenvector with intra-arc node emerges from this procedure applied to the model parameters and chemical potential; it is not equivalent to the inputs by definition, nor obtained by fitting a subset of data and relabeling the output as a prediction. No load-bearing self-citations, uniqueness theorems from the same authors, or ansatzes smuggled via prior work are described. The central claim remains a direct (if approximate) consequence of the stated microscopic model and remains falsifiable by comparison to other channels or experiments.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the Kohn-Luttinger approximation to the Fermi-arc model and on the assumption that electronic interactions dominate the pairing; interaction parameters and chemical potential are varied but not specified as fitted values.

free parameters (2)
  • electronic interaction parameters
    Dependence on these parameters is explicitly studied in the abstract.
  • chemical potential
    Dependence on chemical potential is explicitly studied in the abstract.
axioms (1)
  • domain assumption Kohn-Luttinger approach accurately computes the effective pairing interaction from repulsive forces on Weyl Fermi arcs
    The abstract invokes the method without deriving its validity for this system.

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discussion (0)

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