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arxiv: 2512.05735 · v2 · submitted 2025-12-05 · ❄️ cond-mat.str-el

Sliding phasons in Moir\'e Ladders

Paula Mellado , Francisco Mu\~noz , Javiera Cabezas-Escares This is my paper

Pith reviewed 2026-05-17 01:10 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords moiré ladderincommensurate charge density wavephasonsinterlayer shiftcharge ordertight-binding modelCoulomb interactionsvan der Waals materials
0
0 comments X p. Extension

The pith

A relative shift between ladder legs creates an incommensurate CDW whose neutral phasons remain acoustic and long-lived.

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

The authors examine a half-filled four-band tight-binding model on a ladder whose legs are offset by a fractional shift δ = p/q. This offset generates a moiré supercell that flattens bands near the Fermi level and introduces a modulated inter-leg tunneling. When onsite Coulomb repulsion is included, the system develops a charge-density-wave state with charge maxima on one leg aligned with minima on the other. The broken translational symmetry produces gapless neutral phasons whose velocity depends on the size of the moiré cell and the strength of the inter-leg hopping. The construction isolates how interlayer mismatch alone can stabilize such order, offering a route to understand charge-ordered phases in van der Waals heterostructures.

Core claim

In the half-filled moiré ladder with relative leg shift δ = p/q, the inclusion of local Coulomb repulsion stabilizes an incommensurate CDW state with out-of-phase charge modulation between legs; the associated Goldstone excitations are long-lived neutral acoustic phasons whose velocity is controlled by δ and the inter-leg tunneling amplitude.

What carries the argument

The moiré supercell generated by the relative leg shift δ, which compresses the leg bands into flat minibands and modulates the inter-leg tunneling amplitude.

Load-bearing premise

The half-filled four-band tight-binding model plus local Coulomb interactions on the shifted ladder is enough to capture the onset and phason spectrum of incommensurate charge order in real layered materials.

What would settle it

Spectroscopic measurement of the dispersion of neutral collective modes in a fabricated ladder with controlled leg shift δ, checking whether the mode velocity scales with δ and inter-leg tunneling as predicted by the model.

Figures

Figures reproduced from arXiv: 2512.05735 by Francisco Mu\~noz, Javiera Cabezas-Escares, Paula Mellado.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.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 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
read the original abstract

An incommensurate charge density wave is a periodic modulation of charge that breaks translational symmetry at a momentum that does not coincide with the primitive lattice vectors. Its Goldstone excitation, the phason, comprises collective gapless phase fluctuations. Aiming to unveil the mechanism behind the onset of incommensurate charge order in layered materials, we study a half-filled, four-band tight-binding model on a ladder with a relative shift \(\delta=p/q\) between the legs, induced by the dimerization of one of them. The shift results in a moir\'e supercell comprising \(q\) composite cells and a modulated inter-leg tunneling. The moir\'e potential compresses the leg bands into flat minibands near the Fermi level, resulting in additional low-energy peaks in the density of states. Including Coulomb interactions, we find an incommensurate charge-density-wave phase in which the charge modulation is out of phase between the legs. The collective excitations of this state are long-lived neutral, acoustic phasons whose speed is controlled by the moir\'e parameter \(\delta\) and the inter-leg tunneling amplitude. This model sheds light on the role of interlayer incongruities in the formation of excitonic charge-ordered phases in van der Waals and heterostructured materials.

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 a half-filled four-band tight-binding model on a ladder geometry with a relative shift δ = p/q between the legs, which generates a moiré supercell of q composite cells and a modulated inter-leg tunneling. The moiré potential flattens the leg bands near the Fermi level. Upon adding local Coulomb interactions, the authors report an incommensurate charge-density-wave phase featuring out-of-phase charge modulation between the two legs. The Goldstone modes of this state are identified as long-lived, neutral, acoustic phasons whose velocity is controlled by the moiré parameter δ and the inter-leg tunneling amplitude. The model is presented as a minimal framework for understanding interlayer-incongruity-driven excitonic charge order in van der Waals and heterostructured materials.

Significance. If the central claims are substantiated by the calculations, the work supplies a concrete, tunable lattice model in which an incommensurate CDW and its acoustic phason branch emerge directly from a moiré-induced density-of-states enhancement plus local interactions. The explicit dependence of phason speed on δ and tunneling offers a falsifiable link between microscopic parameters and collective-mode dispersion that could be tested in engineered bilayer systems.

major comments (1)
  1. [Collective excitations / phason spectrum] The abstract asserts that the phasons are 'long-lived' and 'acoustic' with speed 'controlled by' δ and inter-leg tunneling, yet the provided text does not display the explicit dispersion relation, the bosonization or RPA calculation, or the damping rate that would establish these properties. A load-bearing section deriving the phason velocity from the interacting Hamiltonian is required to support the claim.
minor comments (2)
  1. [Model Hamiltonian] The definition of the moiré parameter δ = p/q and the precise form of the modulated inter-leg tunneling should be stated explicitly in the model section, including the range of q considered.
  2. [Results figures] Figure captions and axis labels for the charge-density profile and phason dispersion should indicate the system size, boundary conditions, and interaction strength used.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript, as well as for the positive overall assessment and recommendation for minor revision. We address the single major comment below and have revised the manuscript to incorporate additional detail on the phason spectrum.

read point-by-point responses

  1. Referee: The abstract asserts that the phasons are 'long-lived' and 'acoustic' with speed 'controlled by' δ and inter-leg tunneling, yet the provided text does not display the explicit dispersion relation, the bosonization or RPA calculation, or the damping rate that would establish these properties. A load-bearing section deriving the phason velocity from the interacting Hamiltonian is required to support the claim.

    Authors: We agree that an explicit derivation strengthens the presentation. In the revised manuscript we have added a new subsection (now Section IV.C) that derives the phason dispersion from the interacting Hamiltonian via RPA on the charge susceptibility in the incommensurate CDW state. The resulting mode is shown to be acoustic and gapless, with velocity set by the moiré shift δ and the inter-leg tunneling; the neutral character of the mode and the incommensurability suppress damping, yielding long lifetimes within the approximation. A short complementary discussion of the bosonization treatment is included to connect the microscopic parameters to the collective-mode velocity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper constructs a half-filled four-band tight-binding Hamiltonian on a shifted ladder with explicit moiré parameter δ = p/q and modulated inter-leg tunneling as inputs. It then incorporates local Coulomb interactions to obtain an incommensurate CDW ground state with out-of-phase leg modulation and extracts the Goldstone phason modes whose velocity depends on those same inputs. This constitutes a standard forward derivation from non-interacting minibands through interactions to collective excitations, with no self-definitional loops, fitted parameters re-labeled as predictions, or load-bearing self-citations visible in the model setup or claims. The dependence of phason speed on δ and tunneling is an expected output of the calculation rather than a reduction to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on a half-filled four-band tight-binding Hamiltonian with a periodic moiré shift δ = p/q and added Coulomb repulsion; no explicit free parameters or invented entities are named in the abstract, but the model itself introduces the modulated inter-leg tunneling as a key assumption.

axioms (2)
  • domain assumption Half-filled four-band tight-binding model on a ladder with relative shift δ = p/q between legs
    Stated in abstract as the starting point for the moiré supercell and modulated tunneling.
  • domain assumption Coulomb interactions drive the incommensurate CDW
    Abstract says 'Including Coulomb interactions, we find...' without specifying the interaction form or strength.

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