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arxiv: 2606.02733 · v1 · pith:6WLV6TB7new · submitted 2026-06-01 · ❄️ cond-mat.dis-nn

Coexistence of topologically nontrivial and trivial insulating states in topological Anderson Chern insulator

Bo Yin , Yan Zhang , Anqi Wang , Jie Shen , Zhijun Wang , Quansheng Wu This is my paper

Pith reviewed 2026-06-28 11:30 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn
keywords topological Anderson insulatorquantum anomalous HalldisorderMnBi4Te7Chern insulatorband inversionphase diagramself-consistent Born approximation
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The pith

Disorder drives the time-reversal-broken quantum spin Hall state of ferromagnetic MnBi4Te7 into a quantum anomalous Hall phase called topological Anderson Chern insulator.

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

The paper examines how disorder affects the topological phases of ferromagnetic monolayer MnBi4Te7, which begins in a clean-limit time-reversal-broken quantum spin Hall state. Increasing disorder strength first induces a quantum anomalous Hall phase by suppressing one of two effective band inversions while the other survives. At still stronger disorder this phase coexists with a zero Hall plateau insulating state that has an insulating bulk but diffusive edge channels. The phases are mapped with density functional theory and nonequilibrium Green's function calculations, using self-consistent Born approximation density of states to resolve gapped states under strong disorder.

Core claim

Disorder drives the clean-limit T-broken QSH state of FM monolayer MnBi4Te7 into a QAH phase (TACI) as the two effective band inversions are suppressed at distinct critical disorder strengths, with the survival of a single inversion stabilizing the TACI over a finite window; at strong disorder a zero Hall plateau insulating state coexists with the TACI, distinct from a conventional Chern insulator.

What carries the argument

Topological Anderson Chern insulator (TACI) stabilized when one band inversion survives while the other is closed by disorder, identified by self-consistent Born approximation density of states that distinguishes gapped and ungapped phases.

Load-bearing premise

The self-consistent Born approximation within nonequilibrium Green's functions accurately distinguishes gapped from ungapped topological phases even in the strong disorder regime.

What would settle it

Transport measurement showing a finite disorder window with Hall conductance quantized at e²/h, followed by a higher-disorder regime with zero Hall conductance yet insulating bulk behavior.

Figures

Figures reproduced from arXiv: 2606.02733 by Anqi Wang, Bo Yin, Jie Shen, Quansheng Wu, Yan Zhang, Zhijun Wang.

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 ↗
read the original abstract

The interplay between disorder and topology has become a central theme in condensed matter physics. Disorder can not only destroy topological phases but also induce them, as exemplified by the topological Anderson insulator (TAI). Here we show that, in close analogy, disorder can drive the clean-limit, time-reversal-broken(T-broken) quantum spin Hall state of ferromagnetic(FM) monolayer MnBi4Te7 into a quantum anomalous Hall phase, which was called topological Anderson Chern insulator (TACI). Using density functional theory (DFT) and nonequilibrium Green's func tion (NEGF) calculations in the presence of disorder, we identify disorder induced phases-including T-broken TAI, TACI, Normal insulator, etc., then construct a comprehensive phase diagram. To discriminate multiple phases in the strong disorder regime, we further use the density of states computed within the self-consistent Born approximation (SCBA), which in particular distinguishes gapped and ungapped topological phases. We find that the two effective band inversions of Hamiltonian are suppressed at distinct critical disorder strengths; the survival of a single inversion over a finite disorder window stabilizes the TACI. Remarkably, at strong disorder, we further propose a zero Hall plateau insulating state characterized by an insulating bulk and edge channels subject to diffusive scattering that can coexist with the TACI. This behavior is distinct from a conventional band-gap Chern insulator and provides a clear experimental signature.

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 paper claims that disorder in ferromagnetic monolayer MnBi4Te7 drives the clean-limit time-reversal-broken quantum spin Hall state into a quantum anomalous Hall phase (topological Anderson Chern insulator, TACI) by suppressing two effective band inversions at distinct critical disorder strengths. Using DFT and NEGF calculations, it constructs a phase diagram including TACI, T-broken TAI, and normal insulator phases. At strong disorder, a zero Hall plateau insulating state (insulating bulk with diffusively scattered edge channels) is proposed to coexist with TACI, distinguished via SCBA-computed density of states that identifies gapped versus ungapped topological phases.

Significance. If the central claims hold, the work extends the topological Anderson insulator paradigm to time-reversal-broken Chern systems and identifies a disorder window stabilizing TACI via differential suppression of band inversions. The proposed coexistence of a zero-Hall-plateau state with TACI offers a distinct experimental signature. The methodological use of SCBA within NEGF to resolve multiple phases in the strong-disorder regime is noted, though its validity range requires explicit checks.

major comments (2)
  1. [Abstract; numerical methods (SCBA implementation)] Abstract and numerical methods section on SCBA: The identification of TACI (survival of a single band inversion over a finite disorder window) and the coexistence with the zero Hall plateau state rests exclusively on SCBA-derived density of states to locate gap closings and distinguish gapped/ungapped phases. SCBA is a second-order perturbative resummation whose validity requires the self-energy to remain small relative to the bandwidth; this condition is least secure precisely in the strong-disorder regime where the phase boundaries and coexistence are reported. No cross-check (exact diagonalization, kernel polynomial method, or finite-cluster transport) is described to confirm that the SCBA gap closings survive beyond the approximation.
  2. [Abstract] Abstract: The claim that the two effective band inversions are suppressed at distinct critical disorder strengths (stabilizing TACI) is determined solely from SCBA DOS features. Without an independent verification that SCBA accurately captures the disorder-driven gap closings in this regime, the reported finite disorder window for TACI and the subsequent zero-Hall state cannot be considered secured.
minor comments (2)
  1. Notation for the effective Hamiltonian and the two band inversions should be defined explicitly with equation numbers when first introduced, to allow readers to trace which inversion survives in the TACI window.
  2. Figure captions for the phase diagram should state the precise criterion (e.g., DOS threshold or Hall conductivity value) used to delineate each phase boundary.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments on the use of SCBA. We address each major comment below and agree that the manuscript requires revision to better contextualize the approximation's limitations.

read point-by-point responses

  1. Referee: [Abstract; numerical methods (SCBA implementation)] Abstract and numerical methods section on SCBA: The identification of TACI (survival of a single band inversion over a finite disorder window) and the coexistence with the zero Hall plateau state rests exclusively on SCBA-derived density of states to locate gap closings and distinguish gapped/ungapped phases. SCBA is a second-order perturbative resummation whose validity requires the self-energy to remain small relative to the bandwidth; this condition is least secure precisely in the strong-disorder regime where the phase boundaries and coexistence are reported. No cross-check (exact diagonalization, kernel polynomial method, or finite-cluster transport) is described to confirm that the SCBA gap closings survive beyond the approximation.

    Authors: We agree that SCBA is an approximation whose reliability is reduced in the strong-disorder regime and that the manuscript would benefit from explicit discussion of this point. The SCBA is used here within the NEGF framework solely to track the evolution of the density of states and locate the disorder strengths at which the two band inversions are suppressed; the underlying clean-limit band structure is obtained from DFT. In the revised version we will add a paragraph in the numerical methods section that (i) recalls the regime of validity of SCBA, (ii) cites its prior successful application to TAI problems, and (iii) states that the reported phase boundaries should be regarded as approximate. We will also note that a full non-perturbative verification lies beyond the present scope but would be a natural extension. revision: yes

  2. Referee: [Abstract] Abstract: The claim that the two effective band inversions are suppressed at distinct critical disorder strengths (stabilizing TACI) is determined solely from SCBA DOS features. Without an independent verification that SCBA accurately captures the disorder-driven gap closings in this regime, the reported finite disorder window for TACI and the subsequent zero-Hall state cannot be considered secured.

    Authors: The referee correctly notes that the finite disorder window for TACI is inferred from the SCBA density of states. The two distinct critical disorder strengths arise because the two effective band inversions (identified already in the clean DFT Hamiltonian) respond differently to the same disorder potential; SCBA then tracks when each inversion is lifted. We will revise the abstract and the relevant results section to make this dependence on the approximation explicit and to qualify the TACI window as approximate. This does not alter the qualitative picture but improves transparency. revision: yes

Circularity Check

0 steps flagged

No circularity: phase identification rests on independent numerical outputs

full rationale

The derivation chain relies on DFT band structures feeding into NEGF+SCBA computations of DOS and transport quantities to map phase boundaries. These are standard external approximations whose outputs are not defined in terms of the target TACI or zero-Hall states; the distinctions between gapped/ungapped phases and Hall plateaus emerge from the computed spectra rather than being presupposed by the method. No self-citation is invoked as a uniqueness theorem, no parameter is fitted to the final phase diagram, and no ansatz is smuggled via prior work. The central claims therefore remain falsifiable against the numerical data and do not reduce to their inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard domain assumptions in computational condensed matter without new free parameters or invented entities visible in the abstract.

axioms (2)
  • domain assumption DFT provides an accurate clean-limit Hamiltonian for FM MnBi4Te7
    Used as starting point for disorder calculations.
  • domain assumption NEGF combined with SCBA correctly captures disorder-induced topological transitions and density of states
    Central to constructing the phase diagram and distinguishing phases.

pith-pipeline@v0.9.1-grok · 5794 in / 1255 out tokens · 22044 ms · 2026-06-28T11:30:58.871066+00:00 · methodology

discussion (0)

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