Direct signatures of Anderson orthogonality catastrophe in nonequilibrium quantum dots

Eran Sela; Joshua Folk; Sarath Sankar; Yigal Meir

REVIEW 2 major objections 5 minor 1 cited by

Direct signatures of Anderson orthogonality catastrophe in nonequilibrium quantum dots

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The Anderson orthogonality catastrophe exponent can be read from a quantum dot's charge-curve slope or current-voltage scaling.

desk verdict Clean new extraction formulas for the AOC exponent, but the 'unambiguous' isolation from dephasing is asserted, not shown. read the letter →

arxiv 2507.03763 v1 pith:I7D4WKPI submitted 2025-07-04 cond-mat.mes-hall

Sarath Sankar , Joshua Folk , Yigal Meir , Eran Sela This is my paper · ORCID

classification cond-mat.mes-hall PACS 73.23.-b73.63.Kv72.10.-d

keywords Andersonorthogonalitycatastrophequantumdotchargedetectormeasurementbackactionrateequationssusceptibilitycurrent-voltagescalingthermalimbalance

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

Electrons in a charge detector respond to every tunnel event in a nearby quantum dot, and the resulting Anderson orthogonality catastrophe leaves measurable traces in the dot's nonequilibrium behavior. This paper identifies two simple traces: the slope of the dot's average charge with respect to its level energy, evaluated at the midpoint of the bias-induced step, and the power-law scaling of the peak current with source-drain voltage. Both are shown to be controlled by the same exponent $\alpha$, in a rate-equation formalism that treats the orthogonality catastrophe exactly. The relations are claimed to remain valid for $T, V_{\rm det} \ll V < D$, so a working charge detector does not spoil the measurement. If correct, this supplies a direct, parameter-free experimental route to a quantity that has so far been inferred mainly indirectly.

What carries the argument

The machinery is a rate equation for the dot occupation, with tunnel rates $\Gamma_i^{\rm in/out}$ expressed through the detector correlation functions $A_\pm(E)$, whose Fourier transforms carry the power-law singularity $A_\pm(E)\propto E^{\alpha-1}$ at zero temperature. These functions incorporate the Anderson orthogonality catastrophe exactly, and at finite temperature or detector bias they are evaluated numerically using a generalization of the Nozieres–De Dominicis solution. The rate equation then yields the closed-form occupation and current formulas from which Eqs. (17) and (21) follow.

What would settle it

A concrete check: in a detector-coupled dot with tunable coupling $\lambda$, measure $dN/d\epsilon_d$ at $\epsilon_d=0$ for several voltages $V$ and compare the inferred $\alpha$ from Eq. (17) with the value predicted from the detector parameters via $\alpha=m(\delta/\pi)^2$. If the inferred $\alpha$ changes with $V$ or fails to track the predicted dependence on $m$ and $\lambda$, the claimed parameter-free extraction is wrong. A second check is to compare the two extractions: if the charge-slope and current-scaling values of $\alpha$ disagree outside the regime $T,V_{\rm det}\ll V<D$, the claimed robustness fails.

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Extended reading notes

Core claim

The paper's central claim is that the Anderson orthogonality catastrophe exponent $\alpha$ appears linearly in two easy-to-measure nonequilibrium observables of a weakly tunnel-coupled quantum dot. At the midpoint $\epsilon_d=0$ between the biased leads, the occupation $N_c = \Gamma_L/(\Gamma_L+\Gamma_R)$ is independent of $\alpha$, while the charge susceptibility is $\partial N/\partial\epsilon_d|_{\epsilon_d=0} = -4\alpha\Gamma_L\Gamma_R/[V(\Gamma_L+\Gamma_R)^2]$, yielding $\alpha = -V/[4N_c(1-N_c)]\,\partial N/\partial\epsilon_d|_{\epsilon_d=0}$. The peak current at the same point scales as $I(0)\propto V^{\alpha}$, so $\alpha$ also equals the logarithmic derivative of the peak current with respect to voltage. These two relations are the main results, and the paper argues they survive finite temperature and finite detector bias in the regime $T,V_{\rm det}\ll V<D$, as well as generalization to spinful dots when $V\ll U$. It also offers a thermal-imbalance variant in which the ratio $\eta=\log 2/S_{\max}$ grows monotonically with $\alpha$ through a violation of the Maxwell relation.

Load-bearing premise

The claim that dephasing can be ignored rests on the assumption that dephasing from the biased charge detector does not change the charge susceptibility at $\epsilon_d=0$ or the current peak's voltage scaling in a way that mimics $\alpha$; the paper states the isolation but does not quantitatively model the dephasing channel.

Editorial extensions

If this is right

An experiment can extract $\alpha$ directly from a charge-curve measurement: take the slope $dN/d\epsilon_d$ at the midpoint of the voltage-induced step, normalize by $V$ and by $N_c(1-N_c)$, and no knowledge of tunnel couplings or lever arm is needed.
The same exponent can be cross-checked from the voltage scaling of the peak current; agreement between the two extractions would confirm that both observables are governed by a single $\alpha$.
The relations hold for $T, V_{\rm det}\ll V<D$, so the detector can be biased for readout without ruining the estimate.
In a spinful dot the formulas survive with minor modifications (a factor of 2 in the tunnel-in rates) provided the applied bias stays below the charging energy $U$.
In the thermal-imbalance setup, the ratio $\eta = \log 2/S_{\max}$ provides a further monotonic measure of $\alpha$ that converges to a closed analytic form as $T_0\to 0$.

Reading between the lines

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

Because the midpoint occupation $N_c$ is pinned to $\Gamma_L/(\Gamma_L+\Gamma_R)$, the charge-susceptibility relation may also serve as a built-in consistency check on the lever arm calibration in real devices, something the paper does not discuss.
A natural next test is to vary the detector's capacitive coupling $\lambda$ (which changes the predicted $\alpha$) and check that both extractions track the same predicted value; this would distinguish AOC back action from dephasing, since dephasing would not tie the two observables together.
The thermal-imbalance scheme hints that Maxwell-relation violations measured in entropy experiments could be reinterpreted as AOC probes even without a voltage bias, extending the paper's main idea to equilibrium-noise measurements.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper gives two genuinely useful formulas: Eq. (17), extracting the AOC exponent α from the charge susceptibility at the mid-point of the voltage-bias step, and Eq. (21), extracting α from the V-scaling of the peak current. Both are parameter-free, easy to measure, and robust to finite temperature and detector bias in the stated regime. A third thermal-imbalance route via the violation of a Maxwell relation is also new, with an analytic polylog expression at T0 = 0. The derivations are internally consistent; I checked the step from Eq. (14) to (16) and the log-derivative in Eq. (21), and the A±(E) results from Ref. 3 are used correctly. Figures 2 and 3 back the claims about robustness. The citation pattern is fine, including the reliance on the authors' own prior work, which is standard practice.

The soft spot is the word "unambiguous" in the abstract and intro. The paper never models dephasing from the biased detector. Section III.C computes A±(E) at finite Vdet, but those overlap functions describe the detector's response to a charge switch, not the shot-noise dephasing of the QD itself. A dephasing rate Γφ(Vdet) entering the QD spectral function would add a contribution of order Γφ/V to the charge susceptibility and a weak V-dependence to the peak current, mimicking a small α. The condition Vdet ≪ V may suppress this, but no scaling or estimate is given. That is a real gap in the central claim. It is fixable: either model the dephasing channel or soften the claim to "AOC signatures can be isolated when dephasing is negligible." There is also a minor typo in Eq. (20), where A/α is written as A·α, which would incorrectly make the current vanish at α = 0.

Who is this for? Experimentalists in mesoscopic transport who want a practical route to measure α, and theorists interested in back action and nonequilibrium rate equations. The paper is a solid theoretical contribution that deserves a serious referee, but the "unambiguous" qualifier should be addressed in revision. I would engage with it and cite it if I worked in this area.

Referee Report

2 major / 5 minor

Summary. This paper proposes two nonequilibrium schemes for extracting the Anderson orthogonality catastrophe (AOC) exponent α in a quantum dot capacitively coupled to a charge detector. The authors use a rate-equation formalism in which AOC-modified tunneling rates are taken from prior work, and derive two main experimental estimators: the charge susceptibility at the center of a voltage-bias charge step, Eq. (17), and the voltage scaling of the peak current, Eq. (21). They argue that these estimators remain valid for T, Vdet ≪ V < D, and they propose a thermal-imbalance counterpart based on the violation of the Maxwell relation. The central claim is that these observables provide unambiguous, parameter-free signatures of AOC isolated from dephasing backaction.

Significance. If the central claim holds, the paper offers practical estimators of α that can be implemented in existing quantum-dot setups, addressing a long-standing difficulty in separating AOC backaction from dephasing backaction. The analytic derivations are internally consistent: Eq. (16) follows from Eq. (14), the log-derivative in Eq. (21) is robust to nonuniversal prefactors, and the polylog expression Eq. (24) correctly reduces to the Fermi function for α = 0. The main weakness is that the claimed isolation from dephasing is asserted rather than demonstrated quantitatively; this is load-bearing because the Introduction identifies dephasing as the dominant competing mechanism in prior experiments. With a quantitative dephasing analysis, the paper could become a useful and credible proposal.

major comments (2)

[Secs. I, III.C] The paper's central claim of unambiguous isolation from dephasing backaction is not supported by a quantitative model. The functions A±(E) used in Secs. III.B and III.C describe the detector's response to a QD charge switch, but they do not include a shot-noise dephasing or level-broadening channel acting on the QD. Adding a dephasing rate κ = Γφ(Vdet) to the QD spectral function in Eqs. (3)-(4) would produce an effective contribution to (∂N/∂ϵd)|ϵd=0 of order κ/V and a weak V dependence in the current, mimicking a small α in Eqs. (17) and (21). The regime condition Eq. (22), T,Vdet ≪ V < D, does not by itself rule this out unless Γφ(Vdet) ≪ V is established; the manuscript should provide an estimate of Γφ(Vdet), or a derivation showing that dephasing does not enter the two observables, to justify the word "unambiguous".
[Sec. IV] The thermal-imbalance scheme likewise states, without derivation, that the method works for finite detector bias provided Γφ(Vdet) ≪ T1. Since the Introduction identifies dephasing as the dominant competing backaction mechanism in existing experiments, this condition cannot be taken as granted; the authors should give an explicit model or at least a quantitative estimate of Γφ(Vdet) and demonstrate that the regime Γφ(Vdet) ≪ T1 is compatible with the measurement requirements of the proposed entropy protocol.

minor comments (5)

[Eq. (14)] The inequality defining the central bias window is printed as "V /2 < ϵd < V /2"; it should read "-V /2 < ϵd < V /2".
[Eqs. (8), (12), (20)] The α → 0 limit is not clean: with A = χ/D^α and χ independent of α, the prefactor A/α in Eq. (12) diverges, whereas the exact A±(E) should reduce to δ(E) so that rates are finite. The authors should specify the α dependence of χ, or include the Γ(α) normalization, and comment on the α → 0 limit of Eq. (20).
[Sec. III.A] The statement that Eq. (17) does not require knowledge of the lever arm should be spelled out: the lever arm cancels if the gate-voltage separation between the two charge steps is used as the measure of V in gate-voltage units.
[Eq. (23)] The signs in Γin/out = -Γ A T1^α Li_α(-e^{∓x}) should be explicitly tied to the in/out labels to avoid ambiguity.
[Sec. III.C] The claim that the plotted quantities depend only on α and not on detector parameters would be more convincing with a collapse plot or an explicit statement of the parameter sets used beyond the single example α = 0.2.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the predicted α-relations are derived algebraically from a fixed input exponent and universal rate functions, not fitted to the observables.

full rationale

The paper's central results, Eqs. (17) and (21), are obtained by inserting the power-law forms of A±(E) from Eq. (8) into the rate equations (3)–(4), solving for the steady-state occupation and current (Eqs. (10) and (18)), and then differentiating or taking a logarithmic derivative with respect to V. The AOC exponent α enters as an independent model parameter set by detector parameters via Eq. (2); it is never fitted to the charge susceptibility or current that Eqs. (17) and (21) are meant to predict. The relations are algebraically derived, cancel nonuniversal prefactors and tunnel couplings, and are therefore not equivalent to their inputs by construction. The paper's reliance on Refs. (2), (3), and (15) for the form of A±(t) is a standard import of published results based on the Nozières–De Dominicis solution; the overlap authors include three of the present authors, but the cited work does not presuppose the new measurement relations, and the new predictions remain externally falsifiable. The skeptical concern about unmodeled dephasing in the voltage-bias scheme is a substantive scientific gap regarding the 'unambiguous' claim, but it is not a circularity: a missing quantitative bound on Γφ does not make the derivation reduce to its own inputs. No fitted input is renamed as a prediction, no uniqueness theorem is invoked to forbid alternatives, and no ansatz is smuggled in solely via self-citation. I therefore find no circular step and assign a score of 0.

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

The central claim rests on the standard AOC power-law form and the rate equation framework imported from prior work, plus the specific detector model. No new entities are introduced. The paper's contribution is the derivation of how these inputs appear in non-equilibrium observables.

assumptions (5)

domain assumption The tunnel rates of the quantum dot in the presence of the detector are given by the rate equations (3)-(4) with A±(E) the Fourier transform of the overlap functions (5).
Imported from Ref. 3 (Eqs. 3-5); the paper does not re-derive these. They are the foundation of the rate equation formalism.
domain assumption In the low-energy limit, A±(E) = θ(±E) A |E|^(α-1) (Eq. 8), with universal AOC exponent α and nonuniversal prefactor A.
Standard Anderson orthogonality catastrophe result from Refs. 2, 3, and 15; this power-law form is the key input making the observables depend on α.
domain assumption The rate equation (9) is valid in the weak tunneling limit Γ_L,R << T with hybridization neglected (Section II).
The paper restricts to weak QD-lead coupling; the T -> 0 analytic results are interpreted in the regime T << V.
domain assumption The detector is a noninteracting resonant level with degeneracy m, and α = m(δ/π)^2 (Eq. 2).
Specific model choice; the paper argues the results are more general because the power-law form is universal.
domain assumption The numerical method generalizing Nozières-De Dominicis (Ref. 15) used for the finite T and Vdet results is exact.
The numerical A± functions in Figs. 2-4 are computed with a method imported from Ref. 3; the paper does not describe it.

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Pith. "Pith review of Direct signatures of Anderson orthogonality catastrophe in nonequilibrium quantum dots." pith.science (2026). https://pith.science/paper/I7D4WKPI

@misc{pith2026250703763,
  author       = {Pith},
  title        = {Pith review of: Direct signatures of Anderson orthogonality catastrophe in nonequilibrium quantum dots},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I7D4WKPI}},
  note         = {Machine review of arXiv:2507.03763}
}

abstract

We propose schemes for unambiguous direct observation of Anderson orthogonality catastrophe (AOC) effects in a quantum dot coupled to a charge detector, and to estimate the strength of the AOC exponent $\alpha$. We show that certain easy-to-measure observables have a robust dependence on $\alpha$ in the non-equilibrium regimes of source-drain voltage bias or thermal imbalance. Our results are obtained using a rate equation formalism in which the AOC effects on tunnel rates are incorporated in an exact manner.

Figures

Figures reproduced from arXiv: 2507.03763 by the authors.

**Figure 2.** FIG. 2: Effect of (a) finite temperature and (b) detector bias [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 4.** FIG. 4: (a) The schematic of the setup with different tem [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Anderson Orthogonality as Measurement Backaction in Coupled Quantum Dots
cond-mat.mes-hall 2026-08 conditional novelty 6.0 of 10

Tuning a near-equilibrium quantum-dot charge sensor changes how strongly Anderson orthogonality suppresses resonant tunneling in a coupled dot, demonstrating controllable many-body measurement backaction.

Reference graph

Works this paper leans on

31 extracted references · 29 canonical work pages · cited by 1 Pith paper

[1]

author P. W. Anderson , journal Phys. Rev. Lett. volume 18 , pages 1049 ( year 1967 )

work page 1967
[2]

author I. L. Aleiner , author N. S. Wingreen , and author Y. Meir , journal Phys. Rev. Lett. volume 79 , pages 3740 ( year 1997 )

work page 1997
[3]

Sankar , author C

author S. Sankar , author C. Bertrand , author A. Georges , author E. Sela , and author Y. Meir , journal Phys. Rev. B volume 110 , pages 085133 ( year 2024 )

work page 2024
[4]

Sankar , author M

author S. Sankar , author M. Lotem , author J. Folk , author E. Sela , and author Y. Meir , journal arXiv preprint arXiv:2503.03416 ( year 2025 )

arXiv 2025
[5]

Goldstein , author R

author M. Goldstein , author R. Berkovits , and author Y. Gefen , journal Phys. Rev. Lett. volume 104 , pages 226805 ( year 2010 )

work page 2010
[6]

Ma , author C

author Z. Ma , author C. Han , author Y. Meir , and author E. Sela , journal Phys. Rev. Lett. volume 131 , pages 126502 ( year 2023 )

work page 2023
[7]

Borda , author K

author L. Borda , author K. Vlad \'a r , and author A. Zawadowski , journal Phys. Rev. B volume 75 , pages 125107 ( year 2007 )

work page 2007
[8]

Kashcheyevs , author C

author V. Kashcheyevs , author C. Karrasch , author T. Hecht , author A. Weichselbaum , author V. Meden , and author A. Schiller , journal Phys. Rev. Lett. volume 102 , pages 136805 ( year 2009 )

work page 2009

Show all 31 references

[9]

Buks , author R

author E. Buks , author R. Schuster , author M. Heiblum , author D. Mahalu , and author V. Umansky , journal Nature volume 391 , pages 871 ( year 1998 )

1998
[10]

Avinun-Kalish , author M

author M. Avinun-Kalish , author M. Heiblum , author A. Silva , author D. Mahalu , and author V. Umansky , journal Phys. Rev. Lett. volume 92 , pages 156801 ( year 2004 )

2004
[11]

ung , author S. Gustavsson , author T. Choi , author I. Shorubalko , author T. Ihn , author S. Sch\

author B. K\"ung , author S. Gustavsson , author T. Choi , author I. Shorubalko , author T. Ihn , author S. Sch\"on , author F. Hassler , author G. Blatter , and author K. Ensslin , journal Phys. Rev. B volume 80 , pages 115315 ( year 2009 )

2009
[12]

Bischoff , author M

author D. Bischoff , author M. Eich , author O. Zilberberg , author C. Rossler , author T. Ihn , and author K. Ensslin , journal Nano letters volume 15 , pages 6003 ( year 2015 )

2015
[13]

uller , author D. E. F. Biesinger , author C. P. Scheller , author B. Braunecker , author D. M. Zumb\

author M. S. Ferguson , author L. C. Camenzind , author C. M\"uller , author D. E. F. Biesinger , author C. P. Scheller , author B. Braunecker , author D. M. Zumb\"uhl , and author O. Zilberberg , journal Phys. Rev. Res. volume 5 , pages 023028 ( year 2023 )

2023
[14]

Wen , title Quantum Field Theory of Many-body Systems--from the Origin of Sound to an Origin of Light and Fermions ( publisher Oxford University Press , year 2003 )

author X.-G. Wen , title Quantum Field Theory of Many-body Systems--from the Origin of Sound to an Origin of Light and Fermions ( publisher Oxford University Press , year 2003 )

2003
[15]

Nozier\'es and author C

author P. Nozier\'es and author C. De Dominicis , journal Phys. Rev. volume 178 , pages 1097 ( year 1969 )

1969
[16]

Ng , journal Phys

author T.-K. Ng , journal Phys. Rev. B volume 54 , pages 5814 ( year 1996 )

1996
[17]

Muzykantskii , author N

author B. Muzykantskii , author N. d’Ambrumenil , and author B. Braunecker , journal Phys. Rev. Lett. volume 91 , pages 266602 ( year 2003 )

2003
[18]

Abanin and author L

author D. Abanin and author L. Levitov , journal Phys. Rev. Lett. volume 94 , pages 186803 ( year 2005 )

2005
[19]

Hartman , author C

author N. Hartman , author C. Olsen , author S. L \"u scher , author M. Samani , author S. Fallahi , author G. C. Gardner , author M. Manfra , and author J. Folk , journal Nature Physics volume 14 , pages 1083 ( year 2018 )

2018
[20]

Child , author O

author T. Child , author O. Sheekey , author S. L \"u scher , author S. Fallahi , author G. C. Gardner , author M. Manfra , author A. Mitchell , author E. Sela , author Y. Kleeorin , author Y. Meir , et al. , journal Phys. Rev. Lett. volume 129 , pages 227702 ( year 2022 )

2022
[21]

Adam , author H

author C. Adam , author H. Duprez , author N. Lehmann , author A. Yglesias , author S. Cances , author M. J. Ruckriegel , author M. Masseroni , author C. Tong , author A. O. Denisov , author W. W. Huang , et al. , journal arXiv preprint arXiv:2412.18000 ( year 2024 )

2024
[22]

Cooper and author A

author N. Cooper and author A. Stern , journal Phys. Rev. Lett. volume 102 , pages 176807 ( year 2009 )

2009
[23]

Yang and author B

author K. Yang and author B. I. Halperin , journal Phys. Rev. B volume 79 , pages 115317 ( year 2009 )

2009
[24]

Viola , author S

author G. Viola , author S. Das , author E. Grosfeld , and author A. Stern , journal Phys. Rev. Lett. volume 109 , pages 146801 ( year 2012 )

2012
[25]

Ben-Shach , author C

author G. Ben-Shach , author C. R. Laumann , author I. Neder , author A. Yacoby , and author B. I. Halperin , journal Phys. Rev. Lett. volume 110 , pages 106805 ( year 2013 )

2013
[26]

Ben-Shach , author A

author G. Ben-Shach , author A. Haim , author I. Appelbaum , author Y. Oreg , author A. Yacoby , and author B. I. Halperin , journal Phys. Rev. B volume 91 , pages 045403 ( year 2015 )

2015
[27]

Smirnov , journal Phys

author S. Smirnov , journal Phys. Rev. B volume 92 , pages 195312 ( year 2015 )

2015
[28]

Sela , author Y

author E. Sela , author Y. Oreg , author S. Plugge , author N. Hartman , author S. L \"u scher , and author J. Folk , journal Phys. Rev. Lett. volume 123 , pages 147702 ( year 2019 )

2019
[29]

Hou , author K

author C.-Y. Hou , author K. Shtengel , author G. Refael , and author P. M. Goldbart , journal New J. Phys. volume 14 , pages 105005 ( year 2012 )

2012
[30]

Han , author Z

author C. Han , author Z. Iftikhar , author Y. Kleeorin , author A. Anthore , author F. Pierre , author Y. Meir , author A. K. Mitchell , and author E. Sela , journal Phys. Rev. Lett. volume 128 , pages 146803 ( year 2022 )

2022
[31]

Sankar , author E

author S. Sankar , author E. Sela , and author C. Han , journal Phys. Rev. Lett. volume 131 , pages 016601 ( year 2023 )

2023

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

author P. W. Anderson , journal Phys. Rev. Lett. volume 18 , pages 1049 ( year 1967 )

work page 1967

[2] [2]

author I. L. Aleiner , author N. S. Wingreen , and author Y. Meir , journal Phys. Rev. Lett. volume 79 , pages 3740 ( year 1997 )

work page 1997

[3] [3]

Sankar , author C

author S. Sankar , author C. Bertrand , author A. Georges , author E. Sela , and author Y. Meir , journal Phys. Rev. B volume 110 , pages 085133 ( year 2024 )

work page 2024

[4] [4]

Sankar , author M

author S. Sankar , author M. Lotem , author J. Folk , author E. Sela , and author Y. Meir , journal arXiv preprint arXiv:2503.03416 ( year 2025 )

arXiv 2025

[5] [5]

Goldstein , author R

author M. Goldstein , author R. Berkovits , and author Y. Gefen , journal Phys. Rev. Lett. volume 104 , pages 226805 ( year 2010 )

work page 2010

[6] [6]

Ma , author C

author Z. Ma , author C. Han , author Y. Meir , and author E. Sela , journal Phys. Rev. Lett. volume 131 , pages 126502 ( year 2023 )

work page 2023

[7] [7]

Borda , author K

author L. Borda , author K. Vlad \'a r , and author A. Zawadowski , journal Phys. Rev. B volume 75 , pages 125107 ( year 2007 )

work page 2007

[8] [8]

Kashcheyevs , author C

author V. Kashcheyevs , author C. Karrasch , author T. Hecht , author A. Weichselbaum , author V. Meden , and author A. Schiller , journal Phys. Rev. Lett. volume 102 , pages 136805 ( year 2009 )

work page 2009