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REVIEW 2 major objections 2 minor 86 references

Electron state tomography from quasiparticle interference maps

T0 review · 2 major / 2 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read Quasiparticle interference around on-site impurities reconstructs the full density matrix and quantum geometric tensor of electron states in two-orbital honeycomb models.

desk verdict Symmetry disentanglement of QPI orbital channels is the new element, but the paper needs to show the mapping is actually invertible for the full density matrix. read the letter →

arxiv 2606.18858 v1 pith:HTUXSBJO submitted 2026-06-17 cond-mat.mes-hall

A. Razanajatovo , J. Cayssol , C. Dutreix This is my paper · ORCID
classification cond-mat.mes-hall
keywords quasiparticleinterferencedensitymatrixtomographyquantumgeometrictensorhoneycomblatticeon-siteimpuritiesbackscatteringscanningtunnelingmicroscopytime-reversedstates
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper shows that backscattering between time-reversed states at on-site impurities encodes the populations and coherences of the electron density matrix as distinct orbital contributions in the QPI pattern. Because these orbital signals transform differently under the lattice symmetry group, they can be separated even with an unpolarized tip to recover the complete density matrix and the quantum geometric tensor. The method applies to two-orbital honeycomb lattices relevant to graphene heterostructures and direct-gap semiconductors. A sympathetic reader would see this as turning ordinary local STM measurements into a tomographic tool for wave-function details that momentum-space probes usually supply. The central claim is that symmetry provides the missing orbital resolution without hardware changes.

What carries the argument

The symmetry-distinct orbital decomposition of QPI intensity arising from time-reversed backscattering at on-site impurities, which isolates density-matrix elements and the quantum geometric tensor.

What would settle it

Measure whether the symmetry-filtered components extracted from experimental QPI maps around an on-site impurity in a honeycomb material quantitatively match the independently known density-matrix elements of the scattering states.

Watch

Extended reading notes

Core claim

For on-site impurities, backscattering between time-reversed states directly maps the density matrix populations and coherences into distinct orbital contributions in the interference map. These contributions transform under distinct symmetry group representations and can thus be disentangled to reveal the density matrix and quantum geometric tensor of the scattering states. This establishes impurities as tomographic probes for band structures in scanning tunneling microscopy using conventional, unpolarized tips.

Load-bearing premise

The orbital contributions to the QPI map transform under distinct symmetry group representations that permit clean separation without mixing.

Editorial extensions

If this is right

  • The full density matrix of scattering states becomes accessible from a single local QPI measurement in two-orbital honeycomb systems.
  • The quantum geometric tensor is recovered as a direct byproduct of the same disentanglement procedure.
  • Conventional unpolarized STM tips suffice to obtain orbital information that normally requires spin- or orbital-polarized probes.
  • The technique applies to graphene heterostructures and direct-gap semiconductors modeled by two-orbital honeycomb lattices.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same symmetry-separation logic might be tested in other multi-orbital lattices where point-group representations remain non-overlapping.
  • Local impurity tomography could complement ARPES by supplying real-space geometric information that momentum-resolved methods average over.
  • If the disentanglement remains robust under weak disorder, the method could be applied to disordered samples without requiring perfect crystals.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper proposes an electron state tomography method that reconstructs the density matrix (populations and coherences) and quantum geometric tensor of scattering states from quasiparticle interference (QPI) maps around single on-site impurities. In two-orbital honeycomb-lattice models, backscattering between time-reversed states is claimed to map the density matrix into distinct orbital contributions in the QPI pattern; these contributions are asserted to transform under different representations of the lattice symmetry group, permitting their disentanglement even with conventional, unpolarized STM tips. The approach is positioned as relevant to graphene heterostructures and direct-gap semiconductors.

Significance. If the mapping from density matrix to symmetry-resolved QPI channels is shown to be bijective, the method would provide a practical route to orbital and geometric information from standard STM experiments, extending the utility of impurity-based probes beyond conventional band-structure mapping.

major comments (2)
  1. [Symmetry disentanglement / two-orbital honeycomb model] The central claim that orbital contributions in the QPI map transform under distinct irreps and permit unique reconstruction of the full 2×2 density matrix (including off-diagonal coherences) requires an explicit demonstration of invertibility. No linear-algebra check, character-table decomposition, or numerical example confirming that the symmetry-projected channels are linearly independent for all density-matrix elements is provided in the symmetry-analysis section.
  2. [QPI map derivation] The manuscript states that the QPI map directly encodes the density matrix via backscattering between time-reversed states, yet supplies no derivation of the scattering amplitude or the resulting orbital-channel decomposition (e.g., no explicit form of the T-matrix or the Fourier-transformed LDOS expression that isolates the claimed symmetry channels).
minor comments (2)
  1. [Abstract] The abstract asserts the mapping and disentanglement without referencing the specific equations or symmetry tables that support it; a brief pointer to the relevant section would improve readability.
  2. [Introduction / model definition] Notation for the density matrix elements and the quantum geometric tensor should be introduced consistently when first used in the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments, which help strengthen the presentation of our tomography method. We address each major comment below and will revise the manuscript to incorporate the requested explicit demonstrations and derivations.

read point-by-point responses

  1. Referee: [Symmetry disentanglement / two-orbital honeycomb model] The central claim that orbital contributions in the QPI map transform under distinct irreps and permit unique reconstruction of the full 2×2 density matrix (including off-diagonal coherences) requires an explicit demonstration of invertibility. No linear-algebra check, character-table decomposition, or numerical example confirming that the symmetry-projected channels are linearly independent for all density-matrix elements is provided in the symmetry-analysis section.

    Authors: We agree that an explicit demonstration of invertibility is required for rigor. In the revised manuscript we will expand the symmetry-analysis section with a complete character-table decomposition under the C_{3v} point group appropriate to the local impurity environment. We will explicitly verify that the four symmetry-projected channels (A_1, A_2, and the two components of E) are linearly independent and span the four-dimensional space of the 2×2 density matrix, including off-diagonal coherences. A concrete numerical example will also be added, mapping a general density matrix to the symmetry channels and demonstrating the inverse reconstruction. revision: yes

  2. Referee: [QPI map derivation] The manuscript states that the QPI map directly encodes the density matrix via backscattering between time-reversed states, yet supplies no derivation of the scattering amplitude or the resulting orbital-channel decomposition (e.g., no explicit form of the T-matrix or the Fourier-transformed LDOS expression that isolates the claimed symmetry channels).

    Authors: We acknowledge that the detailed derivation was omitted for brevity. In the revision we will add a dedicated subsection (or appendix) that derives the T-matrix for on-site impurities in the two-orbital honeycomb model, starting from the impurity potential and the unperturbed Green function. We will then obtain the explicit Fourier-transformed LDOS expression and show how the backscattering term between time-reversed states isolates the symmetry channels that encode the density-matrix populations and coherences. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: derivation self-contained via external symmetry arguments

full rationale

The paper proposes a tomography method mapping density-matrix elements to QPI orbital channels via symmetry representations in two-orbital honeycomb models. No equations, fitted parameters, or self-citations appear in the provided abstract or description that reduce any claimed prediction or result to the inputs by construction. The invertibility claim rests on group-representation distinctness (an external mathematical fact), not on self-definition, renaming, or load-bearing self-citation. The derivation chain is therefore independent of its own outputs.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

Abstract-only; no free parameters, invented entities, or non-standard axioms are mentioned. Relies on standard two-orbital honeycomb models and time-reversal symmetry.

assumptions (1)
  • domain assumption Two-orbital models on a honeycomb lattice are relevant to graphene heterostructures and direct-gap semiconductors.
    Explicitly stated as the models considered.

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Cite this review

Pith. "Pith review of Electron state tomography from quasiparticle interference maps." pith.science (2026). https://pith.science/paper/HTUXSBJO

@misc{pith2026260618858,
  author       = {Pith},
  title        = {Pith review of: Electron state tomography from quasiparticle interference maps},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HTUXSBJO}},
  note         = {Machine review of arXiv:2606.18858}
}
read the original abstract

Characterizing electronic band structures requires precise knowledge of wave functions and their quantum geometry. Here, we introduce a tomography method to reconstruct the density matrix of electron states from quasiparticle interference maps around single impurities. We consider two-orbital models on a honeycomb lattice, relevant to graphene heterostructures and direct-gap semiconductors. For on-site impurities, backscattering between time-reversed states directly maps the density matrix populations and coherences into distinct orbital contributions in the interference map. While local probes usually lack orbital resolution, these orbital contributions transform under distinct symmetry group representations and can thus be disentangled to reveal the density matrix and quantum geometric tensor of the scattering states. This establishes impurities as tomographic probes for band structures in scanning tunneling microscopy using conventional, unpolarized tips.

Figures

Figures reproduced from arXiv: 2606.18858 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Honeycomb lattice with two orbitals A and B per [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Elastic backscattering process coupling the pair [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Unpolarized QPI map showing the LDOS intensity [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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