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REVIEW 4 major objections 4 minor 36 references

Phonon-Induced Current Noise in Single-Walled Carbon Nanotubes across the Ballistic-Diffusive Crossover

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Phonon-induced current noise in metallic carbon nanotubes peaks when tube length matches the electron mean free path and falls steeply at longer lengths.

desk verdict First atomistic look at phonon-induced current noise across the ballistic-diffusive crossover in SWCNTs, but the headline exponent is a two-point chord slope. read the letter →

arxiv 2506.02569 v1 pith:FTMIEXQB submitted 2025-06-03 cond-mat.mes-hall

Aina Sumiyoshi , Takahiro Yamamoto This is my paper · ORCID
classification cond-mat.mes-hall PACS 72.70.+m73.63.Fg
keywords currentnoisepowerspectraldensitysingle-walledcarbonnanotubeballistic-diffusivecrossoverelectron-phononscatteringshottime-dependentSchrödingerequationmoleculardynamics
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

This paper tries to establish how electron-phonon scattering shapes the intrinsic current noise of a metallic single-walled carbon nanotube as its length grows from the ballistic to the diffusive transport regime. Using an atomistic simulation that couples time-dependent electron dynamics to classical atomic motion, it finds that the zero-frequency power spectral density of the current noise is non-monotonic: it grows linearly at short lengths, peaks near the electron mean free path, and decays as a steep power law at long lengths. A sympathetic reader cares because the mean free path of a room-temperature nanotube is comparable to the lengths of real device channels, so the predicted noise maximum falls exactly in the operating range of nanotube electronics. The result also indicates that the diffusive-limit scaling exponent is not a universal number but depends on the material's phonon dispersion and scattering processes.

What carries the argument

The central machinery is the Open-TDSE+MD method, a simulation in which the electronic wave function of an open conductor is evolved by the time-dependent Schrödinger equation while the atomic positions move according to classical molecular dynamics; the electron-phonon coupling enters through the time dependence of the $\pi$-orbital tight-binding hopping integrals, set by Harrison's rule. The current is read out at buffer layers with a Landauer-type formula, and the zero-frequency power spectral density is extracted from the variance of the cumulative charge over a long measurement interval. This setup is what lets the authors follow a single metallic nanotube from the ballistic to the diffusive regime without assuming a transport model.

What would settle it

A direct check would be a length-resolved measurement of zero-frequency current noise in a suspended metallic SWCNT at 300 K from about 50 nm to 2 $\mu$m: the claimed picture fails if the noise does not peak near $L \approx 346$ nm and if the long-length decay is not a power law with exponent near 3.81.

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Extended reading notes

Core claim

The paper claims that in a (5,5) single-walled carbon nanotube at 300 K, phonon-induced current noise is maximally enhanced when the tube length $L$ equals the electron mean free path $L_0 \approx 346$ nm. For short tubes ($L/L_0 \ll 1$) the power spectral density increases in proportion to $L$, consistent with a nearly transparent conductor whose shot noise grows with the scattering probability; for long tubes ($L/L_0 \gg 1$) it decays as $L^{-\alpha}$ with $\alpha = 3.81$. This decay is faster than earlier predictions from simple models, which gave $L^{-2}$ or $L^{-2/5}$, because the realistic nanotube includes multiple electron-phonon scattering processes and a complex energy dependence of the phonon relaxation time. The crossover region itself, around $L/L_0 \approx 1$, shows the noise maximum, where the probabilities of transmitting and being scattered become comparable.

Load-bearing premise

The noise result rests on the assumption that representing electron-phonon scattering by a time-dependent tight-binding Hamiltonian with classically moving atoms and simple featureless electrodes captures the inelastic scattering correctly; if that representation is wrong, the noise peak and the $L^{-3.81}$ decay do not follow.

Editorial extensions

If this is right

  • In a metallic SWCNT, phonon-induced current noise is worst when the device length is near the roughly 350 nm mean free path, so devices built at that scale face maximum intrinsic current fluctuation.
  • At lengths much shorter than the mean free path the noise rises linearly with length, matching the shot-noise expectation for nearly transparent channels.
  • At lengths much longer than the mean free path the noise falls as $L^{-3.81}$, a faster decay than the $L^{-2}$ and $L^{-2/5}$ laws from earlier simple models, meaning longer tubes become quieter faster than those models predicted.
  • Because real SWCNTs used in electronics are a few hundred nanometers long, they sit in the crossover region where the noise is maximal, making noise control an explicit design concern.
  • The same qualitative behavior (linear growth, peak at $L \sim L_0$, power-law decay) is expected to hold for other one-dimensional quantum wires, though the exponent may change.

Reading between the lines

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

  • One open extension is to check whether the peak position tracks the temperature-dependent mean free path: if it does, noise spectroscopy could be used to extract $L_0$ directly.
  • The exponent $\alpha = 3.81$ is a prediction for (5,5) tubes; other chiralities and diameters, with different phonon dispersions and electron-phonon couplings, would be a direct test of the claimed material dependence.
  • The absence of inter-valley scattering in this calculation means the predicted scaling is for clean, long-wavelength phonons; including short-wavelength or inter-valley phonons may alter the exponent.
  • A natural computational extension suggested by the paper is to compute the full counting statistics (skewness, kurtosis) from the same trajectory ensemble, which would tell whether the non-Gaussian noise carries the same crossover signatures.
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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

4 major / 4 minor

Summary. The manuscript studies the length dependence of phonon-induced current noise in (5,5) single-walled carbon nanotubes at room temperature using the Open-TDSE+MD simulation method. Five nanotube lengths from 50 nm to 2004 nm are simulated. The authors report that the zero-frequency current-noise power spectral density is maximal when the tube length equals the fitted electron mean free path L0=346 nm, grows linearly with length in the ballistic limit, and decays as L^{-α} with α=3.81 in the diffusive limit. They interpret the results in terms of a phenomenological transmission formula and compare the exponent with earlier theoretical predictions.

Significance. If the central quantitative claim (α=3.81) is robust, the paper would provide the first large-scale atomistic determination of phonon-induced noise scaling across the ballistic-diffusive crossover in a realistic material, and it would demonstrate material-dependence of the noise decay exponent. The qualitative features—a noise peak near the mean free path and linear growth in the ballistic regime—are plausible and supported by the five simulated lengths. The paper's strengths are the realistic atomistic model of electron-phonon coupling and the direct time-domain computation of the noise; however, the headline exponent rests on very limited data, and the method's inelastic-scattering validity and the statistical convergence are not fully documented in the manuscript.

major comments (4)
  1. [Section 3.3, Fig. 5] The power-law exponent α=3.81 is claimed as the central quantitative result, but it is extracted from only two simulated lengths (L=1002 nm and 2004 nm, i.e., L/L0≈2.9 and 5.8) with no error analysis. These points are in a regime where leading finite-size corrections of order L0/L are roughly 35% and 17%, so the chord slope between them need not equal the asymptotic exponent; a small statistical fluctuation or an additional simulation at a longer length could change α substantially. Please fit more diffusive-regime lengths, report uncertainties, and show the dependence of the fitted α on the fit range and on the measurement time τ.
  2. [Section 3.2, Eq. (24) and Section 3.3] The identification L0=346 nm comes from fitting Eq. (24) to the same simulated conductance data, and this L0 is then used to normalize the length axis in Fig. 5 and to conclude that the noise peak is at L≈L0. In addition, the ballistic-limit scaling in Eq. (30) uses Eq. (23) with the same fitted L0, so the explanation is partly self-referential. Presenting the noise data on an absolute length scale and comparing L0 with an independent estimate (e.g., previous theoretical work cited in Refs. [25,30,31]) would strengthen the claim.
  3. [Section 2.2, Eqs. (15)-(17)] The correctness of the Open-TDSE+MD scheme for the inelastic electron-phonon scattering underlying the noise calculation is assumed from Refs. [25-27] and not re-examined here. In particular, the wide-band-limit self-energies in Eq. (17) and the identification of the instantaneous current via Eqs. (18)-(21) are used to compute a variance that is sensitive to inelastic processes. Please provide a validation of the method for a case with known noise behavior, or a convergence test with respect to buffer-layer length and the time step, to justify the transferability.
  4. [Section 3.3, Eq. (29)] The ensemble size is stated only for L=350 nm (N=240) and the τ-independence of SKK is asserted without a plot. The two diffusive points that determine α and all other points need their respective trial counts and τ-convergence checks documented, because the noise variance is a second-order statistic and statistical errors directly affect the exponent.
minor comments (4)
  1. [Section 3.3] The fitting procedure for α is not described; please specify the least-squares range, the functional form used, and the number of points included in the fit.
  2. [Fig. 5 caption] The dashed and dotted lines should be explicitly associated with the ∝L and ∝L^{-α} asymptotes to avoid ambiguity.
  3. [Eq. (29)] The notation ⟨(∆q(τ)²)⟩ is unusual; please clarify whether the square is inside or outside the ensemble average.
  4. [General] There are repeated formatting artifacts such as 'di ffusive' and other spacing irregularities in the arXiv version; a careful proofread before resubmission is advisable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the noise peak and diffusive exponent are direct simulation outputs; the conductance-fitted L0 is used only for normalization and interpretation.

full rationale

The paper's central result—the nonmonotonic length dependence of the phonon-induced current-noise PSD, with a peak near L ≈ 350 nm and a diffusive decay S_KK ∝ L^{-α}, α = 3.81—is obtained by explicitly simulating time-dependent currents in (5,5) SWCNTs with the Open-TDSE+MD method and computing the PSD from Eq. (29). The mean free path L0 = 346 nm is fitted to the separately computed conductance G(L) using the Landauer-type expression Eq. (24); it is used only to normalize the horizontal axis and to identify the observed peak as lying at L/L0 ≈ 1, not as an input that constructs or forces S_KK. The ballistic-branch rationalization in Eq. (30) uses the same effective transmission formula Eq. (23), but it is a post-hoc explanation of the short-length trend already present in the simulated data, not the formula that generated those data. The diffusive exponent α = 3.81 is determined directly from the simulated PSD points and is insensitive to the L0 normalization except as a horizontal offset. The self-citations to Refs. [25-27] are prior methodological papers by the same group; they supply the time-dependent transport tool, not the length-scaling result claimed here, so they do not make the new result circular. Concerns about the statistical robustness of α—only two points in the diffusive branch, no error bars or convergence analysis—are correctness and reproducibility issues, not circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claims rest on the Open-TDSE+MD simulation method (prior work by the same group), the classical MD treatment of phonons, the tight-binding model, and two fitted parameters: L0 = 346 nm and α = 3.81. The method's validity for inelastic scattering is assumed and referenced to prior papers, and the fitted parameters are used in the interpretation of the noise results.

free parameters (2)
  • Mean free path L0 = 346 nm
    Fitted to the simulated conductance versus length using Eq. (24) in Sec. 3.2; used to normalize the length axis and to identify the noise peak at L/L0 ≈ 1.
  • Diffusive noise exponent α = 3.81
    Estimated in Sec. 3.3 from the slope of the PSD versus L in the diffusive regime, where only two lengths (1002 and 2004 nm) lie; no error bar is reported.
assumptions (5)
  • domain assumption Born-Oppenheimer approximation with classical nuclear motion on an adiabatic potential surface; nuclei relax to thermal equilibrium via NTV ensemble with velocity scaling.
    Section 2 states nuclear quantum effects are neglected and classical MD with Tersoff potential describes C-C interactions; this is standard for room-temperature transport simulations but an approximation.
  • domain assumption π-orbital tight-binding Hamiltonian with nearest-neighbor hopping obeying Harrison's rule, γ_ij(t) = γ0 |R0|^2 / |R(t)|^2, with γ0 = -2.7 eV.
    Section 2.2, Eqs. (13)-(14). Electron-phonon coupling enters only through time-dependent hopping; the Tersoff potential and tight-binding parametrization are taken from prior literature.
  • domain assumption Low-frequency current noise is dominated by long-wavelength phonons, so intervalley (K-K') scattering is negligible and S_KK' can be dropped.
    Section 3.3, after Eq. (27). This relies on small-q phonons not connecting valleys in a metallic (5,5) SWCNT.
  • ad hoc to paper The open-system TDSE with source and sink terms, Eqs. (15)-(17), and the identification of current via Eqs. (18)-(21) correctly describe time-dependent transmission in the presence of electron-phonon scattering.
    This is the Open-TDSE+MD method developed by the authors' group (Refs. 25-27); its validity for inelastic noise is referenced, not proven in this paper. If it is invalid, the central noise result fails.
  • domain assumption Electron temperature Te = 0 K and phonon temperature 300 K; only the two Fermi-level channels at K and K' contribute to the current.
    Section 3.1 states this is reasonable for metallic SWCNTs; the noise is purely phonon-induced, with no thermal electron noise contribution.

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Pith. "Pith review of Phonon-Induced Current Noise in Single-Walled Carbon Nanotubes across the Ballistic-Diffusive Crossover." pith.science (2026). https://pith.science/paper/FTMIEXQB

@misc{pith2026250602569,
  author       = {Pith},
  title        = {Pith review of: Phonon-Induced Current Noise in Single-Walled Carbon Nanotubes across the Ballistic-Diffusive Crossover},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FTMIEXQB}},
  note         = {Machine review of arXiv:2506.02569}
}
abstract

We theoretically elucidate the system length ($L$) dependence of phonon-induced current noise in carbon nanotubes at room temperature over a broad range, encompassing the quantum ballistic and classical diffusive regimes. The power spectral density for the current noise is maximally enhanced when $L$ is comparable to the mean free path $L_0$ of an electron. In the ballistic limit of $L/L_0\ll 1$, the power spectral density increases in proportion to $L$, whereas in the diffusive limit of $L/L_0\gg 1$, it shows a power-law decay $L^{-\alpha}$ with a scaling parameter $\alpha=3.81$. The noise decay for single-walled carbon nanotubes is faster than that previously predicted based on a simple model because of the various electron-phonon scattering processes and the complex energy dependence of the phonon relaxation time.

Figures

Figures reproduced from arXiv: 2506.02569 by the authors.

Figure 1
Figure 1. (Color online) Simulation setup of Open-TDSE+MD method con￾sisting of three regions: central region with finite length and semi-infinite left and right leads without atomic vibration. The central region is composed of a scattering region with atomic vibration and two buffer layers without vibra￾tion, each of which is composed of two unit cells (L1 and L2 or R1 and R2). the zero-frequency limit, S (0) = lim τ→∞ 2⟨(∆Q… view at source ↗
Figure 3
Figure 3. shows the L dependence of G in a (5,5) SWCNT at T = 300 K. In the short-L limit (ballistic limit), G is in￾dependent of L and its value approaches 4e 2 /h(:= 2G0). On the other hand, in the long-L limit (diffusive limit), G obeys Ohm’s law and is thus inversely proportional to L. Similar conductance (or resistance) behavior has been obtained using the wave packet diffusion method.29, 30) The obtained L de￾pendence o… view at source ↗
Figure 2
Figure 2. (Color online) Time dependence of current carried by electrons at the K point in (5,5) SWCNTs with lengths L = 50, 125, 350, 1002, and 2004 nm at 300 K, where current is scaled by J0 = 2e 2V/h. The average current for each length L is indicated by the arrow. 3.2 Length dependence of conductance Using Eq. (21), the conductance G in a (5,5) SWCNT is given by G := lim V→0 ⟨J⟩ V = 2e 2 h (ζK + ζK′ ), (22) where ζK(K′ ) … view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: (Color online) Time dependence of total charge (dimensionless cu￾mulative charge) q(t) passing through (5,5) SWCNT with L = 350 nm at 300 K. Here, τ is the measurement time interval; it is taken to be 5.0 ps. See the main text for the definition of q(t). The gray curve…

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