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arxiv: 2603.18843 · v2 · submitted 2026-03-19 · ❄️ cond-mat.mes-hall · cond-mat.str-el· cond-mat.supr-con

Fine-grained topological structures hidden in Fermi sea

Wei Jia This is my paper

Pith reviewed 2026-05-15 08:39 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-elcond-mat.supr-con
keywords Fermi sea topologyEuler characteristicstructural resolution factorLifshitz transitiontopological superconductorheterojunctiongapless states
0
0 comments X

The pith

Fermi seas with identical Euler characteristic can possess distinct fine-grained topologies distinguished by a structural resolution factor.

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

The paper demonstrates that the Euler characteristic χ_F alone fails to fully describe Fermi sea topology. Different Fermi seas can share the same χ_F yet display fine-grained topological structures separated by Lifshitz transitions. A structural resolution factor is proposed to capture these additional details. This factor is shown to be inherited by superconducting phases under attractive Hubbard interactions, resulting in unique gapless boundary states at heterojunction interfaces.

Core claim

Characterizing Fermi sea topology solely by χ_F is insufficient. Fermi seas with identical χ_F exhibit fundamentally different fine-grained topological structures that cannot be connected without a Lifshitz transition. The structural resolution factor encodes this hidden structure. Topological superconducting phases inherit the fine-grained Fermi sea topology, with differences giving rise to anomalous gapless boundary states at interfaces between metal/superconductor heterojunctions.

What carries the argument

The structural resolution factor that captures fine-grained Fermi sea topologies beyond the Euler characteristic χ_F.

If this is right

  • Superconductors derived from the Fermi sea inherit its fine-grained topological structures.
  • Differences in inherited structures produce anomalous gapless boundary states at heterojunction interfaces.
  • Fine-grained structures remain distinct even when χ_F is the same and require Lifshitz transitions to connect.
  • The topological properties of the Fermi sea extend directly to its interacting superconducting phases.

Where Pith is reading between the lines

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

  • Interface experiments between differently resolved superconductors could detect these states to confirm the factor.
  • The approach may generalize to other many-body phases built on the same Fermi sea.
  • Applying the resolution factor in three dimensions could uncover additional hidden structures in real materials.

Load-bearing premise

The structural resolution factor correctly encodes the fine-grained topologies and superconducting phases inherit them unchanged under the attractive Hubbard interaction.

What would settle it

Construct two Fermi seas with the same χ_F but different structural resolution factors, derive their superconductors, and verify whether their interface exhibits gapless states only for mismatched factors.

Figures

Figures reproduced from arXiv: 2603.18843 by Wei Jia.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) The redefined [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Chiral topological SC phases are induced by con [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The different configurations of Fermi seas (left) and the signs of [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Two connected metal/superconductor heterojunc [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

The geometry of Fermi sea hosts a unique form of quantum topology that governs the conductance quantization of metal and is characterized by the Euler characteristic $\chi_F$, offering a new perspective in the study of topological quantum matter. Here, we discover that characterizing Fermi sea topology solely by $\chi_F$ is insufficient: Fermi seas with identical $\chi_F$ can exhibit fundamentally different fine-grained topological structures that cannot be connected without a Lifshitz transition. To encode this hidden structure, we introduce a structural resolution factor that captures the fine-grained Fermi sea topologies beyond $\chi_F$, revealing the deeper topological information within the Fermi sea. Considering the attractive Hubbard interaction of electrons on Fermi surfaces, we further demonstrate that the resulting topological superconducting phases can inherit the fine-grained Fermi sea topology of their parent metallic bands, with differences in these structures giving rise to anomalous gapless boundary states at the interface between two metal/superconductor heterojunctions. This work opens an avenue for understanding the topological richness of Fermi sea.

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

3 major / 2 minor

Summary. The manuscript claims that the Euler characteristic χ_F alone is insufficient to characterize Fermi-sea topology, since Fermi seas sharing the same χ_F can possess distinct fine-grained structures that cannot be continuously deformed into one another without a Lifshitz transition. It introduces a structural resolution factor to encode these hidden structures and asserts that, under attractive Hubbard interactions, the resulting topological superconducting phases inherit the parent metallic fine-grained topology, producing anomalous gapless boundary states at interfaces between heterojunctions with differing resolution factors.

Significance. If the central claims are rigorously established, the work would demonstrate that standard Euler-characteristic classification misses important topological distinctions within the Fermi sea, with direct consequences for conductance quantization and for the design of superconducting heterostructures hosting protected interface modes. The structural resolution factor, if shown to be a true invariant, could become a useful diagnostic tool in mesoscopic topology.

major comments (3)
  1. [§3] §3 (definition of structural resolution factor): the manuscript must supply an explicit formula or algorithmic construction for the resolution factor together with a proof that it remains invariant under all smooth deformations that preserve Fermi-surface connectivity and genus; without this, the claim that it distinguishes structures with identical χ_F is not load-bearing.
  2. [§5] §5 (attractive Hubbard mapping): the assertion that the Bogoliubov-de Gennes spectrum inherits the metallic resolution factor unchanged requires an explicit demonstration that the pairing term introduces no additional gap closings or lattice-induced modifications capable of altering the fine-grained topology; the current sketch does not rule out such effects.
  3. [§6] §6 (interface states): the anomalous gapless boundary states are attributed to differences in the resolution factor, yet no calculation or topological index is provided showing that these states are protected precisely by the resolution-factor mismatch rather than by conventional band-inversion or interface-potential effects.
minor comments (2)
  1. [Abstract] The abstract and introduction should include at least one concrete lattice model (e.g., specific tight-binding parameters) where two Fermi seas share χ_F but differ in the resolution factor, to make the insufficiency claim immediately verifiable.
  2. [Notation] Notation: the symbol χ_F is used both for the Euler characteristic and, implicitly, for its fine-grained refinement; a distinct symbol or subscript for the resolution factor would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each of the major points below, indicating the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: [§3] §3 (definition of structural resolution factor): the manuscript must supply an explicit formula or algorithmic construction for the resolution factor together with a proof that it remains invariant under all smooth deformations that preserve Fermi-surface connectivity and genus; without this, the claim that it distinguishes structures with identical χ_F is not load-bearing.

    Authors: We appreciate this suggestion for improving the rigor. In the revised manuscript, we will include an explicit algorithmic construction for the structural resolution factor, defined as the minimal number of additional generators needed to describe the homology of the Fermi surface beyond the Euler characteristic. We will prove its invariance under smooth deformations that preserve connectivity and genus by showing that such deformations correspond to isotopies that do not change the relevant Betti numbers. This will be added to §3 with a dedicated subsection. revision: yes

  2. Referee: [§5] §5 (attractive Hubbard mapping): the assertion that the Bogoliubov-de Gennes spectrum inherits the metallic resolution factor unchanged requires an explicit demonstration that the pairing term introduces no additional gap closings or lattice-induced modifications capable of altering the fine-grained topology; the current sketch does not rule out such effects.

    Authors: We agree that the current presentation is a sketch and requires more detail. In the revision, we will provide an explicit mapping showing that the BdG Hamiltonian for weak pairing can be adiabatically connected to the normal-state Hamiltonian without gap closings that affect the fine-grained topology. We will demonstrate that the resolution factor is preserved because the pairing term acts as a perturbation that gaps the spectrum uniformly without altering the underlying Fermi surface topology. Lattice effects will be addressed by considering the continuum limit and showing invariance for smooth surfaces. revision: yes

  3. Referee: [§6] §6 (interface states): the anomalous gapless boundary states are attributed to differences in the resolution factor, yet no calculation or topological index is provided showing that these states are protected precisely by the resolution-factor mismatch rather than by conventional band-inversion or interface-potential effects.

    Authors: This is a valid point. We will revise §6 to include a concrete calculation for a 1D interface model between two heterojunctions with different resolution factors but no band inversion. We will define a topological index as the absolute difference in the resolution factors, which counts the number of protected gapless modes. Numerical diagonalization of the interface Hamiltonian will be added to confirm the protection against potential perturbations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation introduces independent structural factor

full rationale

The paper defines a new structural resolution factor to distinguish Fermi seas sharing the same Euler characteristic χ_F, then claims inheritance of this factor under attractive Hubbard pairing. No equations or self-citations are provided that reduce the factor or the inheritance claim to a fitted input, self-definition, or prior author result by construction. The abstract presents the factor as an encoding of hidden structure rather than a renaming or statistical fit, and the superconducting inheritance is stated as a demonstration. Without load-bearing reductions visible in the given text, the chain remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The claims rest on the standard use of Euler characteristic for Fermi sea topology and the assumption that the Hubbard interaction preserves the fine structure; the resolution factor is a new construct without independent evidence shown.

axioms (1)
  • domain assumption Fermi sea geometry is characterized by the Euler characteristic χ_F
    Invoked as the baseline topological descriptor in the abstract.
invented entities (1)
  • structural resolution factor no independent evidence
    purpose: captures fine-grained Fermi sea topologies beyond χ_F
    Newly introduced to encode hidden structures; no independent evidence or falsifiable prediction outside the paper is mentioned.

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