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REVIEW 3 major objections 5 minor 56 references

Long-range electron coherence in Kagome metals

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Flux-quantum magnetoresistance oscillations in the kagome metal CsV3Sb5 persist on micrometer scales and above 20 K, where single-particle coherence should be dead.

desk verdict Robust h/e oscillations in CsV3Sb5, but the long-range coherence interpretation outruns the evidence—worth refereeing with the coherence claim treated as an open hypothesis. read the letter →

arxiv 2504.13564 v1 pith:5BZRRQCD submitted 2025-04-18 cond-mat.str-el cond-mat.mtrl-scicond-mat.supr-con

Chunyu (Mark) Guo , Kaize Wang , Ling Zhang , Carsten Putzke , Dong Chen , Maarten R. van Delft , Steffen Wiedmann , Fedor F. Balakirev
show 11 more authors
Ross D. McDonald Martin Gutierrez-Amigo Manex Alkorta Ion Errea Maia G. Vergniory Takashi Oka Roderich Moessner Mark H. Fischer Titus Neupert Claudia Felser Philip J.W. Moll
This is my paper · ORCID
classification cond-mat.str-elcond-mat.mtrl-scicond-mat.supr-con PACS 72.15.Gd73.23.-b
keywords h/eoscillationsAharonov-BohmeffectKagomemetalCsV3Sb5long-rangecoherencemagnetoresistancechargeorderquantuminterference
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 attempts to establish that electrons in the layered kagome superconductor CsV3Sb5 can interfere coherently over distances and temperatures that are far beyond the limits set by single-particle scattering. The evidence is a set of magnetoresistance oscillations in micron-sized pillars whose period is set by one magnetic flux quantum $h/e$ threading between adjacent kagome layers, with no adjustable material parameter. If correct, this means a cooperative or collective electronic state, not ballistic quasiparticles, is carrying the quantum phase information. The result would tie the long-debated $T'\sim 30$ K electronic crossover in CsV3Sb5 to a macroscopic quantum-interference phenomenon and make kagome metals a promising platform for interaction-stabilized electron coherence.

What carries the argument

The central object is the flux-quantum box: a rectangular loop of width $w$ (the pillar width) and height $c$ (the spacing between adjacent kagome planes) threaded by the in-plane magnetic field. The identity $\Delta B = \Phi_0/(w c)$ with $\Phi_0 = h/e$ turns every measured oscillation period into a parameter-free geometric prediction, and the systematic variation of $w$ across devices tests that identity directly. The enabling mechanism on the experimental side is the suspended microstructure: focused-ion-beam carved pillars mounted on soft silicon-nitride membranes, because strain from a rigid substrate suppresses the oscillations by more than 90 percent. The non-analytic angular response, including the 45-degree switching that is independent of the device aspect ratio, is the signature that identifies the field-selected interfering path.

What would settle it

A decisive experiment would tune the correlated electronic state near 30 K (for example, by uniaxial strain or controlled disorder) while monitoring the h/e oscillation amplitude: the cooperative-mechanism claim predicts the oscillations vanish together with that state even if the mean free path barely changes, whereas a single-particle interference origin predicts they survive whenever the mean free path is long enough.

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Extended reading notes

Core claim

The central claim is that out-of-plane transport through micron-sized pillars of CsV3Sb5, with magnetic field applied in the kagome planes, shows oscillations whose period obeys $\Delta B \cdot w \cdot c = h/e = \Phi_0$, where $c$ is the interlayer spacing and $w$ is the pillar width chosen by fabrication. Because this relation contains no material-specific parameter, the authors interpret it as an atomic-scale Aharonov-Bohm effect: a flux quantum is enclosed between adjacent kagome layers. The oscillations survive above 20 K and in devices far wider than the measured quantum and transport mean free paths, collapse when the field tilts more than about 5 degrees out of plane, jump discontinuously at 45 degrees for in-plane rotation, and track the $T'\sim 30$ K temperature scale seen in many other probes of CsV3Sb5. The authors conclude that single-particle interference and semiclassical Bloch-Lorentz orbits both fail to account for the data, and that a correlated many-body state establishes the long-range coherence.

Load-bearing premise

The argument that the oscillations outlive single-particle coherence assumes that the mean free paths extracted from c-axis Shubnikov-de Haas oscillations and from in-plane Drude resistivity apply to the actual out-of-plane, in-plane-field transport in the pillars; if some carrier population is effectively ballistic in that geometry, the semiclassical explanation would not be excluded.

Editorial extensions

If this is right

  • The period obeys $\Delta B \cdot w \cdot c = h/e$ with no fit parameters, so the same experiment in another layered metal should show the same period for the same width and spacing if the mechanism is generic.
  • The survival of oscillations above 20 K and on micrometer scales implies an effective coherence length exceeding the single-particle mean free path, so the coherence must be carried by a collective or interaction-stabilized degree of freedom.
  • The amplitude tracks the $T'\sim 30$ K scale observed in many other probes of CsV3Sb5, linking the interference to the correlated electronic order rather than to the normal Fermi surface.
  • The sharp suppression beyond 5 degrees of out-of-plane tilt and the 45-degree in-plane switching rule out simple semiclassical Bloch-Lorentz orbits and indicate a non-analytic response of the correlated state.
  • Strain suppresses the oscillations, so the effect requires the unstrained, delicately suspended environment and is not a generic ballistic artifact of clean microstructures.

Reading between the lines

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

  • If the cooperative picture is right, the h/e signal is carried by degrees of freedom distinct from the Landau quasiparticles that produce Shubnikov-de Haas oscillations; a testable consequence is that the h/e amplitude should not follow the Lifshitz-Kosevich thermal envelope governing those oscillations.
  • A natural extension is to search for the same parameter-free h/e periodicity in other layered kagome or frustrated metals that possess a $T'$-like correlated state, with the period predicted solely by device width and interlayer spacing.
  • Because the 45-degree switching is independent of the device aspect ratio, the interfering paths appear to be selected by the magnetic field's orientation relative to the crystal lattice rather than by the sample boundaries; a pillar with a non-rectangular cross-section would test this.
  • If the coherence is interaction-stabilized, small out-of-plane magnetic fields may tune the correlated state and should suppress the oscillation amplitude in the same manner as the field-switchable diode effect reported for this material.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript reports magnetic-field-periodic magnetoresistance oscillations in micron-sized pillars of CsV3Sb5 with current along the c-axis and magnetic field applied in the ab plane. The oscillation period follows ΔB = h/e/(w c) with the pillar width w and the interlayer spacing c, and a fit across eight devices yields c' = 9.11 ± 0.36 Å against the known c = 9.28 Å. The oscillations persist to temperatures above 20 K, are strongly suppressed when the field tilts out of plane by more than about 5 degrees, switch abruptly at 45-degree in-plane rotation, and are suppressed in a strained control device. The authors argue that, because the single-particle quantum and transport mean free paths are far below the device width, the oscillations cannot be explained by standard ballistic or semiclassical transport and instead imply interaction-stabilized long-range electron coherence linked to the correlated state below T'.

Significance. If the coherence interpretation is correct, this would be a striking result: h/e-periodic interference-like magnetotransport at high temperature and on micrometer length scales in a strongly correlated Kagome metal, with a period set only by geometry and the flux quantum rather than by Fermi-surface details. The paper has real strengths: the width-period scaling is convincingly documented across eight devices by a parameter-free relation, two independent background-subtraction methods agree on the oscillatory signal, the extracted interlayer spacing matches the lattice constant, and the temperature dependence tracks a broad set of independent experimental probes. The authors are also candid that the microscopic mechanism is currently unexplained. However, the central claim that the oscillations require long-range electron coherence is not yet established: the mean-free-path estimates are not made in the oscillation geometry, and the semiclassical simulations do not cover the actual reconstructed Fermi surface or momentum-dependent scattering.

major comments (3)
  1. [Supplement F / Fig. 2a] The Dingle analysis is performed with B parallel to the c-axis and current along c, so the extracted quantum lifetimes characterize closed cyclotron orbits in the ab plane. The h/e oscillations, by contrast, are measured with B in the plane and current along c; the relevant carriers traverse the in-plane width, and the lifetime of the states responsible for these oscillations need not equal the lifetime of the γ and δ pockets observed in SdH. The manuscript's central assertion that the oscillations occur 'well exceeding the single-particle mean free path' therefore depends on transferring scattering rates between two different geometries and, potentially, between different Fermi-surface sheets. Supplement E explicitly concedes the key loophole: one could invoke 'substantially suppressed scattering for some regions of one of the Fermi surfaces to reach a quasi-ballistic limit for these few select states only.' That possibility is dismissed as 'highly unusual,' but no quantitative argument is given to exclude it, either from the CDW-reconstructed Fermi surface or from measurements of quantum oscillations with B in-plane. This is the load-bearing point for the coherence claim, and it needs to be addressed directly.
  2. [Supplement H / Fig. S10] The semiclassical Bloch-Lorentz simulations test only cylindrical and hexagonal model Fermi surfaces with a uniform relaxation time and fully diffusive boundaries. The real system has a reconstructed, multiband CDW Fermi surface, and the simulations therefore do not rule out a semiclassical mechanism operating on a minority Fermi-surface sheet with weak scattering or on a restricted region of k-space. The Discussion's statement that it is 'highly implausible that a non-interacting band structure can account for the observed phenomenology' is accordingly stronger than the evidence presented. Closing this gap requires either a semiclassical calculation on the reconstructed Fermi surface with momentum-dependent τ or an experimental measurement that directly constrains the lifetime of the states involved in the in-plane-field geometry.
  3. [Supplement D / Fig. S4] The strained-device comparison (S9 versus S6) is used to argue for a 'fundamental link between long-range coherence and correlated electronic order.' However, the strained device differs from the strain-free device not only in the correlated state (the charge-order temperature is raised) but potentially also in defect density, inhomogeneous strain, and scattering rates introduced by the rigid mounting and glue. The argument that a lattice-constant change below 0.5% cannot by itself account for the suppression through inhomogeneous dephasing does not exclude strain-induced disorder scattering. As presented, this control experiment is suggestive but does not isolate the correlated-order mechanism.
minor comments (5)
  1. [Abstract] The phrase 'periodicity is independent of materials parameters' is imprecise because the period explicitly depends on the lattice constant c; the intended meaning is presumably independence from electronic parameters such as Fermi-surface geometry or carrier density, and this should be stated more carefully.
  2. [Supplement D] The word 'deconstructive interference' should be 'destructive interference.'
  3. [Fig. 4 / text] The claim that all plotted quantities fall on a 'universal temperature scaling' would be more convincing if the comparison were shown on normalized axes or with a quantitative collapse analysis; the current figure is qualitative.
  4. [Data and code availability] The manuscript states that data and code 'will be deposited' with a link 'displayed here,' but the v1 manuscript does not yet provide the link; the revised version should include a working repository identifier.
  5. [Fig. 2a] The color bar indicating Fermi-velocity anisotropy in the inset is difficult to read at the printed size; a larger inset or a separate panel would improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the h/e period law is a parameter-free consistency check, and the T′ and chiral-transport connections are external comparisons rather than inputs.

full rationale

The paper's central relation ΔB·w·c = h/e is tested empirically by measuring the oscillation period as a function of device width and comparing the extracted interlayer spacing c′ = 9.11 ± 0.36 Å with the known lattice constant c = 9.28 Å. The paper explicitly describes the dashed line as fitting-parameter-free, so this is a consistency check rather than a fitted input relabeled as a prediction. The coherence claim is built on independent Dingle and Drude mean-free-path estimates (l_q < 200 nm above 1 K; l_t ≈ 500 nm at Tc and ≈150 nm at 20 K). These estimates are not fitted to the h/e oscillation amplitude, and although Supplement E concedes that a quasi-ballistic minority Fermi-surface region cannot be fully excluded, that is an evidence gap, not a circular reduction. The connections to T′ and to chiral transport use prior same-group work (Refs. 20, 22, 36) as analogous experimental observations for comparison, not as premises from which the h/e period or its angular dependence is derived. No uniqueness theorem is imported from the authors' prior work, no ansatz is smuggled in via self-citation, and no known result is renamed. The paper even states that the oscillations currently remain theoretically unexplained, so it does not present a derivation that could be equivalent to its own inputs. Overall, the derivation chain is self-contained and no circular step is present.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

No new particles, forces, or conserved quantities are introduced. Speculative candidates such as loop currents, excitonic order, and sliding density order are borrowed from the existing literature and are not defined as new entities.

free parameters (6)
  • Cyclotron masses of SdH pockets = m_c ≈ 0.43 m_e and 1.12 m_e
    Extracted from Lifshitz-Kosevich fits to temperature-dependent SdH amplitude (Fig. S6b); used to convert Dingle slopes into quantum mean free paths.
  • Dingle slopes (quantum lifetimes) = Not tabulated; extracted per pocket and temperature
    Linear fits of f(B^-1) in Fig. S7 give τ_q used for the l_q < 200 nm statement in Fig. 2a.
  • Carrier density n = ≈1.86×10^22 cm^-3
    Inferred from Hall resistivity at 5 K and 14 T under a single-band assumption (Supplement E); input to the Drude transport mean free path estimate.
  • Effective in-plane Fermi wavevector = Derived from n and hexagonal 2D Fermi surface geometry
    Used in Eq. S2 to convert conductivity to l_t; the authors note it may overestimate the average Fermi velocity.
  • Zero-width onset temperature T' = ≈33 K
    Obtained by linearly extrapolating the temperature at which oscillation amplitude reaches 5% of its 2 K value versus device width (Fig. S13e); used to associate the effect with the T'≈30 K scale.
  • Effective interlayer spacing c' from width-period fit = 9.11 ± 0.36 Å
    Obtained by fitting ΔB = Φ0/(w·c') to eight devices (Supplement B); the closeness to crystallographic c = 9.28 Å is cited as confirmation of the h/e scaling, so it is not an ad hoc input to the claim.
assumptions (5)
  • domain assumption Lifshitz-Kosevich and Dingle analysis correctly describe the SdH oscillations in CsV3Sb5 and yield the quantum lifetime.
    Used in Supplement F and Fig. 2a to infer l_q below 200 nm from B∥c oscillations.
  • domain assumption A single-band Drude model with a hexagonal two-dimensional Fermi surface gives a valid upper bound for the transport mean free path.
    Supplement E uses this to claim l_t ≤ 500 nm at T_c and ≈150 nm at 20 K; the authors acknowledge the crudeness.
  • domain assumption The interference area for the h/e period is exactly the pillar width times the interlayer spacing, S=w·c.
    The identification of the observed period as h/e flux quantization in Fig. 1a and Fig. 1f depends on this geometry.
  • domain assumption The background-subtraction procedures do not generate the periodic oscillations.
    Supplement C compares second derivative and fifth-order polynomial subtraction and finds a π phase shift, but this is not a uniqueness proof.
  • ad hoc to paper The near-complete suppression of oscillations in the strained control device is caused by strain modifying the correlated electronic state, not by a change in mean free path or geometry.
    Supplement D interprets the S9 comparison as evidence for a link between coherence and correlated order; the interpretation is not independently established.

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Pith. "Pith review of Long-range electron coherence in Kagome metals." pith.science (2026). https://pith.science/paper/5BZRRQCD

@misc{pith2026250413564,
  author       = {Pith},
  title        = {Pith review of: Long-range electron coherence in Kagome metals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5BZRRQCD}},
  note         = {Machine review of arXiv:2504.13564}
}
abstract

The wave-like nature of electrons lies at the core of quantum mechanics, distinguishing them from classical particles. Landmark experiments have revealed phase coherence of mobile electrons within solids, such as Aharonov-Bohm interference in mesoscopic rings. However, this coherence is typically limited by numerous environmental interactions. Controlling and ideally mitigating such decoherence remains a central challenge in condensed matter physics. Here, we report magnetoresistance oscillations in mesoscopic pillars of the Kagome metal CsV$_3$Sb$_5$ for fields applied parallel to the Kagome planes. Their periodicity is independent of materials parameters, simply given by the number of flux quanta $h/e$ threading between adjacent Kagome layers akin to an atomic-scale Aharonov-Bohm interferometer. Intriguingly they occur under conditions not favorable for typical interference in solids, at temperatures above 20 K and in micrometer-scale devices well exceeding the single-particle mean free path. Further, the oscillations exhibit non-analytic field-angle dependence and scale consistently with a broad range of key electronic responses in CsV$_3$Sb$_5$, pointing to a cooperative mechanism that establishes intrinsic coherence. Our findings provide new insights into the debated origin of correlated order in CsV$_3$Sb$_5$ and establish Kagome metals as a promising platform for interaction-stabilized long-range electron coherence - crucial for both fundamental studies and technological advancements in quantum interference in metallic systems.

Figures

Figures reproduced from arXiv: 2504.13564 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
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Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.