Hyperbolic Phonon Polariton Electroluminescence as an Electronic Cooling Pathway

B. Placais; C. Voisin; E. Baudin

REVIEW 3 major objections 6 minor 63 references

Hyperbolic Phonon Polariton Electroluminescence as an Electronic Cooling Pathway

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper argues that in graphene-on-hBN transistors, Zener-Klein tunneling pumps electron-hole pairs whose recombination emits hyperbolic phonon polaritons, cooling the electron gas with powers about nine orders of magnitude above LED…

desk verdict A genuinely useful review of HPhP-mediated cooling in graphene/hBN, but the central experimental claim is undermined by an unaddressed shot-noise alternative and parameter circularity; the theory deserves peer review, the cooling conclusion does not yet. read the letter →

arxiv 1908.02953 v1 pith:BETCIZWF submitted 2019-08-08 cond-mat.mes-hall

E. Baudin , C. Voisin , B. Placais This is my paper · ORCID

classification cond-mat.mes-hall

keywords hyperbolicphononpolaritonselectroluminescentcoolingZener-Kleintunnelinggraphenehexagonalboronnitridenoisethermometrysuper-Planckianthermalemissionradiativeheattransfer

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 review argues that radiative cooling, normally negligible in electronics, can become the dominant heat-release pathway in a biased bilayer graphene transistor resting on hexagonal boron nitride (hBN). The key regime is Zener-Klein tunneling at high bias, where the electric field continuously creates electron-hole pairs whose interband recombination emits hyperbolic phonon polaritons, mid-infrared photons supported by the anisotropic hBN substrate in its Reststrahlen band near 200 meV. Noise thermometry shows the electronic temperature dropping as Joule power increases above the Zener-Klein threshold, which the authors read as electroluminescent cooling of the electron gas. They estimate cooling powers near 10 mW in a few-micrometer device, about nine orders of magnitude larger than the best LED-based refrigerator. If correct, this turns a normally inefficient black-body radiator into an engineered cooling channel for nanoelectronics.

What carries the argument

The load-bearing object is the hyperbolic phonon polariton (HPhP), a propagating electromagnetic mode sustained by anisotropic hBN inside its Reststrahlen bands, where the in-plane and out-of-plane dielectric permittivities have opposite signs and the dispersion relation $k_z^2/\epsilon_t + k_t^2/\epsilon_z = \omega^2/c^2$ becomes hyperbolic, allowing in-plane wavevectors far outside the vacuum light cone. The argument is carried by an impedance-matching factor $M = 4\,\mathrm{Re}(Z^{-1})\,\mathrm{Re}(\sigma)/|Z^{-1}+\sigma|^2$ from transmission-line theory, which quantifies how much of the channel's current noise is radiated into the substrate; the out-of-equilibrium interband noise is described by the van Roosbroeck-Shockley relation with a photon chemical potential $\mu_\mathrm{ph}=\mu_c-\mu_v$. Zener-Klein tunneling provides the electrical pumping that populates these interband transitions, and microwave Johnson-Nyquist noise thermometry supplies the measured temperature.

What would settle it

Measure the mid-infrared emission from the device in the 170-200 meV hBN Reststrahlen band while simultaneously recording the noise temperature: if the detected HPhP radiated power is far below the inferred ~10 mW cooling power, or if an independent temperature probe such as Raman thermometry shows no genuine drop in electron temperature at the Zener-Klein threshold, the central claim fails.

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Extended reading notes

Core claim

The central claim is that in the Zener-Klein tunneling regime of a high-mobility graphene transistor, the graphene electron gas is cooled by electroluminescence of hyperbolic phonon polaritons (HPhPs) in the hBN substrate, and that this radiative channel, not ordinary thermal emission, explains the sudden drop in noise temperature observed as the bias exceeds the Zener-Klein threshold. Zener-Klein tunneling is the field-driven interband tunneling that continuously creates electron-hole pairs, and their recombination radiates into the hyperbolic modes of hBN. Because the injection energy per electron-hole pair, $E_\mathrm{inj}=\beta_\mathrm{zk} l_\mathrm{zk} eE$, falls below the HPhP emission energy $\hbar\Omega_\mathrm{II}$, the missing energy is supplied by the thermal energy of the electron gas, producing net cooling rather than heating. The inferred cooling power is about 10 mW in a $3.6\times 3\,\mu$m device, and the associated heat conductance rises from roughly 50 kW m$^{-2}$K$^{-1}$ at low bias to 1.3 MW m$^{-2}$K$^{-1}$ above the threshold.

Load-bearing premise

The claim rests on Johnson-Nyquist noise thermometry faithfully tracking the average electron temperature in the Zener-Klein regime; if the measured noise-temperature drop is a calibration artifact or a change in coupling rather than real cooling, the cooling-power estimate collapses.

Editorial extensions

If this is right

Bias above the Zener-Klein threshold turns the graphene/hBN channel into a mid-infrared electroluminescent cooler rather than a Joule heater, so nanoscale devices can run at high power density without thermal runaway.
The measured heat conductance jumps from about 50 kW m$^{-2}$K$^{-1}$ to 1.3 MW m$^{-2}$K$^{-1}$ once HPhP electroluminescence ignites, a radiative conductance comparable to good phonon-based heat sinks.
Because the same mechanism is reported in single-, bi-, and tri-layer graphene, the effect is generic to gapless high-mobility channels on hyperbolic substrates, not a sample-specific curiosity.
The mechanism gives a design rule: cooling is maximal when the injected energy per pumped electron-hole pair, $E_\mathrm{inj}=\beta_\mathrm{zk} l_\mathrm{zk} eE$, sits below the substrate's Reststrahlen photon energy $\hbar\Omega_\mathrm{II}$, so substrates with higher optical-phonon energy push the cooling window to higher bias.
With a semi-infinite hBN thickness the emitted HPhPs escape before being reabsorbed, opening a route to active cooling stages embedded in hyperbolic dielectrics.

Reading between the lines

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

A direct test not reported in the paper would be to measure the emitted mid-infrared spectrum above the Zener-Klein threshold and correlate the 170-200 meV band intensity with the inferred ~10 mW cooling power, providing a photon-count check of the electroluminescence interpretation.
If noise thermometry overestimates the hot-electron temperature at high drift velocity, as the paper's footnotes concede, the true cooling could be even larger, or the apparent drop could be partly a thermometer artifact; an independent temperature probe such as Raman or photocurrent thermometry would separate these possibilities.
The same transmission-line framework suggests that other hyperbolic materials with Reststrahlen bands in the near-infrared, such as tetradymites, could push electroluminescent cooling to higher temperatures and smaller devices, but the paper only sketches this extension.
The inferred photon chemical potential $\mu_c-\mu_v\simeq 0.16$ eV at maximum cooling sits near the lower edge of hBN band II, implying the device is essentially a tunable mid-infrared emitter whose emission energy is set by the substrate's phonon bands rather than a material bandgap.

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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 thing to know about this paper is that it is a review of the authors' own prior results, not a new experiment. The theoretical part is solid: the transmission-line treatment of super-Planckian emission and the appendix computation of the nonlocal conductivity are clear and correct as far as I can tell. If someone wants the standard formalism for HPhP-mediated radiative heat transfer in graphene/hBN, this is a usable entry point.

The experimental claim is another matter. The central evidence for "electroluminescent cooling" is the drop in the noise temperature TN=SI/(4kBGds) at the Zener-Klein threshold. The paper never separates the Nyquist thermal noise from the shot noise that is expected in a tunneling regime. In Section V.B they even write the current noise as SI=2eFI with F~0.1, but they never subtract that term from TN. With the constant Gzk=0.45 mS, a shot-noise component alone gives TN_shot=(eF/2kB)V, about 580 K per volt for F=0.1. That is a linear-in-voltage "cold branch" of the same shape as the one in Fig. 4b, and at 1-2 V it is a large fraction of the observed 1400 K floor. Footnotes [52] and [59] say TN can overestimate the electronic temperature at large drift velocity, but that goes the wrong way: an overestimate would mean the true drop is larger, not that it is an artifact. The shot-noise alternative is not discussed. I think this is a genuine hole, and the cooling power estimate of ~10 mW is not established until it is closed.

There is also some circularity: the parameters beta_zk, l_zk, and mu_c-mu_v are extracted from the same transport and noise data that the model is then compared with. That is fine for a phenomenological fitting exercise, but it is not an independent test of the model. The "nine orders of magnitude larger than LEDs" headline is also context-dependent; the authors themselves admit the device is not a refrigerator, so the comparison is rhetorical.

To be fair, the paper is honest about being a review, and the physical picture—Zener pumping followed by HPhP recombination—is plausible. The theoretical machinery is worth having. But at present it is a conditional story: if the shot noise is ruled out, the cooling claim is strong; if not, the cold branch may be an artifact of the thermometer.

I would send this to peer review—the theory is useful enough and the claim important enough—but a serious referee should insist on a quantitative bound for the shot-noise contribution and a re-analysis of the original data before the cooling conclusion can be accepted.

Referee Report

3 major / 6 minor

Summary. The paper develops a transmission-line theory of radiative heat transfer from a two-dimensional electronic channel into a hyperbolic phonon-polariton substrate, separating equilibrium (super-Planckian) thermal emission from out-of-equilibrium electroluminescent emission. It applies this framework to a bilayer graphene-on-hBN transistor in the Zener-Klein tunneling regime, re-analyzing transport and noise data originally reported in Ref. [3]. The central claim is that above the Zener-Klein threshold, interband recombination assisted by hyperbolic phonon polaritons cools the electron gas, producing the observed drop in noise temperature with increasing Joule power, with inferred cooling powers around 10 mW and a claimed advantage of nine orders of magnitude over conventional LED refrigerators. The paper includes a derivation of the nonlocal conductivity in the appendix and discusses the role of hBN thickness, doping, and the threshold field for the cooling regime.

Significance. If the central claim holds, the paper identifies a qualitatively new cooling pathway in graphene-based transistors and provides a theoretical framework for engineering hyperbolic-substrate cooling in other material systems. The transmission-line formulation with a nonlocal conductivity and the impedance-matching analysis is a useful and internally consistent contribution, and the explicit nonlocal Lindhard calculation in the appendix is a valuable technical addition. The paper also makes falsifiable predictions about the doping-dependent threshold and the boundary between heating and cooling, which is a strength. However, the experimental support is not yet convincing because the noise-temperature analysis does not separate thermal noise from shot noise, and the model parameters are extracted from the same data that the model is used to explain. These issues are load-bearing for the claimed cooling power and for the comparison with LED refrigerators.

major comments (3)

[Section III.C and Section V.B] The noise thermometry analysis does not subtract or bound the shot-noise contribution, which directly threatens the central cooling claim. The noise temperature is defined as T_N = S_I/(4 k_B G_ds), an identification that is valid only for Johnson-Nyquist thermal noise. In the Zener-Klein tunneling regime the current is carried by interband tunneling events, whose partition noise contains a shot-noise component S_I^shot = 2 e F I. With the approximately constant differential conductance G_zk ≈ 0.45 mS, this component alone yields an apparent T_N^shot = (e F / (2 k_B)) V, i.e., a linear-in-voltage 'cold' branch of the kind observed in Fig. 4b after the drop. Footnotes [52] and [59] discuss only an overestimate of T_N at large drift velocity, which is a different and even opposite concern, and the paper does not provide a Fano factor or any independent decomposition of the measured S_I. Unless the authors show that the measured noise in the ZK regime is dominated by thermal fluctuations, the drop in T_N cannot be taken as evidence of genuine electron-gas cooling by HPhP electroluminescence.
[Section III.B and Section III.D] The quantitative support for the electroluminescence model relies on parameters extracted from the same data that the model is supposed to explain. In Section III.B, β_zk and l_zk are obtained from the differential conductance G_zk and from the matching of the boundary line I_sat = (2/β_zk) G_zk V_zk, so the agreement of the transport boundary is to a significant degree by construction. In Section III.D, the chemical potential imbalance μ_c - μ_v ≈ 0.16 eV is deduced from the noise-temperature data under the assumption that the cooling power is governed by the photon occupation factor; the subsequent consistency of the threshold therefore does not independently validate the cooling mechanism. An independent check, such as a prediction of the threshold voltage from known hBN and graphene parameters without fitting, or a direct measurement of the emitted HPhP radiation, is needed to support the central claim.
[Section III.D and Fig. 1] The inferred cooling power of about 10 mW is obtained from a power-balance model in which HPhP electroluminescence is treated as the dominant bias-dependent cooling channel, and the paper does not quantify competing channels in this device: acoustic phonon emission to the 4.2 K bath, heat conduction through the hBN and contacts, or changes in the Wiedemann-Franz contribution as the differential conductance saturates. Since the electron temperature itself is inferred from the noise temperature, whose interpretation in the tunneling regime is questionable (see the first major comment), the 10 mW figure and the nine-orders-of-magnitude comparison with LED refrigerators are not established by the present analysis. At minimum, the authors should state that this is an upper bound and provide an error budget that includes these alternative cooling pathways.

minor comments (6)

[Section I] The abstract and Introduction use 'bi-dimensional'; the conventional term is 'two-dimensional'.
[Section III.C] The sentence 'The former corresponds to a a superlinear bias dependence' contains a duplicated article 'a'.
[Section III.C] The word 'interpretaed' should be 'interpreted'.
[Section II.B, Eq. (11)] The symbol n_ph is used both for the equilibrium Planck function in Eq. (3) and for the Bose function with photon chemical potential in Eq. (11); using distinct symbols would avoid confusion.
[Figure 4b / Section III.D] The dashed line marking the boundary between electroluminescent cooling and heating is defined by E_th = ℏΩ_II/(β_zk l_zk e), but the figure caption does not state the values of β_zk and l_zk used to draw it; please specify them.
[Appendix, Eqs. (18)-(19)] The branch condition for the square root is stated as 'for ℏω/µ > (q/k_F)^2', but the relevant condition is on the discriminant (ℏω/µ - y^2)^2 - 4y^2; the text should state this more precisely.

Circularity Check

2 steps flagged · score 6.0 of 10

The ZK-regime cooling threshold reuses parameters fitted to the same data, and the linear 'cold branch' is indistinguishable from uncorrected shot noise, so the HPhP-electroluminescence cooling claim is only partially supported.

fitted input called prediction [Section III.B–D (ZK parameter extraction and Eth boundary definition)]
"Experimentally, one can extract the product βzklzk∝ 1/kF from the constant differential conductance Gzk≃ 0.45 mS. ... From the slope of the line we extract βzk≃ 0.5, and finally deduce lzk(|n|). ... This allows obtaining the characteristic electric field for which injection energy balances HPhP emission energy ℏΩII by electron-hole pair recombination. This electric field ... defines the boundary between electroluminescent cooling and heating, it is indicated in Figure 4-b (dashed line) and it matches well the voltage for which the minimal temperature is reached."

The 'predicted' cooling/heating boundary is not an independent prediction: βzk and lzk are extracted from the same constant ZK conductance Gzk and from the fitted Isat–Vzk line of the same device in Section III.B. The threshold Eth is just the assumed hBN phonon energy divided by the fitted product βzklzk times e. The match with the noise-temperature minimum is therefore a consistency check between two observables of the same dataset within the same model, not a first-principles test of the electroluminescence-cooling mechanism. Presenting this as a confirmation moves a fitted parameter into the role of a predicted threshold.
other [Section III.C and V.B (noise temperature definition and linear 'cold branch'), Fig. 4b]
"a quasi-linear dependence TN ∝ Vds at high bias ... Writing thermal noise as SI = 2eFI, where F ∼0.1 is a typical thermal Fano factor, one estimates a 1/f-corner frequency ..."

Combining the paper's own formulas, TN = SI/(4GdskB) and SI = 2eFI, with the constant ZK conductance Gzk, gives TN = (eF/2kB)V, a strictly linear-in-voltage 'cold branch' of exactly the form observed after the drop in Fig. 4b. The paper never subtracts or bounds the shot/partition noise of interband Zener-Klein tunneling; footnotes [52] and [59] only discuss drift-velocity overestimates of TN. The central cooling signature is therefore not uniquely tied to a cooled electron gas: by the paper's own noise formulas, the linear branch reduces by construction to shot noise if the ZK excess noise is non-thermal, so the electroluminescent-cooling interpretation is not forced by the data.

full rationale

The theoretical framework—hyperbolic impedance matching, nonlocal conductivity, and the van Roosbroeck–Shockley source term—is largely self-contained and cross-checked against independent literature, so the paper is not wholly circular. The circularity enters in the experimental validation chain: the ZK parameters used to construct the cooling/heating boundary are fitted to the very device data that are then said to confirm the boundary, and the linear 'cold branch' is exactly what the paper's own SI=2eFI shot-noise expression produces for constant Gzk. The heavy reliance on the authors' own Ref. [3] for the sample, the ZK regime, and the thermometry is a self-citation chain, but the reproduced data and independent theoretical ingredients prevent an 8–10 score. The correct finding is partial circularity: the central claim that the temperature drop is caused by HPhP electroluminescent cooling is not independently established, because the threshold check reuses fitted parameters and the shot-noise alternative is not excluded.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard electromagnetic and fluctuation-dissipation theory, with domain assumptions about the electronic distribution in the Zener regime and the temperature of the hBN substrate. Three parameters (beta_zk, l_zk, mu_c - mu_v) are extracted from the experimental data and are then used in the model to 'predict' the cooling threshold, which is the main source of circularity.

free parameters (3)

beta_zk (smooth junction factor) = approx 0.5
Extracted from the slope of the intraband/interband boundary line Isat = (2/beta_zk) G_zk V_zk in Section III.B; used to compute Einj and Eth.
l_zk (electron-hole diffusion length) = proportional to 1/sqrt(|n|)
Deduced from the constant Zener-Klein conductance G_zk approx 0.45 mS in Section III.B; enters Eth and Einj.
mu_c - mu_v (interband chemical potential imbalance) = approx 0.16 eV
Inferred from the temperature drop data in Section III.D assuming the cooling power scales with the photon occupation factor; used to place the emission at the RS band edge.

assumptions (4)

standard math Fluctuation-dissipation theorem for thermal current noise: |j|^2 = (1/(2pi)^3) 4Re(sigma) hbar omega n_ph(T,omega) d^2q domega.
Used in Eq. (3) to express thermal radiation from the channel; standard result in near-field heat transfer.
domain assumption van Roosbroeck-Shockley relation for interband out-of-equilibrium emission with photon chemical potential, Eq. (11).
Extends the thermal fluctuation formula to electroluminescence; requires two quasi-Fermi distributions and ultrafast electron-electron thermalization, as stated in Section II.B.
domain assumption Isotropic parabolic dispersion and unitary Bloch wave projection: |<chi_k|chi_{k+q}>|^2 approx 1 and E_k = hbar^2 k^2 / 2m*.
Used in Section II.A to derive the nonlocal conductivity and matching factor; monolayer graphene is referenced to prior work, but the parabolic-band calculation is a simplification.
domain assumption The hBN substrate remains cold and the back thermal flux from hBN to the channel is negligible.
Assumed in Section II before Eq. (4) to allow treating the emitted power as one-way; relies on the gold backgate sinking heat.

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Cite this review

Pith. "Pith review of Hyperbolic Phonon Polariton Electroluminescence as an Electronic Cooling Pathway." pith.science (2026). https://pith.science/paper/BETCIZWF

@misc{pith2026190802953,
  author       = {Pith},
  title        = {Pith review of: Hyperbolic Phonon Polariton Electroluminescence as an Electronic Cooling Pathway},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BETCIZWF}},
  note         = {Machine review of arXiv:1908.02953}
}

abstract

Engineering of cooling mechanism is of primary importance for the development of nanoelectronics. Whereas radiation cooling is rather inefficient in nowadays electronic devices, the strong anisotropy of 2D materials allows for enhanced efficiency because their hyperbolic electromagnetic dispersion near phonon resonances allows them to sustain much larger ($\sim 10^5$) number of radiating channels. In this review, we address radiation cooling in 2D materials, specifically graphene hexagonal boron nitride (hBN) heterostructures. We present the hyperbolic dispersion of electromagnetic waves due to anisotropy, and describe how the spontaneous fluctuations of current in a 2D electronic channel can radiate thermal energy in its hyperbolic surrounding medium. We show that both the regime of (i) thermal current fluctuations and (ii) out-of-equilibrium current fluctuations can be described within the framework of transmission line theory leading to (i) superPlanckian thermal emission and (ii) electroluminescent cooling. We discuss a recent experimental investigation on graphene-on-hBN transistors using electronic noise thermometry. In a high mobility semimetal like graphene at large bias, a steady-state out-of-equilibrium situation is caused by the constant Zener tunneling of electrons opening a route for electroluminescence of hyperbolic electromagnetic modes. Experiments reveal that, compared to superPlanckian thermal emission, electroluminescence cooling is particularly prominent once the Zener tunneling regime is reached: observed cooling powers are nine orders of magnitude larger than in conventional LEDs.

Figures

Figures reproduced from arXiv: 1908.02953 by the authors.

**Figure 2.** FIG. 2: Real part of the optical admittance ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** represents the matching factor taking into account only the conduction band of bilayer graphene for increasing doping. The allowed transitions in the degenerate regime restrict the HPhP radiation window in the wavevector range [(p 1 + µ −1 r − 1)kF , p 1 + µ −1 r + 1)kF ], which is centered on qc = kF / √µr = √ 2m∗~ΩII /~ ' 4.43 108 m−1 . For semimetals (like few layer graphene), the wavevector window for impedance … view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4: Transport and noise of a hBN-supported graphene ZKT transistor. Panel a) current saturation and Zener-Klein regimes [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 1.** Figure 1: For −n = 1.25 × 1012 cm−2 doping, the maximum temperature TN ' 3200 K is reached at ZK threshold for an injected Joule power 0.25 mW µm−2 , and drop to a minimal temperature TN ' 1400 K for 1 mW µm−2 . Assuming the cooling power variation with the electronic bath state…

**Figure 5.** Figure 5: FIG. 5: SuperPlanckian material dependent factor at null temperature [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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The computation of the nonlocal conductivity is given in appendix

Unitary Bloch wave projection: Due to the small extent of the Fermi sea compared to the Brillouin zone, we can approximate|⟨χk|χk+q⟩|2∼ 1. The computation of the nonlocal conductivity is given in appendix. In the degenerate case, one has σ(ω,q ) = G0 gsgv 4π S(µ/ℏω,q/kF ), where S is a simple geometric function. Consequently, the prefactor AF is a functio...

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Since RS bands are narrow ∆ω≪ Ω, the photon population is nearly constant over a RS band and given by the occupancy at mid-band nph(T,ω )≃ nph(T, Ω)

Matching Factor Let us ﬁrst consider thermal emission by a single band. Since RS bands are narrow ∆ω≪ Ω, the photon population is nearly constant over a RS band and given by the occupancy at mid-band nph(T,ω )≃ nph(T, Ω). The radiated power (4) in the RS band energy then reads Prad =AFk2 F ℏΩnph(T, Ω)∆ω , (6) with AF = 1 (2π)2∆ω ˆ ωLO ωT O dω ˆ ∞ 0 xdxM(ω...

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The speciﬁc case of graphene has been dealt in detail in the literature [14]

Isotropic parabolic dispersion: Except for monolayer graphene, isotropic parabolic dispersion covers most nat- urally occurring cases. The speciﬁc case of graphene has been dealt in detail in the literature [14]

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hot" electrons (dotted black line) in the former, dropping toward a linear dependence characteristic of

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