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arxiv: 2511.14134 · v1 · submitted 2025-11-18 · ❄️ cond-mat.dis-nn · cond-mat.mes-hall· cond-mat.str-el

Topological transition induced by selective random defects on a honeycomb lattice

Sogen Ikegami , Kiyu Fukui , Shun Okumura , Yasuyuki Kato , Yukitoshi Motome This is my paper

Pith reviewed 2026-05-17 21:18 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.mes-hallcond-mat.str-el
keywords topological transitionrandom defectshoneycomb latticedepleted latticehopping modulationelectronic propertiestopological properties
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0 comments X

The pith

Selective random defects induce a topological transition on a honeycomb lattice in certain regimes.

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

The paper examines electron systems on a lattice that interpolates between the honeycomb structure and its 1/6-depleted version by introducing selective random defects. In some parameter regimes the topological properties of the two endpoint lattices connect smoothly, while in others the defects drive a clear topological transition. An effective model accounts for these behaviors by recasting the defects as a modulation of electron hopping amplitudes. This perspective indicates a route to tune spectral features and topological character through controlled defect placement in electronic materials.

Core claim

We investigate how the spectral and topological properties of electron systems evolve on a lattice that interpolates between the honeycomb and its 1/6-depleted structures through the introduction of selective random defects. We find that in certain parameter regimes, the topological properties of the two lattice systems are smoothly connected, whereas in other regimes, selective random defects induce a topological transition. Analysis based on an effective model reveals that the effect of selective random defects can be understood as a modulation of hopping amplitudes.

What carries the argument

Selective random defects interpreted via an effective model as a modulation of hopping amplitudes that drives the interpolation between honeycomb and 1/6-depleted lattices.

If this is right

  • Topological character can be switched between connected and transitioned states by tuning defect parameters.
  • Spectral gaps and band structures evolve in a manner controlled by the effective hopping changes.
  • The mechanism supports design of electronic systems with targeted topological properties across material platforms.
  • The smooth connection regime preserves topological features while altering lattice geometry.

Where Pith is reading between the lines

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

  • Similar selective-defect engineering could apply to other two-dimensional lattices beyond honeycomb.
  • Experimental tests in graphene or transition-metal dichalcogenides might realize the predicted transitions via controlled vacancies.
  • The effective model opens questions about robustness when electron-electron interactions are added.
  • This defect-based interpolation suggests a general approach for navigating topological phase diagrams in lattice systems.

Load-bearing premise

The effective model that interprets selective random defects as a modulation of hopping amplitudes accurately captures the spectral and topological evolution of the system.

What would settle it

A direct calculation of the topological invariant on the full lattice with selective defects that yields a different phase than the effective hopping-modulation model predicts.

Figures

Figures reproduced from arXiv: 2511.14134 by Kiyu Fukui, Shun Okumura, Sogen Ikegami, Yasuyuki Kato, Yukitoshi Motome.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic pictures of the hierarchy of two dimensional [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic picture of the Haldane model on the honeycomb [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. A real space distribution of (a) the local Chern marker and [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Spectral properties of the Haldane model in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Spectral properties of the Haldane model at [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Spectral properties of the e [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Energy dependencies of (a) the Berry curvature density and [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a) [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
read the original abstract

We investigate how the spectral and topological properties of electron systems evolve on a lattice that interpolates between the honeycomb and its 1/6-depleted structures through the introduction of selective random defects. We find that in certain parameter regimes, the topological properties of the two lattice systems are smoothly connected, whereas in other regimes, selective random defects induce a topological transition. Analysis based on an effective model reveals that the effect of selective random defects can be understood as a modulation of hopping amplitudes. Our results highlight the potential for designing and controlling the spectral and even topological properties of electronic systems across a wide range of material platforms.

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 / 2 minor

Summary. The manuscript studies the evolution of spectral and topological properties in electron systems on a lattice interpolating between the honeycomb and 1/6-depleted structures via selective random defects. It reports that topological properties are smoothly connected in some parameter regimes but undergo a defect-induced transition in others. An effective model is used to interpret the defects as a modulation of hopping amplitudes.

Significance. If the central mapping holds, the work provides a route to engineer topological transitions or connections through controlled disorder, with relevance to defect engineering in 2D materials. The distinction between smooth-connection and transition regimes is a concrete, falsifiable outcome that could guide experiments.

major comments (1)
  1. [Effective-model section] Effective-model section (around the derivation following the abstract claim): the reduction of selective random defects to a deterministic hopping modulation assumes that ensemble-averaged amplitudes dominate over random scattering and Anderson localization. The manuscript should show explicitly that topological invariants (e.g., real-space Chern numbers or edge-state robustness) computed on the effective clean Hamiltonian remain consistent with direct calculations on multiple disordered realizations; otherwise the reported transition may be an artifact of the averaging step.
minor comments (2)
  1. Clarify in the methods or results section how the topological invariant is defined and computed for the disordered ensemble (e.g., whether it is averaged or computed per realization).
  2. Figure captions should explicitly state the defect density range and the precise definition of the 'selective' defect placement used in each panel.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation of the work's significance and for the constructive comment on the effective-model section. We address the concern below and will revise the manuscript to incorporate additional validation.

read point-by-point responses

  1. Referee: [Effective-model section] Effective-model section (around the derivation following the abstract claim): the reduction of selective random defects to a deterministic hopping modulation assumes that ensemble-averaged amplitudes dominate over random scattering and Anderson localization. The manuscript should show explicitly that topological invariants (e.g., real-space Chern numbers or edge-state robustness) computed on the effective clean Hamiltonian remain consistent with direct calculations on multiple disordered realizations; otherwise the reported transition may be an artifact of the averaging step.

    Authors: We agree that explicit validation of the effective model against disordered realizations is important to confirm that the topological transition is not an artifact of ensemble averaging. Our derivation of the effective hopping modulation relies on averaging over defect configurations, which is appropriate in the parameter regimes where selective defects suppress strong localization effects. To address this, the revised manuscript will include direct comparisons: we will compute real-space Chern numbers and examine edge-state robustness on the effective clean Hamiltonian and compare these with results averaged over multiple independent disordered realizations at representative points in both the smooth-connection and transition regimes. These additions will be placed in the effective-model section, along with a discussion of the conditions under which the averaging approximation holds. revision: yes

Circularity Check

0 steps flagged

No circularity: effective-model interpretation is independent interpretive step

full rationale

The paper numerically or analytically examines selective random defects interpolating between honeycomb and 1/6-depleted lattices, reports regime-dependent topological transitions or smooth connections, and then invokes an effective model to reinterpret defects as hopping-amplitude modulations. No quoted equation or self-citation reduces a claimed prediction or topological invariant to a quantity defined by the same model or prior author work; the effective-model step functions as post-hoc interpretation rather than a load-bearing premise that forces the result by construction. The derivation therefore remains self-contained against external benchmarks such as direct diagonalization or topological invariant calculations on the disordered ensemble.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on a standard tight-binding description of electrons on a lattice plus an effective model that equates defect effects to hopping modulation; no free parameters or new entities are mentioned in the abstract.

axioms (1)
  • domain assumption Electrons on the lattice are described by a tight-binding Hamiltonian with nearest-neighbor hopping
    Standard starting point for honeycomb-lattice electron systems; invoked implicitly when discussing spectral and topological properties.

pith-pipeline@v0.9.0 · 5418 in / 1152 out tokens · 31713 ms · 2026-05-17T21:18:48.387449+00:00 · methodology

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Reference graph

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