Beyond the band edge: Unveiling high-mobility hot carriers in a two-dimensional conjugated coordination polymer

Guoquan Gao; Hai I. Wang; Heng Zhang; Jianjun Zhang; Jiaxu Zhang; Keming Li; Lei Gao; Mike Hambsch; Min Liu; Mischa Bonn

REVIEW 3 major objections 5 minor 1 references

Beyond the band edge: Unveiling high-mobility hot carriers in a two-dimensional conjugated coordination polymer

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Ultrafast terahertz and microscopy measurements show that hot carriers in the two-dimensional coordination polymer Cu3BHT move with ~2,000 cm² V⁻¹ s⁻¹ mobility and cross grain boundaries up to ~300 nm within a picosecond.

desk verdict First credible case for hot-carrier transport in a 2D coordination polymer; the 2,000 cm²/Vs headline is an order-of-magnitude estimate, not a measured value. read the letter →

arxiv 2501.08742 v1 pith:ZNLB4VIX submitted 2025-01-15 cond-mat.mtrl-sci cond-mat.soft

Shuai Fu , Xing Huang , Guoquan Gao , Petko St. Petkov , Wenpei Gao , Jianjun Zhang , Lei Gao , Heng Zhang

show 14 more authors

Min Liu Mike Hambsch Wenjie Zhang Jiaxu Zhang Keming Li Ute Kaiser Stuart S. P. Parkin Stefan C. B. Mannsfeld Tong Zhu Hai I. Wang Zhiyong Wang Renhao Dong Xinliang Feng Mischa Bonn

This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.soft

keywords hotcarriersterahertzspectroscopytwo-dimensionalconjugatedcoordinationpolymersCu3BHTchargemobilityDrudetransporttransientabsorptionmicroscopyphononbottleneck

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 claims that in films of the two-dimensional conjugated coordination polymer Cu3BHT, photoexcited hot carriers keep their excess kinetic energy for hundreds of femtoseconds and move with a mobility near 2,000 cm² V⁻¹ s⁻¹, crossing grain boundaries up to 300 nm within a picosecond. Once the carriers cool to the band edge, they continue to move by Drude-like band transport with a mobility around 400 cm² V⁻¹ s⁻¹ and an intrinsic diffusion length beyond one micrometre. The authors separate the two regimes with time-resolved terahertz spectroscopy, transient absorption spectroscopy, and transient absorption microscopy, and they identify a hot-phonon bottleneck that slows cooling at high excitation densities. If the interpretation holds, it overturns the assumption that organic-based systems cool too quickly and transport too poorly to host hot-carrier phenomena, opening a route to hot-carrier devices built from solution-processed two-dimensional coordination polymers.

What carries the argument

The central object is the time-resolved THz photoconductivity transient $\Delta\sigma(t) = n e \mu$, normalized by the absorbed photon number $N_\mathrm{abs}$. Under the assumption that the carrier density $n$ is constant over the first ~10 ps, $\Delta\sigma/N_\mathrm{abs}$ directly tracks the temporal evolution of carrier mobility, and the paper's 'fast decay is a mobility drop' interpretation is carried by the photon-energy dependence of $\Delta\sigma_\mathrm{peak}/\Delta\sigma_\mathrm{offset}$ together with Drude and Drude-Smith fits to the frequency-resolved complex photoconductivity. The Drude-Smith model, with its backscattering parameter $c$ between 0 and $-1$, supplies the description of hot carriers whose long excursions across grain boundaries make them susceptible to backscattering, while the Drude model describes the delocalized band-edge carriers. A secondary mechanism is the hot-phonon bottleneck: low-energy optical phonons near 100 cm⁻¹ and acoustic-optical phonon up-conversion slow carrier cooling at high excitation densities.

What would settle it

Measure the carrier density directly in the first picosecond, for example by time-resolved photoemission or by comparing the early-time spectrally integrated transient absorption amplitude with the THz photoconductivity, and check whether the density is constant while the THz signal decays. If the density decays on the same ~500 fs timescale as the fast component, the fast decay is carrier loss, not hot-carrier cooling, and the ~2,000 cm² V⁻¹ s⁻¹ estimate collapses.

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Extended reading notes

Core claim

The central claim is that the fast-decaying component of the THz photoconductivity transient in Cu3BHT films is a mobility drop, not a carrier-density drop. Under photoexcitation above the ~0.5 eV band edge, the normalized photoconductivity $\Delta\sigma/N_\mathrm{abs}$ rises to a peak and decays within about one picosecond to a plateau that persists beyond a nanosecond; the ratio $\Delta\sigma_\mathrm{peak}/\Delta\sigma_\mathrm{offset}$ grows with pump photon energy and extrapolates to unity at ~560 meV, matching the absorption edge. The authors therefore assign the peak to hot carriers with a mobility of ~2,000 cm² V⁻¹ s⁻¹, obtained by scaling the Drude mobility of band-edge carriers (~405 cm² V⁻¹ s⁻¹, from fits with a scattering time of ~41 fs and a reduced mass of 0.187 $m_0$) by the measured peak-to-offset ratio. Hot-carrier cooling times of ~500 fs, rising to ~750 fs above a fluence threshold, plus a blue shift in the transient absorption band that tracks the THz decay, support the assignment. Real-space imaging by transient absorption microscopy shows an ultrafast expansion with diffusion coefficients from ~680 to ~1,200 cm² s⁻¹, with the larger value at higher photon energy.

Load-bearing premise

The claim rests on the assumption that the photogenerated carrier density stays constant during the first ~10 picoseconds, so the fast drop in the normalized THz signal is a drop in mobility rather than a drop in the number of carriers; if trapping or recombination removes a significant fraction of carriers within the first picosecond, the inferred hot-carrier mobility would be too high.

Editorial extensions

If this is right

If the interpretation is right, Cu3BHT becomes a candidate for hot-carrier photovoltaic and hot-electron transistor devices that require charge extraction before the carriers cool.
The ~750 fs hot-carrier cooling time, comparable to lead-halide perovskites, means solution-processable two-dimensional coordination polymers could work as organic hot-carrier platforms despite their normally strong electron-phonon coupling.
The intrinsic diffusion length of band-edge carriers exceeding one micrometre implies that Cu3BHT films can transport carriers across typical device feature sizes without recombination losses.
Because two-dimensional conjugated coordination polymers are tunable through metal substitution and ligand design, the same transport regimes should be searchable across the wider family, making the result a proof-of-principle rather than a single-material curiosity.

Reading between the lines

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

A testable extension the authors do not report: vary the grain size of Cu3BHT films and check whether the hot-carrier propagation length stays near 300 nm; if it scales with grain size, the cross-boundary claim is directly confirmed, and if it does not, grain boundaries are not the main scatterers.
The extrapolated critical photon energy of ~560 meV matching the Tauc edge suggests the same peak-to-offset ratio could become a quick spectroscopic estimate of the band gap in other coordination polymers, without transport modelling.
The hot-phonon bottleneck picture implies the fluence threshold for cooling slowdown should shift if the phonon spectrum is altered by isotope substitution or by exchanging copper for another metal; measuring the threshold in a series of substituted films would probe the mechanism directly.

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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

Here's the short version: this is the first paper I know of that makes a credible case for hot-carrier transport in a 2D conjugated coordination polymer, and the multi-technique attack is genuinely good. But the headline number—~2,000 cm²/Vs for hot carriers—is softer than the abstract implies, and the paper would be stronger if the authors said so.

What's new: the synthesis and structural work is careful (AC-HRTEM, GIWAXS, XANES), and the TRTS data show a clean Drude-like response at late times with a scattering time of ~41 fs and a band-edge mobility of ~400 cm²/Vs, with an Arrhenius temperature dependence pointing to a ~8 meV phonon mode. The photon-energy dependence of the early THz transient, together with the Tauc edge at ~0.5 eV and the extrapolated critical photon energy of ~560 meV, is a nice internal check. The TAM experiment is the most convincing independent evidence: the initial spatial expansion is fast, with diffusion coefficients of ~700–1200 cm²/s, and it increases with pump photon energy. That's a real observation of a highly mobile non-equilibrium species.

Where I'd push back: the conversion of the early-time THz decay into a hot-carrier mobility relies on n being constant over the first ~10 ps. The linear ∆σ_offset vs Nabs check doesn't rule out a fluence-independent fast trapping channel that removes a fixed fraction of carriers within the first picosecond—and the paper itself invokes trap-assisted recombination (t2 ≈ 1.2 ns), so traps are clearly present. I don't see a direct sub-picosecond population measurement anywhere. Second, the early-time THz spectrum is fit with Drude-Smith, not Drude, so the ratio of photoconductivity at the THz probe frequency to the Drude DC mobility is not automatically valid; without reporting c and τ_DS and applying the finite-frequency correction, the ~2,000 cm²/Vs value is an estimate, not a measurement. The authors should give an uncertainty budget for that number, or at minimum present it as an order-of-magnitude inference.

That said, the stress-test concern doesn't sink the paper. The TAM data independently establish that something fast and mobile exists, and the qualitative picture—hot carriers with higher mobility than band-edge carriers—survives. The quantitative value needs work.

Who this is for: anyone working on 2D c-CPs, hot-carrier physics in organic or hybrid systems, or ultrafast THz spectroscopy. It deserves a serious referee. I'd recommend sending it out, but with a request for the Drude-Smith parameters, error bars on the 2,000 cm²/Vs, and a more careful treatment of the n=const assumption.

Referee Report

3 major / 5 minor

Summary. The manuscript presents a combined time-resolved terahertz spectroscopy (TRTS), transient absorption spectroscopy (TAS), and transient absorption microscopy (TAM) study of photogenerated carriers in thin films of the two-dimensional conjugated coordination polymer Cu3BHT. The authors identify two transport regimes following above-gap photoexcitation: a non-equilibrium regime in which a fast (~500 fs) decay of the THz photoconductivity is assigned to hot-carrier cooling with an inferred hot-carrier mobility of ~2,000 cm2 V-1 s-1, and a quasi-equilibrium regime in which the photoconductivity spectra are Drude-like with a band-edge mobility of ~400 cm2 V-1 s-1 and an intrinsic diffusion length exceeding 1 um. The interpretation is supported by the photon-energy dependence of the THz transients, the temperature dependence of the Drude scattering rate, the blue shift of the transient absorption band, and direct real-space imaging of an ultrafast expansion of the photoexcited population.

Significance. If correct, this would be the first observation of hot-carrier transport in a two-dimensional conjugated coordination polymer, with record mobility values for organic-based systems and potential relevance to hot-carrier photovoltaics and transistors. The paper has notable strengths: the critical photon energy extrapolated from the THz ratio (~560 meV) agrees with the independent Tauc absorption edge (~0.5 eV); the TAM measurements provide a real-space, technique-independent signature of ultrafast carrier spreading; and the temperature-dependent Drude scattering rate shows a positive temperature coefficient consistent with band-like transport. These complementary elements make the qualitative picture of high-mobility hot carriers credible, but the quantitative claims require additional scrutiny.

major comments (3)

[Observation of highly mobile hot carriers and hot phonon bottleneck in Cu3BHT (Fig. 2c)] The assertion that the carrier density n is constant during the first 10 ps is not established by the data shown. The linear dependence of Δσ_offset on Nabs (Fig. 2b) demonstrates only that the surviving population at 6–8 ps scales linearly with absorbed photon number; a fluence-independent fast trapping or recombination channel that removes a fixed fraction of carriers within the first picosecond would produce the same linear dependence. Because the paper itself assigns t2 ≈ 1.2 ns to trap-assisted recombination, traps are demonstrably present, and no independent sub-picosecond measurement of n(t) is provided, the conversion of Δσ(t)/Nabs into μ(t) is not uniquely justified. This directly affects the headline value of ~2,000 cm2 V−1 s−1 for the hot-carrier mobility.
[Crossover from non-equilibrium to quasi-equilibrium transport regime (Fig. 3b) and Methods] The estimate μ_hot ≈ 2,000 cm2 V−1 s−1 is obtained by scaling the Drude DC mobility (405 ± 30 cm2 V−1 s−1) by the ratio Δσ_peak/Δσ_offset. This scaling is not quantitatively valid without a finite-frequency correction: at Δσ_peak the conductivity spectrum is described by the Drude-Smith model, with a negative imaginary component and a suppressed low-frequency real part (Fig. 3b), while 405 cm2 V−1 s−1 is the Drude DC limit. The Drude-Smith parameter c is not reported in the main text, so the reader cannot evaluate whether the measured ratio over- or underestimates the true mobility ratio. The authors should either report the frequency-resolved ratio at the probe frequency with the corresponding c value or provide the corrected mobility.
[Spatiotemporal and energetic evolution of non-equilibrium photoexcitation (Fig. 4g)] The TAM-derived hot-carrier diffusion coefficients of 677 ± 59 cm2 s−1 (at 1.77 eV) and 1224 ± 94 cm2 s−1 (at 2.59 eV) imply, through the Einstein relation at room temperature, ambipolar mobilities of roughly 26,000–47,000 cm2 V−1 s−1 if the carriers are in quasi-equilibrium with the lattice. The paper does not reconcile these values with the claimed hot-carrier mobility of ~2,000 cm2 V−1 s−1; if the discrepancy is meant to be resolved by a high effective carrier temperature, that temperature and its uncertainty should be stated and propagated into the TAM-based propagation lengths.

minor comments (5)

[Synthesis and characterization of Cu3BHT films] In the sentence 'the Cu valence state can sever as an effective knob', 'sever' should be 'serve'.
[Main text, introductory paragraphs] 'Owning to the low optical phonon energy' should read 'Owing to the low optical phonon energy'.
[Synthesis and characterization of Cu3BHT films] The triclinic lattice parameters are reported as 'a = β = 99.94°, and g = 60.12°'; these should presumably be α = β = 99.94° and γ = 60.12°.
[Spatiotemporal and energetic evolution of non-equilibrium photoexcitation] 'D of hot carriers observed in the synthesized Cu3BHT film is superior that of hot carriers' should be 'superior to that of hot carriers'.
[Abstract and main text] The abstract states 'traversing grain boundaries up to 300 nm within a picosecond' while the text says the propagation length ranges from 200 to 320 nm; please ensure consistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the headline mobility values are derived from independent TRTS, TAS, and TAM measurements, with no fitted parameter renamed as prediction and no load-bearing self-citation.

full rationale

The paper's central derivations are experimentally self-contained rather than circular. The band-edge mobility of 405 ± 30 cm2 V–1 s–1 is obtained by fitting the measured frequency-resolved complex THz photoconductivity with the Drude model, using m* = 0.187 m0 from DFT; the hot-carrier mobility of ~2000 cm2 V–1 s–1 is then obtained by scaling this value by the measured photoconductivity ratio Δσ_peak/Δσ_offset. This is a model-based inference from measured data, not a parameter fitted to a target and then renamed a prediction. The critical photon energy of ~560 ± 50 meV is extrapolated from the photon-energy dependence of the same ratio and is explicitly checked against an independent Tauc absorption edge of ~0.5 eV. The TAM diffusion measurements and the TA blue-shift analysis are independent observables used for consistency, not inputs to the mobility derivation. The assumption that n remains constant within the first 10 ps is an interpretive premise that could be challenged on physical grounds (e.g., fast trapping), but it is not definitional and does not make the result equivalent to its inputs by construction. Self-citations (e.g., refs. 32, 33, 37, 38) concern synthesis methods and prior materials characterization; they do not supply the load-bearing transport result or import a uniqueness theorem. No step in the derivation chain reduces to an equation already assumed, so the circularity score is 0.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claims rest on a small set of fitted and calculated parameters: the Drude scattering time and the DFT effective mass set the quasi-equilibrium mobility scale; the recombination lifetime enters the diffusion length; the constant-n assumption is required to map the photoconductivity transient to mobility. No new physical entities are introduced.

free parameters (4)

Drude scattering time tau = 41 ± 3 fs
Fitted from the complex THz photoconductivity in the quasi-equilibrium regime (Fig. 3b bottom). The band-edge mobility is μ = eτ/m*, so any error in τ propagates directly to the central claim.
Reduced effective mass m* = 0.187 m0
Taken from DFT calculations, not fitted to transport data. It is the divisor in μ = eτ/m*, so the absolute mobility scale depends on the accuracy of this calculated value.
Carrier recombination lifetime t2 = ~1.2 ns
Extracted from bi-exponential fits to the THz photoconductivity decay. Used together with μ to compute the intrinsic diffusion length L = sqrt(μkTt2/e), which is reported as exceeding 1 um.
Drude-Smith backscattering parameter c = not reported
Fitted to the non-equilibrium complex photoconductivity using the Drude-Smith model. The value is not quoted in the text, which weakens the reproducibility of the non-equilibrium transport characterization.

assumptions (4)

domain assumption Drude and Drude-Smith models describe the frequency-resolved THz photoconductivity of Cu3BHT in the quasi-equilibrium and non-equilibrium regimes, respectively.
Invoked in Fig. 3b and in Methods (Drude-Smith model equation). The fits are good but the models are phenomenological; a different model could change the extracted scattering times and mobilities.
domain assumption The carrier density n is constant during the first 10 ps after photoexcitation.
Stated in the main text before Fig. 2c discussion ('Within the first 10 ps time where n can be considered constant'). This is load-bearing for reading Δσ/Nabs as a mobility transient and for scaling the hot-carrier mobility.
domain assumption The reduced effective mass m* = 0.187 m0 from DFT is accurate enough to convert the Drude scattering time into a mobility.
Used in the section 'Crossover from non-equilibrium to quasi-equilibrium transport regime' to compute μ = eτ/m*. The DFT calculation depends on the structural model (slipped-AA stacking) and the treatment of mixed Cu valence.
domain assumption Each absorbed photon creates a mobile electron-hole pair with a quantum yield that is independent of photon energy in the range studied.
The normalization by N_abs in Fig. 2c assumes that the initial free-carrier density scales linearly with absorbed photon number across hν. If the quantum yield varies with photon energy, the comparison of transients across hν would be distorted.

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Cite this review

Pith. "Pith review of Beyond the band edge: Unveiling high-mobility hot carriers in a two-dimensional conjugated coordination polymer." pith.science (2026). https://pith.science/paper/ZNLB4VIX

@misc{pith2026250108742,
  author       = {Pith},
  title        = {Pith review of: Beyond the band edge: Unveiling high-mobility hot carriers in a two-dimensional conjugated coordination polymer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZNLB4VIX}},
  note         = {Machine review of arXiv:2501.08742}
}

read the original abstract

Hot carriers, inheriting excess kinetic energy from high-energy photons, underpin numerous optoelectronic applications involving non-equilibrium transport processes. Current research on hot carriers has predominantly focused on inorganic materials, with little attention paid to organic-based systems due to their ultrafast energy relaxation and inefficient charge transport. Here, we overturn this paradigm by demonstrating highly mobile hot carriers in solution-processable, highly crystalline two-dimensional conjugated coordination polymer (2D c-CP) Cu3BHT (BHT = benzenehexathiol) films. Leveraging a suite of ultrafast spectroscopic and imaging techniques, we unravel the microscopic charge transport landscape in Cu3BHT films following non-equilibrium photoexcitation across temporal, spatial, and frequency domains, revealing two distinct high-mobility transport regimes. In the non-equilibrium transport regime, hot carriers achieve ultrahigh mobility of ~2,000 cm2 V-1 s-1, traversing grain boundaries up to 300 nm within a picosecond. In the quasi-equilibrium transport regime, free carriers exhibit Drude-type band-like transport with a remarkable mobility of ~400 cm2 V-1 s-1 and an intrinsic diffusion length exceeding 1 micrometer. These findings establish 2D c-CPs as versatile platforms for exploring high-mobility non-equilibrium transport, unlocking new opportunities for organic-based hot carrier applications.

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Works this paper leans on

1 extracted references · 1 canonical work pages

[1]

Petkov4, Wenpei Gao5, Jianjun Zhang1, Lei Gao2, Heng Zhang2, Min Liu2, Mike Hambsch6, Wenjie Zhang7, Jiaxu Zhang1, Keming Li3, Ute Kaiser8, Stuart S

1 Beyond the band edge: Unveiling high-mobility hot carriers in a two-dimensional conjugated coordination polymer Shuai Fu1,2,12, Xing Huang1,12, Guoquan Gao3,12, Petko St. Petkov4, Wenpei Gao5, Jianjun Zhang1, Lei Gao2, Heng Zhang2, Min Liu2, Mike Hambsch6, Wenjie Zhang7, Jiaxu Zhang1, Keming Li3, Ute Kaiser8, Stuart S. P. Parkin7, Stefan C. B. Mannsfeld...

work page 2021

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Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Petkov4, Wenpei Gao5, Jianjun Zhang1, Lei Gao2, Heng Zhang2, Min Liu2, Mike Hambsch6, Wenjie Zhang7, Jiaxu Zhang1, Keming Li3, Ute Kaiser8, Stuart S

1 Beyond the band edge: Unveiling high-mobility hot carriers in a two-dimensional conjugated coordination polymer Shuai Fu1,2,12, Xing Huang1,12, Guoquan Gao3,12, Petko St. Petkov4, Wenpei Gao5, Jianjun Zhang1, Lei Gao2, Heng Zhang2, Min Liu2, Mike Hambsch6, Wenjie Zhang7, Jiaxu Zhang1, Keming Li3, Ute Kaiser8, Stuart S. P. Parkin7, Stefan C. B. Mannsfeld...

work page 2021