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arxiv: 2605.09690 · v1 · submitted 2026-05-10 · ❄️ cond-mat.supr-con

Recognition: 1 theorem link

· Lean Theorem

Hole-Doping Suppresses Competing Magnetism in High-DOS C136 Carbon Schwarzite: A Computational Route Toward Superconductivity in Negative-Curvature Carbon Networks

Eugene Yashin
Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:22 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords C136 schwarzitehole dopingmagnetismdensity of statesnegative curvature carbonsuperconductivityDFT calculations
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The pith

Hole doping in C136 carbon schwarzite suppresses competing magnetism while preserving high density of states at the Fermi level.

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

This paper uses first-principles calculations to explore how doping affects the electronic and magnetic properties of a specific carbon schwarzite structure with 136 atoms. Neutral C136 shows strong magnetism with about 11 Bohr magnetons per cell that competes with potential metallic superconductivity. Removing electrons progressively reduces the magnetic moment, reaching 4.76 Bohr magnetons after removing eight electrons. At this doping level the density of states near the Fermi energy stays high at roughly 45 states per electronvolt per cell. The calculations therefore point to hole doping as a way to remove the magnetic competitor without destroying the electronic features that could support superconductivity, though actual pairing calculations are not performed here.

Core claim

Neutral D-type C136 schwarzite possesses a robust magnetic state with total magnetization of 11.01-11.03 Bohr magnetons per cell. Hole doping leads to a monotonic suppression of this magnetization, yielding 9.61, 8.02, 6.34, and 4.76 Bohr magnetons per cell upon removal of 2, 4, 6, and 8 electrons respectively. In the most heavily hole-doped configuration the density of states at the Fermi level remains high, approximately 44.7 states per eV per cell, indicating that the material stays metallic with a large number of states available for possible electron pairing.

What carries the argument

Spin-polarized density-functional-theory calculations on charged cells, which track the evolution of total magnetization and the electronic density of states as electrons are removed from the C136 unit cell.

If this is right

  • The magnetic moment decreases steadily with each additional hole introduced.
  • High density of states is retained even after substantial magnetism reduction.
  • This doped state provides a concrete starting point for further calculations of electron-phonon coupling.
  • The observed electron-hole asymmetry implies that p-type doping is more effective than n-type for suppressing magnetism in this system.

Where Pith is reading between the lines

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

  • Other schwarzite topologies with similar high-DOS features could be screened using the same doping protocol.
  • If electron-phonon coupling proves strong enough in the h8 state, the material might exhibit superconductivity at accessible temperatures.
  • Experimental synthesis of hole-doped schwarzites would allow direct tests of the predicted magnetization suppression.
  • The approach highlights the potential of curvature-engineered carbon networks as tunable platforms beyond flat graphene.

Load-bearing premise

That the results of spin-polarized density functional theory calculations give a reliable picture of the competition between magnetism and high-density-of-states metallic behavior without accounting for strong electron correlations or lattice vibrations.

What would settle it

A calculation of the electron-phonon coupling constant in the eight-hole-doped C136 structure that yields a superconducting transition temperature above zero, or an experimental measurement showing the absence of magnetism in hole-doped samples of this schwarzite.

Figures

Figures reproduced from arXiv: 2605.09690 by Eugene Yashin.

Figure 1
Figure 1. Figure 1: Hole-doping suppression of the competing magnetic branch in C136 carbon schwarzite. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Spin-resolved density of states for h8-doped C136 carbon schwarzite. The h8 state [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
read the original abstract

Carbon schwarzites are negative-curvature carbon networks with electronic structures distinct from graphene, fullerenes, and conventional carbon allotropes. Here we report a spin-polarized first-principles screening study of D-type C136 carbon schwarzite focused on the competition between magnetism, doping, and high-DOS metallic behavior. Neutral C136 has a robust competing magnetic branch, with total magnetization of about 11.01-11.03 Bohr magnetons per 136-atom cell. Charged-cell calculations reveal a clear electron-hole asymmetry: adding two electrons per cell increases the total magnetization to 12.11 Bohr magnetons per cell, while removing two electrons reduces it to 9.61. Further hole doping suppresses the magnetic branch monotonically, giving 8.02, 6.34, and 4.76 Bohr magnetons per cell for removal of 4, 6, and 8 electrons, respectively. The most strongly hole-doped point, h8, was examined with spin-polarized NSCF and density-of-states calculations on a 4x4x4 k-point mesh. The NSCF Fermi energy, -0.7414 eV, agrees with the SCF value, -0.7413 eV. The DOS remains high near the Fermi level: at E = -0.740 eV, the total DOS is about 44.69 states/eV/cell, with DOS_up = 33.11 and DOS_down = 11.58 states/eV/cell. Thus h8 combines substantial suppression of the competing magnetic branch with preservation of a high-DOS metallic state. We do not claim superconductivity in C136. Instead, these calculations identify hole doping as a route for suppressing a competing magnetic instability while preserving electronic conditions relevant for further superconductivity screening. Lattice stability, electron-phonon coupling, and transition-temperature estimates remain open problems.

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 / 1 minor

Summary. The manuscript reports spin-polarized first-principles DFT calculations on D-type C136 carbon schwarzite, showing that neutral C136 exhibits a magnetic moment of ~11.01-11.03 μB per cell that decreases monotonically with hole doping (to 9.61, 8.02, 6.34, and 4.76 μB/cell for 2, 4, 6, and 8 holes) while electron doping increases it; the h8 case is further analyzed with NSCF DOS yielding ~44.69 states/eV/cell near E_F, identifying hole doping as a route to suppress competing magnetism while preserving high-DOS metallic character for potential superconductivity screening.

Significance. If the reported trends hold, the work supplies a concrete computational map of doping-dependent magnetism in a high-DOS negative-curvature carbon network, highlighting electron-hole asymmetry and a specific h8 point that retains substantial DOS after moment reduction; this could usefully guide targeted experimental doping studies, though the lack of electron-phonon coupling or Tc estimates keeps the superconductivity link prospective.

major comments (2)
  1. [Abstract] Abstract and results: the central claim that hole doping suppresses a 'robust competing magnetic branch' is not load-bearing without total-energy comparisons; no ΔE values between spin-polarized and non-spin-polarized solutions are given for neutral or doped cells, so the monotonic drop in moment (11.01 → 4.76 μB/cell) does not establish that the magnetic configurations are the physically relevant lower-energy states being suppressed.
  2. [Results (h8 NSCF/DOS)] h8 DOS analysis: the reported high DOS (44.69 states/eV/cell at E_F = -0.740 eV) is obtained only for the still-magnetic spin-polarized solution; without a parallel non-magnetic DOS calculation it is unclear whether the metallic character and DOS value survive once magnetism is fully suppressed.
minor comments (1)
  1. [Abstract] The abstract states that 'lattice stability, electron-phonon coupling, and transition-temperature estimates remain open problems' but does not indicate whether any preliminary phonon or stability checks were performed even at the neutral or h8 points.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results: the central claim that hole doping suppresses a 'robust competing magnetic branch' is not load-bearing without total-energy comparisons; no ΔE values between spin-polarized and non-spin-polarized solutions are given for neutral or doped cells, so the monotonic drop in moment (11.01 → 4.76 μB/cell) does not establish that the magnetic configurations are the physically relevant lower-energy states being suppressed.

    Authors: We agree that the manuscript does not report total-energy differences (ΔE) between spin-polarized and non-spin-polarized solutions, which limits the strength of the claim that hole doping suppresses a 'robust competing magnetic branch.' The reported moments are obtained from spin-polarized calculations, but without ΔE we cannot quantitatively demonstrate that the magnetic state is the lower-energy configuration whose stability is being reduced. In the revised manuscript we will add non-spin-polarized total-energy calculations for the neutral and all doped cells, report the corresponding ΔE values, and update the Results and Abstract to reflect these data. This will directly address the concern and strengthen the interpretation of the doping trend. revision: yes

  2. Referee: [Results (h8 NSCF/DOS)] h8 DOS analysis: the reported high DOS (44.69 states/eV/cell at E_F = -0.740 eV) is obtained only for the still-magnetic spin-polarized solution; without a parallel non-magnetic DOS calculation it is unclear whether the metallic character and DOS value survive once magnetism is fully suppressed.

    Authors: The referee correctly observes that the NSCF DOS for the h8 case was computed on the spin-polarized solution (residual moment 4.76 μB/cell). No non-magnetic DOS was provided for comparison. We will perform additional non-spin-polarized NSCF DOS calculations for the h8 structure on the same k-point mesh and include the results in the revised manuscript. The new data will be presented alongside the spin-polarized DOS, with explicit discussion of whether the high DOS near E_F persists when magnetism is removed. This revision will be placed in the Results section and will clarify the electronic character relevant to further superconductivity screening. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are direct DFT outputs

full rationale

The paper's central results consist of magnetization values (11.01-11.03 μB/cell neutral, monotonic drop to 4.76 μB/cell at h8) and DOS (~44.69 states/eV/cell at E_F for h8) obtained from explicit spin-polarized DFT calculations on chosen doping levels. These quantities are reported as computed outputs rather than derived via any internal equations, fitted parameters renamed as predictions, or self-citations. No ansatz, uniqueness theorem, or renaming of known results is invoked to support the claims. The derivation chain is self-contained within standard first-principles methods without reduction to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard spin-polarized DFT approximations for carbon magnetism and metallic DOS; no new free parameters are fitted and no new entities are postulated.

axioms (1)
  • domain assumption Spin-polarized DFT (unspecified functional) correctly ranks magnetic versus non-magnetic states in this carbon network
    Invoked throughout the screening study to interpret magnetization changes with doping.

pith-pipeline@v0.9.0 · 5663 in / 1259 out tokens · 52231 ms · 2026-05-12T04:22:55.790351+00:00 · methodology

discussion (0)

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Reference graph

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