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arxiv: 2606.02371 · v1 · pith:Y2YR6PLPnew · submitted 2026-06-01 · ❄️ cond-mat.supr-con

Phonon-driven nodal surface superconductivity of Fermi arcs

Francesco Buccheri , Alessandro de Martino , Jeroen van den Brink This is my paper

Pith reviewed 2026-06-28 12:10 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords Fermi arcsWeyl semimetalssurface superconductivityphonon pairingnodal gapCoulomb screeningPtBi2
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The pith

Phonon interactions with surface and bulk modes produce nodal superconductivity on disconnected Fermi arcs when Coulomb screening is weak.

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

The paper shows that surface superconductivity on Fermi arcs in time-reversal-invariant Weyl semimetals can be driven by electrons coupling to both surface and bulk phonons, even when the bulk remains normal. Two pairing channels compete: intra-arc pairing within each disconnected arc and inter-arc pairing that connects them. Their relative strength is set by how effectively the surface screens long-range Coulomb repulsion. Weak screening plus arc disconnection forces nodes into the gap function, reproducing the momentum-space structure seen in recent photoemission data on PtBi2. The work identifies surface screening as a tunable parameter that can alter the gap size, symmetry, and critical temperature.

Core claim

In time-reversal-invariant Weyl semimetals the superconducting gap on Fermi arcs is generated by electron-phonon coupling to both surface and bulk phonons. Intra-arc and inter-arc pairing channels compete; their balance is controlled by the efficiency of Coulomb screening at the surface. Because the arcs are topologically disconnected and screening is inefficient, the gap acquires nodes whose locations and symmetry match the recent observations on PtBi2.

What carries the argument

Competition between intra-arc and inter-arc pairing channels whose relative strength is set by surface Coulomb screening efficiency.

If this is right

  • Surface superconductivity appears without bulk superconductivity.
  • Nodes form in the gap because arcs are disconnected and screening is weak.
  • Coating the surface to change screening can raise or lower the critical temperature.
  • The size and symmetry of the surface gap become experimentally tunable.

Where Pith is reading between the lines

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

  • The same phonon-driven nodal mechanism may appear in other materials whose surface states are topologically disconnected.
  • If screening can be tuned continuously, the nodal-to-nodeless transition itself becomes a measurable signature of the pairing-channel competition.

Load-bearing premise

Phonon-mediated pairing dominates over other possible mechanisms and the relative strength of the two channels is controlled solely by screening efficiency.

What would settle it

If the gap nodes disappear when a surface coating is added that improves Coulomb screening while leaving phonon spectra unchanged, the proposed mechanism is falsified.

Figures

Figures reproduced from arXiv: 2606.02371 by Alessandro De Martino, Francesco Buccheri, Jeroen van den Brink.

Figure 1
Figure 1. Figure 1: FIG. 1. Fermi arcs, with fixed energy [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Left: illustration of the intra- (blue) and inter-arc [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Critical temperature for intra- (solid) and inter- [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Left: intra-arc interaction potentials Right: inter-arc [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
read the original abstract

According to recent observations, the topological surface states of Weyl semimetals may develop a superconducting gap, while bulk superconductivity remains absent. What drives the formation of this novel superconducting state is an open question. Here, we show that this phenomenon can arise from the interaction of Fermi arc electrons with both surface and bulk phonons in time-reversal-invariant Weyl semimetals. We identify two competing pairing channels, intra-arc and inter-arc, whose relative strength is governed by the efficiency of Coulomb screening at the surface. The combined effect of the Fermi arcs being disconnected and the weak screening of the Coulomb repulsion at the system's surface causes nodes to appear in the superconducting gap, as observed recently by photoelectron spectroscopy experiments on PtBi2. This suggests manipulation of the Coulomb screening, e.g. by a surface layer coating, as a pathway to engineer the critical temperature, as well as size and symmetry of the surface superconducting gap.

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

2 major / 2 minor

Summary. The manuscript proposes that in time-reversal-invariant Weyl semimetals, electron-phonon coupling to both surface and bulk phonons can induce superconductivity on the Fermi arcs even when the bulk remains normal. Two competing channels (intra-arc and inter-arc pairing) are identified whose relative strength is controlled by the efficiency of surface Coulomb screening; the combination of disconnected arcs and weak screening is argued to produce nodes in the surface gap, consistent with recent ARPES data on PtBi2. Manipulation of screening (e.g., via surface coating) is suggested as a route to engineer Tc and gap symmetry.

Significance. If the central mechanism is rigorously established, the work would supply a concrete phonon-mediated route to surface-only superconductivity in Weyl semimetals and would link the nodal structure directly to the topology of the arcs plus surface dielectric response. The suggestion that screening can be tuned externally is potentially useful for experiment. However, the absence of an explicit evaluation of the screened Coulomb matrix elements leaves the key competition between channels as an assumption rather than a derived result.

major comments (2)
  1. [Sections describing the pairing channels and screening (around the discussion of intra- vs. inter-arc competition)] The central claim that weak surface screening preferentially suppresses the repulsive inter-arc channel relative to the attractive intra-arc channel (thereby producing nodes) is stated without a derivation or numerical evaluation of the momentum-dependent screened Coulomb interaction between arc states. No surface RPA calculation, first-principles dielectric function, or explicit matrix-element evaluation for PtBi2 is presented; the nodal outcome therefore rests on an input assumption about screening efficiency rather than emerging from the phonon-interaction calculation.
  2. [Model Hamiltonian and interaction terms] The model assumes that phonon-mediated pairing dominates over other mechanisms and that the surface/bulk phonon spectrum can be treated with a single effective coupling strength. No quantitative estimate or comparison is given showing that the phonon contribution exceeds residual Coulomb or other interactions once realistic screening is included.
minor comments (2)
  1. [Introduction and model section] Notation for the screening-efficiency parameter should be defined explicitly at first use and its relation to the dielectric function clarified.
  2. [Abstract and discussion] The abstract states that nodes appear 'as observed recently by photoelectron spectroscopy experiments on PtBi2'; a brief comparison of the predicted nodal positions or symmetry with the cited experimental data would strengthen the manuscript.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and will revise the text to improve clarity on the assumptions made.

read point-by-point responses

  1. Referee: [Sections describing the pairing channels and screening (around the discussion of intra- vs. inter-arc competition)] The central claim that weak surface screening preferentially suppresses the repulsive inter-arc channel relative to the attractive intra-arc channel (thereby producing nodes) is stated without a derivation or numerical evaluation of the momentum-dependent screened Coulomb interaction between arc states. No surface RPA calculation, first-principles dielectric function, or explicit matrix-element evaluation for PtBi2 is presented; the nodal outcome therefore rests on an input assumption about screening efficiency rather than emerging from the phonon-interaction calculation.

    Authors: We agree that the relative strength of the channels is argued on the basis of general physical considerations of surface dielectric response rather than an explicit computation. The manuscript emphasizes that weak surface screening (a standard feature of reduced-dimensional systems) combined with the disconnected nature of the arcs leads to nodes; this is presented as a qualitative mechanism consistent with PtBi2 ARPES data. An explicit surface RPA or first-principles evaluation for PtBi2 lies outside the scope of the present work, which focuses on the phonon-mediated pairing channels. We will revise the relevant sections to state this assumption more explicitly and to highlight the suggested experimental route of tuning screening via surface coating. revision: partial

  2. Referee: [Model Hamiltonian and interaction terms] The model assumes that phonon-mediated pairing dominates over other mechanisms and that the surface/bulk phonon spectrum can be treated with a single effective coupling strength. No quantitative estimate or comparison is given showing that the phonon contribution exceeds residual Coulomb or other interactions once realistic screening is included.

    Authors: The work is framed as a phonon-driven mechanism, as stated in the title and abstract, motivated by the experimental observation of surface superconductivity without bulk order. The effective coupling is introduced as a minimal model capturing both surface and bulk phonons. We acknowledge that no direct quantitative comparison to residual Coulomb interactions (after screening) is provided. Such a comparison would require extensive ab initio work beyond the present theoretical proposal. We will add a brief discussion of this modeling assumption in the revised manuscript. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper proposes that phonon interactions with surface and bulk modes drive surface superconductivity on Fermi arcs, with nodes arising from the interplay between disconnected arcs and the relative strength of intra-arc versus inter-arc pairing channels as governed by surface Coulomb screening efficiency. No quoted equations or text in the abstract or described full manuscript demonstrate a self-definitional reduction, a fitted parameter renamed as a prediction, or a load-bearing self-citation chain that collapses the nodal outcome to an input by construction. The screening efficiency is invoked as an external physical input rather than derived tautologically from the phonon calculation itself, leaving the central claim with independent content.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only; no explicit free parameters, invented entities, or non-standard axioms are identifiable. Standard domain assumptions about Weyl semimetal surface states are implicit.

axioms (1)
  • domain assumption Time-reversal-invariant Weyl semimetals host disconnected Fermi arcs on their surfaces.
    Standard background fact in the field, invoked to explain node formation.

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Reference graph

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