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arxiv: 2607.02267 · v1 · pith:L7GMHVJQnew · submitted 2026-07-02 · ❄️ cond-mat.supr-con · cond-mat.dis-nn

Disorder-induced superconductivity in graphene

Jannes van Poppelen , Tomas L\"othman , Annica M. Black-Schaffer This is my paper

Pith reviewed 2026-07-03 03:49 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.dis-nn
keywords disorder-induced superconductivitygraphenesuperconductivityvacancieshydrogenationsuperfluid weights-wave pairinggeometrical superfluid weight
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The pith

Disorder from vacancies or hydrogenation induces superconductivity in graphene for arbitrarily weak attractive interactions.

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

Clean graphene requires strong interactions for superconductivity because of its semi-metallic band structure. The paper shows that low concentrations of vacancies or hydrogenation create a large density of low-energy states. These states produce a finite superconducting order parameter for conventional s-wave pairing even at arbitrarily weak attractions. Global phase coherence then follows from a finite superfluid weight that arises purely from geometry rather than from disconnected superconducting regions. The same disorder mechanism yields a finite transition temperature for hydrogenation away from the chiral limit and preserves phase coherence for unconventional nearest-neighbor pairing, although with quantum-critical-like behavior and mixed d-wave symmetries.

Core claim

For conventional s-wave pairing, disorder induces a finite superconducting order parameter for arbitrarily weak attractive interactions. Rather than forming isolated superconducting puddles, global phase coherence is established through a finite superfluid weight of purely geometrical origin. Away from the chiral limit of vacancies, hydrogenation similarly yields a finite transition temperature and nonzero superfluid weight for weak interactions. For unconventional nearest-neighbor pairing, superconductivity exhibits quantum-critical-like behavior, yet phase coherence persists at low interaction strengths, with mixed d-wave symmetries.

What carries the argument

Disorder-generated low-energy density of states that enables mean-field pairing together with a purely geometrical contribution to the superfluid weight.

If this is right

  • Superconductivity emerges from disorder alone without requiring strong clean-limit interactions.
  • Global phase coherence is achieved through a geometrical superfluid weight rather than isolated puddles.
  • The effect holds for both vacancies in the chiral limit and for hydrogenation.
  • Unconventional pairing still supports phase coherence at low interaction strengths despite quantum-critical-like signatures.

Where Pith is reading between the lines

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

  • The same disorder route may apply to other two-dimensional semimetals that lack superconductivity in the clean limit.
  • Varying vacancy or adatom density could provide experimental control over the transition temperature.
  • The geometrical origin of the superfluid weight may confer robustness to additional forms of disorder.

Load-bearing premise

Low concentrations of vacancies or hydrogenation produce a sufficiently large density of low-energy states that can be treated within the chosen theoretical framework to yield finite order parameter and geometrical superfluid weight for weak interactions.

What would settle it

An experiment finding zero superconducting transition temperature and zero superfluid weight in graphene with controlled low-concentration vacancies or hydrogenation at weak interaction strengths would falsify the claim.

Figures

Figures reproduced from arXiv: 2607.02267 by Annica M. Black-Schaffer, Jannes van Poppelen, Tomas L\"othman.

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 ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
read the original abstract

Correlated phases of matter are typically investigated in crystalline systems, where disorder is considered to be detrimental. However, intriguing exceptions exist, such as superconductivity being enhanced in amorphous realizations of Al and Bi. Here, we demonstrate that superconductivity can even emerge entirely from disorder, using monolayer graphene as an example. In the clean limit, the semi-metallic nature of graphene requires prohibitively strong electronic interactions to achieve superconductivity. Despite the inherently random nature of disorder, we show that introducing low concentrations of vacancies or hydrogenation in graphene provides a large density of low-energy states that easily induce superconductivity. For conventional $s$-wave pairing, disorder induces a finite superconducting order parameter for arbitrarily weak attractive interactions. Rather than forming isolated superconducting puddles, global phase coherence is established through a finite superfluid weight of purely geometrical origin. Away from the chiral limit of vacancies, hydrogenation similarly yields a finite transition temperature and nonzero superfluid weight for weak interactions. For unconventional nearest-neighbor pairing, typically more disrupted by disorder, superconductivity exhibits quantum-critical-like behavior, yet phase coherence persists at low interaction strengths, with mixed $d$-wave symmetries. Our work demonstrates the robust emergence of macroscopic superconducting phase coherence engineered entirely from microscopic disorder.

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

0 major / 1 minor

Summary. The manuscript claims that introducing low concentrations of vacancies or hydrogenation into monolayer graphene induces superconductivity for arbitrarily weak attractive interactions by generating a large density of low-energy states. For conventional s-wave pairing, disorder produces a finite superconducting order parameter, with global phase coherence arising from a finite superfluid weight of purely geometrical origin rather than isolated puddles. Hydrogenation yields a finite transition temperature and nonzero superfluid weight away from the chiral limit. For unconventional nearest-neighbor pairing, the system exhibits quantum-critical-like behavior yet maintains phase coherence at low interaction strengths with mixed d-wave symmetries.

Significance. If the central claims are supported by the derivations and numerics, the result would be significant for demonstrating that disorder can induce rather than suppress superconductivity in a clean-limit semi-metal, with the geometrical superfluid weight providing a mechanism for phase coherence. This offers a theoretical route to disorder-engineered macroscopic coherence in 2D materials and highlights how low-energy DOS from vacancies can enable mean-field pairing at weak V.

minor comments (1)
  1. [Abstract] The abstract packs multiple distinct results (s-wave vs. unconventional, vacancies vs. hydrogenation) into long sentences; splitting the final two sentences would improve readability without altering content.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work on disorder-induced superconductivity in graphene and for recommending minor revision. The report raises no specific major comments requiring point-by-point responses.

Circularity Check

0 steps flagged

No circularity; derivation self-contained

full rationale

The provided abstract and mechanism description rely on standard BCS-like mean-field response to disorder-induced finite DOS at low energies, yielding finite order parameter for weak attraction, plus a geometrical contribution to superfluid stiffness. No equations, self-citations, or fitted parameters are quoted that reduce a claimed prediction or uniqueness result back to the input by construction. The central claims remain independent of the paper's own fitted values or prior self-citations in a load-bearing way, consistent with externally verifiable lattice models of disordered graphene superconductivity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Assessment based solely on abstract; full details on model assumptions, parameters, and derivations unavailable. No explicit free parameters, axioms, or invented entities identifiable from abstract alone.

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discussion (0)

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Reference graph

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    J. van Poppelen, T. L¨ othman, and A. M. Black-Schaffer, Data for “Disorder-induced superconductivity in graphene” (2026), https://doi.org/10.5281/zenodo.21133299. 9 METHODS Normal state We consider a graphene latticeGwithNsites, with nearest-neighbor hoppingt. Vacancies are introduced by removing a set of sitesV, corresponding to a vacancy con- centratio...

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