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REVIEW 3 major objections 5 minor 65 references

Two-color harmonic spectroscopy of ultrafast Dirac electron dynamics

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read In graphite, the fourth harmonic is emitted about 17.5 femtoseconds before the driving pulse peaks, and the paper attributes this timing shift to ultrafast saturation of electrons near the Dirac point.

desk verdict Clean measurement of a saturation-induced four-wave emission delay in HOPG, but the mechanism is only as strong as the assumed T2. read the letter →

arxiv 2505.24290 v2 pith:7Q5IIY2D submitted 2025-05-30 physics.optics cond-mat.mes-hall

Zhaopin Chen , Camilo Granados , Eyal Uzner , Ido Nisim , Daniel Kroeger , Ofer Neufeld , Marcelo F. Ciappina , Michael Krüger This is my paper
classification physics.opticscond-mat.mes-hall
keywords high-harmonicgenerationHOPGgraphiteDiracsemimetalcarriersaturationstateblockingtwo-colorspectroscopysemiconductorBlochequationsultrafastdynamics
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

Using a weak second-harmonic pulse as a delay-scanned probe of harmonic emission, the authors find that the fourth harmonic from HOPG graphite peaks at a two-color delay of about $-17.5\pm 0.2$ fs, while the above-bandgap harmonic from a ZnO reference peaks exactly at zero delay. They attribute the negative delay to ultrafast carrier saturation near the Dirac point: the gapless band structure lets the driving pulse populate conduction and valence bands toward half-filling before the field maximum, and the state-blocking factor $(1-f_c-f_v)$ in the semiconductor Bloch equations suppresses interband emission during the trailing edge. If this interpretation is right, harmonic generation in gapless Dirac materials is a nonparametric, saturating process that leaves long-lived hot carriers behind, and the timing of harmonic emission becomes an all-optical clock for femtosecond carrier excitation.

What carries the argument

The organizing object is the state-blocking factor $(1 - f_c(k,t) - f_v(k,t))$ in the interband driving term of the semiconductor Bloch equations; when both bands approach half-filling, this factor vanishes and interband harmonic emission is cut off. The experimental machinery is a two-color $\omega_0$–$2\omega_0$ delay scan in which the weak second harmonic samples harmonic emission that is generated mainly by the fundamental. The analytical machinery is the population equation $dP/(1-2P)=w(t)\,dt$, whose solution $P(t)=\frac{1}{2}\left(1-e^{-2\int_0^t w(\tau)d\tau}\right)$ and depleted rate $w_{\mathrm{depletion}}(t)=e^{-2\int_0^t w(\tau)d\tau}w(t)$ give the intensity dependence of the emission-time shift.

What would settle it

Measure the interband decoherence time of HOPG independently (for example, by transient absorption or degenerate four-wave mixing at 1980 nm) while repeating the two-color H4 scan: if $T_2$ comes out above roughly 16 fs and the harmonic maximum still sits near $-17.5$ fs, the state-blocking explanation is incomplete; and if a sample whose Fermi level is moved away from the Dirac point shows no negative shift, the Pauli-blocking mechanism is directly refuted.

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Extended reading notes

Core claim

The paper's central claim is that HOPG supports nonperturbative harmonic generation already at intensities near $10^{10}$ W cm$^{-2}$, and that in this regime the harmonic emission time carries a direct imprint of ultrafast carrier dynamics. Concretely, the maximum of the two-color fourth harmonic occurs at $\mu_0 = -17.5\pm 0.2$ fs, before the $\omega_0$ and $2\omega_0$ pulses overlap, because the populations of conduction and valence states near the Dirac cone reach half-filling before the driving field peaks; the resulting state blocking weakens the interband polarization that produces harmonics, so the strongest emission happens just before saturation sets in. The authors support this with SBE simulations in 1D and 2D, an analytical model in which the excitation rate is multiplied by the depleted factor $e^{-2\int w\,d\tau}$, and an intensity scan in which the shift grows with peak intensity, and they show that gapped references (ZnO and WS$_2$) exhibit no analogous shift.

Load-bearing premise

The load-bearing premise is the choice of the interband decoherence time $T_2 = 6.6$ fs, which the paper assumes rather than measures for HOPG; the negative shift from the 2D graphene model turns positive for $T_2 \gtrsim 16$ fs, and the 3D HOPG model that could settle this is deferred to a separate manuscript.

Editorial extensions

If this is right

  • If the interpretation is correct, harmonic generation in gapless Dirac materials is nonperturbative already at about $10^{10}$ W cm$^{-2}$ and is nonparametric: the pulse leaves a sizable conduction-band population behind, so the material is not returned to its initial state.
  • The quadratic relation between the two-color shift $\mu_0$ and the single-color quarter-excitation time $t_c$ ($R^2 = 0.99$) means the timing of harmonic emission carries quantitative carrier-population information by itself.
  • For petahertz optoelectronics in gapless materials, full reversibility of light-driven currents requires staying below the state-blocking threshold; above it, a pre-excitation pulse can act as an all-optical switch that suppresses nonlinear conversion.
  • The negative shift should grow with driving intensity and shrink as the bandgap is reopened; the paper reports both trends (intensity scan in Figure 4 and the gap-reduction simulations in the Supplementary).
  • Saturation-induced depletion in a nonparametric harmonic process may allow upconverted emission with nonclassical photon statistics, a consequence the authors extend from gas-phase predictions to solids.

Reading between the lines

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

  • Beyond the paper, the $T_2$ sensitivity makes the measured shift a candidate all-optical probe of interband dephasing: matching $\mu_0$ against SBE simulations for a range of $T_2$ values would estimate $T_2$ in HOPG, and an independent $T_2$ measurement would test whether state blocking alone produces the shift.
  • Beyond the paper, the same two-color scan on encapsulated or cleaner graphene, where $T_2$ is expected to be longer, should either reproduce the negative $\mu_0$ or expose the limits of the constant-$T_2$ dephasing ansatz, since the 2D model flips sign near $T_2 \approx 16$ fs.
  • Beyond the paper, the strong $t_c$-$\mu_0$ correlation suggests that a single-color time-frequency analysis of harmonic emission could replace the two-color delay scan when a phase-locked second harmonic is unavailable.
  • Beyond the paper, the mechanism predicts a negative emission-time shift in other gapless or narrow-gap conductors driven to comparable excitation fractions; Weyl semimetals and engineered narrow-gap systems would provide direct tests.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript reports a two-color (omega0-2 omega0) harmonic spectroscopy study on highly oriented pyrolytic graphite (HOPG). The main experimental observation is that the maximum of the fourth harmonic signal occurs about 17.5 +/- 0.2 fs before the temporal overlap of the two pulses, whereas the same measurement in ZnO and WS2 yields a maximum at zero delay. The authors attribute this negative emission-time shift to ultrafast carrier saturation and state blocking near the Dirac point, which suppresses interband harmonic emission before the driving field reaches its peak. Support is provided by one-, two-, and three-dimensional semiconductor Bloch equation (SBE) simulations as well as an analytical rate model, and by the observation that the shift becomes more negative as the driving intensity increases.

Significance. If the interpretation is correct, the work introduces a new all-optical observable, the negative emission-time shift, that is sensitive to strong-field carrier saturation in gapless materials at intensities as low as ~10^10 W cm^-2. The experimental controls are strong: the same setup and analysis give zero shift for gapped reference materials, and the intensity trend is monotonic and reproduced by the 1D SBE and by the analytical model. The transparent SI reveals a potential fragility of the theoretical support, which is discussed below. The potential impact on ultrafast optoelectronics and on the understanding of nonperturbative harmonic generation in Dirac materials is significant, provided the theoretical attribution is put on firmer footing.

major comments (3)
  1. [Methods and Supplementary Fig. S11] The predicted sign of the H4 delay in the 2D graphene SBE model is strongly dependent on the phenomenological decoherence time T2: Fig. S11 shows the delay crossing zero near T2 approximately 16 fs and becoming positive for longer T2, while the Methods section sets T2 = 6.6 fs without an independent experimental determination for HOPG. The 1D model does not exhibit this T2 sensitivity, so the two theory levels presented disagree about the robustness of the central simulated result. The assertion in the SI that the phenomenological T2 is a 'bad approximation' in this regime is qualitative and is not supported by a microscopic dephasing model. Since the experimental data provide only the value of the shift and not the mechanism, the attribution of the negative shift to state blocking is not fully established until this T2 dependence is resolved or the interpretation is appropriately qualified.
  2. [Introduction and Methods, Eq. (1)] The manuscript correctly notes that harmonic suppression could arise from state blocking or from excitation-induced dephasing, but the SBE simulations use a constant T2 and do not include a density-dependent dephasing channel. The experimental H4 shift increases with intensity, which is consistent with either increased state blocking or increased dephasing at higher carrier densities. The simulations therefore do not uniquely identify the microscopic mechanism; the conclusion that state blocking is responsible should either be supported by a model that incorporates density-dependent dephasing or be softened to reflect the remaining ambiguity.
  3. [SI, 'Theoretical model for high harmonic generation from HOPG'] The 3D HOPG SBE model used for the single-color time-frequency analysis in Fig. 3d is referenced only to unpublished work ('manuscript in preparation', SI ref. [13]) and is not fully specified: the tight-binding Hamiltonian, the analytical diagonalization, the dipole and momentum matrix element derivations, and the convergence parameters are only briefly sketched. Since Fig. 3d is presented as corroborating evidence from a more realistic model, the omission prevents verification of this result. Please provide the full model equations and parameters in the SI, or remove the 3D panel from the main-text evidence chain.
minor comments (5)
  1. [Abstract] The sentence 'Our finding reveal that field-driven carrier saturation plays a critical role' contains a grammatical error; it should read 'Our findings reveal' or 'Our finding reveals'.
  2. [Methods, Eq. (12)] The statement 'the emitted harmonic intensity is proportional to the instantaneous excitation rate, I_HH(t) ~ w_depletion(t)' is asserted without derivation. In the SBE framework the interband current involves time derivatives of the interband polarization, so this identification is an additional assumption; please clarify that it is a heuristic approximation used only for the analytical rate model.
  3. [Fig. 4b] Please indicate whether the 'Analyt.' curve involves any adjustable overall amplitude or prefactor in w0(k,t), or whether all constants are fixed by the experimental parameters. Without this information it is difficult to assess whether the agreement with the experimental points is parameter-free or fitted.
  4. [Supplementary Fig. S10] The caption of Fig. S10 should explicitly state that panel (b) uses T2 = 26 fs and that this longer dephasing time yields a positive shift, so that readers who focus on the main text's discussion of the T2 = 6.6 fs case are not misled about the sign of the 2D result.
  5. [Fig. 2 caption] The axis label in Fig. 2 is written as 'omega - 2omega delay (fs)', but the text uses 'omega0-2omega0 delay'; please harmonize the notation.

Circularity Check

1 steps flagged · score 2.0 of 10

The analytical rate model embeds the saturation mechanism in its definition of harmonic intensity, but the main experimental and SBE evidence is independent; no central circularity.

  1. self definitional [Methods, 'Analytical form of population dynamics', Eqs. 7-12; Fig. 4b]
    "The actual (depleted) instantaneous excitation rate is given by wdepletion(t) = dP(t)/dt = e^{-∫0^t 2w(τ)dτ} · w(t). For interband-driven harmonic generation, the emitted harmonic intensity is proportional to the instantaneous excitation rate, IHH(t) ∼ wdepletion(t)."

    The analytical 'prediction' of an intensity-dependent negative delay is built into the definition of the observable: harmonic intensity is set proportional to the depletion rate wdepletion, whose exponential factor e^{-∫2w} (equivalently (1-2P)) is exactly the saturation/state-blocking effect under test. Maxima of IHH(t) therefore shift earlier than the field peak by construction whenever P grows appreciably before the peak. The model can illustrate the proposed mechanism and match the trend in Fig. 4b, but it cannot independently establish that saturation causes the shift; independent support comes from the SBE simulations and the ZnO/WS2 control measurements.

full rationale

The central claim—that the H4 maximum in HOPG appears ~17.5 fs before zero delay and that this shift reflects ultrafast carrier saturation—does not reduce to any fitted constant. The experimental measurement is direct, the ZnO and WS2 controls peak at zero delay, and the SBE simulations (Eq. 1) predict the sign and approximate magnitude of the shift without being calibrated to the H4 delay. The one partially self-definitional element is the analytical population model (Eqs. 7-12), which assumes harmonic intensity ∝ depleted excitation rate and thus produces the early-time peak as a consequence of its own ansatz; this limits the model's evidentiary weight but not the overall derivation. The disclosed T2 sensitivity (Fig. S11: negative shift only for T2 ≲ 16 fs in the 2D model, with T2=6.6 fs chosen in Methods) is a robustness/parameter-uncertainty concern, not a circular reduction. The brief deferral of the 3D HOPG model to an unpublished companion manuscript by overlapping authors (SI ref. 13) is a missing-support caveat for the supplementary 3D panel, but it is not load-bearing for the main two-color result.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard SBE machinery, one load-bearing phenomenological parameter (T2), and one modeling ansatz for the analytical trend (I_HH ~ w_depletion). No new physical entities are introduced. Data and code are not archived, and the 3D model is partly deferred to an unpublished manuscript.

free parameters (3)
  • T2 (interband decoherence time) = 6.6 fs
    Set to one optical cycle of the 2 um driving field. The sign of the simulated two-color delay shift in the 2D model reverses for T2 greater than about 16 fs, so this choice is load-bearing for the central claim.
  • T1 (population relaxation time) = 13 ps
    Chosen from graphene literature; authors state results are insensitive to it.
  • Interlayer hopping in 3D HOPG TB model = 0.0127 eV
    Fitted to the gap opening between bands at K obtained from DFT simulations, as described in the SI.
assumptions (6)
  • domain assumption Dirac-cone approximation for HOPG with v_F = 10^6 m/s
    Invoked in Methods; assumes laser-driven carriers remain near the Dirac point at the moderate intensities used.
  • domain assumption Undoped HOPG with Fermi level at the Dirac point (mu ~ 0)
    Results section; based on ARPES measurements cited in the paper, with kT much smaller than the photon energy.
  • domain assumption Phenomenological relaxation and decoherence times T1, T2 in the SBEs
    Methods; T2 = 6.6 fs is the critical parameter, and the 2D result changes sign for longer T2 (Fig. S11).
  • ad hoc to paper Harmonic intensity is proportional to the instantaneous excitation rate, I_HH(t) ~ w_depletion(t)
    Analytical model, Eq. 12; asserted for interband-driven harmonics and used to derive the mu_0 versus intensity trend.
  • domain assumption Reflection-geometry emission originates from a thin near-surface layer, and depth averaging does not create the delay
    SI penetration-depth analysis using graphite optical constants; verified with coherent averaging in gapped and gapless cases.
  • ad hoc to paper Interlayer hopping obtained by fitting TB gap to DFT
    SI theoretical model; the 3D simulation depends on this fitted coupling, which is not independently measured.

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Pith. "Pith review of Two-color harmonic spectroscopy of ultrafast Dirac electron dynamics." pith.science (2026). https://pith.science/paper/7Q5IIY2D

@misc{pith2026250524290,
  author       = {Pith},
  title        = {Pith review of: Two-color harmonic spectroscopy of ultrafast Dirac electron dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7Q5IIY2D}},
  note         = {Machine review of arXiv:2505.24290}
}
abstract

High-harmonic generation (HHG), the hallmark effect of attosecond science, is a nonperturbative nonlinear process leading to the emission of high-harmonic light from gases and solids. In gases, extreme driving laser pulse intensities can deplete the ground state, suppressing harmonic emission during the trailing edge of the pulse. Here, we report a similar effect, pronounced ultrafast carrier saturation dynamics and harmonic emission suppression during nonperturbative harmonic generation (NPHG) in a gapless Dirac semimetal -- highly oriented pyrolytic graphite (HOPG). Remarkably, HOPG supports NPHG at laser intensities as low as $\sim 10^{10}$ W cm$^{-2}$, facilitated by its vanishing bandgap. Ultrafast carrier saturation strongly modulates the interplay between interband and intraband currents, a key characteristic of NPHG in Dirac materials. Using two-color spectroscopy, we reveal the excitation dynamics of Dirac electron-hole pairs as it affects the emission of harmonics during the presence of the driving laser pulse. The excitation of out-of-equilibrium hot carriers and the concomitant saturation near the Dirac points leads to a marked suppression of interband harmonics and induces measurable temporal shifts. These observations are supported by simulations based on semiconductor Bloch equations. Our finding reveal that field-driven carrier saturation plays a critical role in gapless solid NPHG. We demonstrate the potential of NPHG and HHG as a sensitive, all-optical probe of ultrafast carrier dynamics, offering novel opportunities for ultrafast optoelectronics in Dirac materials.

Figures

Figures reproduced from arXiv: 2505.24290 by the authors.

Figure 1
Figure 1. Nonperturbative harmonic generation from HOPG by a two-color pulse. a, Conceptual sketch of nonperturbative harmonic generation in HOPG driven by a strong driving laser pulse with 1980 nm central wavelength and a weak second harmonic pulse. b, Three-step model of interband HHG around the Dirac cone. c, Experimentally measured harmonic spectrum with a laser peak intensity of 72 GW cm−2 and 3% second harmonic admixtur… view at source ↗
Figure 2
Figure 2. Harmonic intensity as a function of ω0–2ω0 delay. a, Experimentally measured harmonic intensities as function of the ω0–2ω0 delay for the fourth harmonic (H4) in HOPG with ω0 peak intensity 72 GWcm−2 . b, The same for the sixth harmonic (H6) in ZnO with a laser intensity of 430 GWcm−2 . c and d, Corresponding theoretical results simulated based on the semiconductor Bloch equations (Eq. 1) for comparison with the exp… view at source ↗
Figure 3
Figure 3. Population saturation dynamics around Dirac points. a, Calculated conduction band electron population dynamics and b, interband polarization dynamics in momentum space during the excitation driven solely by the fundamental pulse at an intensity of 72 GW cm−2 . In the gapless Dirac cone, carrier populations can reach up to 50% at each k-point, leading to pronounced saturation effects. c, The total conduction band pop… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: H4 emission time shift as a function of laser intensity. a, Experimentally measured normalized H4 intensity as a function of ω0–2ω0 delay at different laser intensities. The relative delay position (µ0) of the maximum H4 intensity shifts to earlier times as the laser i…
Figure 5
Figure 5. Figure 5: Analysis of Dirac electron population dynamics via emission time shift. a, Electron dynamics associated with fourth harmonic generation. The green shaded area indicates the region in momentum space where electron population contributes to H4 generation as the bandgap e…

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Reference graph

Works this paper leans on

65 extracted references · 61 canonical work pages

  1. [13]

    C., Burnett, K

    Rae, S. C., Burnett, K. & Cooper, J. Generation and propagation of high-or der harmonics in a rapidly ionizing medium. Phys. Rev. A 50, 3438–3446 (1994)

    work page 1994

  2. [1]

    Boyd, R. W. Nonlinear Optics, Third Edition (Academic Press, 2008), 3 edn

    work page 2008

  3. [2]

    F., Lompre, L

    Ferray, M., L’Huillier, A., Li, X. F., Lompre, L. A., Mainfray, G. & Manu s, C. Multiple- harmonic conversion of 1064 nm radiation in rare gases. J. Phys. B: At. Mol. Opt. Phys 21, L31 (1988)

    work page 1988

  4. [3]

    S., McIntyre, I

    McPherson, A., Gibson, G., Jara, H., Johann, U., Luk, T. S., McIntyre, I. A., Boyer, K. & Rhodes, C. K. Studies of multiphoton production of vacuum-ultravi olet radiation in the rare gases. J. Opt. Soc. Am. B 4, 595–601 (1987)

    work page 1987

  5. [4]

    Y., L’Huiller, A

    Lewenstein, M., Balcou, P., Ivanov, M. Y., L’Huiller, A. & Corkum, P. B. Theory of high- harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132 (1994)

    work page 1994

  6. [5]

    D., Sistrunk, E., Agostini, P., DiMauro, L

    Ghimire, S., DiChiara, A. D., Sistrunk, E., Agostini, P., DiMauro, L. F. & Reis, D. A. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011). 19

    work page 2011

  7. [6]

    J., Thir´ e, N., Schmidt, B

    Vampa, G., Hammond, T. J., Thir´ e, N., Schmidt, B. E., L´ egar´ e, F.,McDonald, C. R., Brabec, T. & Corkum, P. B. Linking high harmonics from gases and solids. Nature 522, 462–464 (2015)

    work page 2015

  8. [7]

    & Reis, D

    Ghimire, S. & Reis, D. A. High-harmonic generation from solids. Nat. Phys. 15, 10–16 (2019)

    2019

Show all 65 references
  1. [8]

    & Kira, M

    Borsch, M., Meierhofer, M., Huber, R. & Kira, M. Lightwave electr onics in condensed matter. Nat. Rev. Mater. 8, 668–687 (2023)

    2023

  2. [9]

    Heide, C., Kobayashi, Y., Haque, S. R. U. & Ghimire, S. Ultrafast high-h armonic spectroscopy of solids. Nat. Phys. 20, 1546–1557 (2024)

    2024

  3. [10]

    & Kr¨ uger, M

    Chen, Z., Levit, M., Kern, Y., Roy, B., Goldner, A. & Kr¨ uger, M. A ttosecond pulses from a solid driven by a synthesized two-color field at megahertz repetition rate. ACS Photonics 12, 2819–2827 (2025)

    2025

  4. [11]

    Schafer, K. J. & Kulander, K. C. High harmonic generation from ultrafast pump lasers. Phys. Rev. Lett. 78, 638–641 (1997)

    1997

  5. [12]

    J., Lee, D

    Shin, H. J., Lee, D. G., Cha, Y. H., Hong, K. H. & Nam, C. H. Generation of nonadiabat ic blueshift of high harmonics in an intense femtosecond laser field. Phys. Rev. Lett. 83, 2544– 2547 (1999)

    1999

  6. [15]

    H., Xu, J., Blaga, C

    Wang, Z., Park, H., Lai, Y. H., Xu, J., Blaga, C. I., Yang, F., Agostini, P. & DiMau ro, L. F. The roles of photo-carrier doping and driving wavelength in high harmoni c generation from a semiconductor. Nat. Commun. 8, 1686 (2017)

    2017

  7. [16]

    & Liu, K

    Cheng, Y., Hong, H., Zhao, H., Wu, C., Pan, Y., Liu, C., Zuo, Y., Zhang, Z., Xie, J ., Wang, J., Yu, D., Ye, Y., Meng, S. & Liu, K. Ultrafast optical modulation of harmoni c generation in two-dimensional materials. Nano Lett. 20, 8053–8058 (2020)

    2020

  8. [17]

    C., Liu, F., Heinz, T

    Heide, C., Kobayashi, Y., Johnson, A. C., Liu, F., Heinz, T. F., Reis, D. A. & Ghimire, S. Probing electron-hole coherence in strongly driven 2D materials usin g high-harmonic genera- tion. Optica 9, 512–516 (2022)

    2022

  9. [18]

    J., Nie, Z., de Keijzer, B

    van Essen, P. J., Nie, Z., de Keijzer, B. & Kraus, P. M. Toward comp lete all-optical intensity modulation of high-harmonic generation from solids. ACS Photonics 11, 1832–1843 (2024). 20

    2024

  10. [19]

    & Blum, S

    Pappis, J. & Blum, S. L. Properties of pyrolytic graphite. J. Am. Ceram. Soc. 44, 592–597 (1961)

    1961

  11. [20]

    Blackman, L. C. F. & Ubbelohde, A. R. J. P. Stress recrystallization of graphite. Proc. R. Soc. Lond. A Math. Phys. Sci. 266, 20–32 (1962)

    1962

  12. [21]

    Dresselhaus, M. S. & Dresselhaus, G. Intercalation compounds of grap hite. Adv. Phys. 51, 1–186 (2002)

    2002

  13. [22]

    T., Riemensberger, J., Eberle, K., Cui, Y., Kleineberg, U., Burgd¨ orfer, J., Barth, J

    Potamianos, D., Schnitzenbaumer, M., Lemell, C., Scigalla, P., Libi sch, F., Schock-Schmidtke, E., Haimerl, M., Schr¨ oder, C., Sch¨ affer, M., K¨ uchle, J. T., Riemensberger, J., Eberle, K., Cui, Y., Kleineberg, U., Burgd¨ orfer, J., Barth, J. V., Feulner, P., Allegr etti, F. ...

    2024

  14. [23]

    Zhou, S., Gweon, G.-H., Graf, J., Fedorov, A., Spataru, C., Diehl, R ., Kopelevich, Y., Lee, D.-H., Louie, S. G. & Lanzara, A. First direct observation of Dirac fermions i n graphite. Nat. Phys. 2, 595–599 (2006)

    2006

  15. [24]

    Kumar, N., Kumar, J., Gerstenkorn, C., Wang, R., Chiu, H.-Y., Smirl , A. L. & Zhao, H. Third harmonic generation in graphene and few-layer graphite films. Phys. Rev. B 87, 121406 (2013)

    2013

  16. [25]

    & Elsaesser, T

    Breusing, M., Ropers, C. & Elsaesser, T. Ultrafast carrier dynamic s in graphite. Phys. Rev. Lett. 102, 086809 (2009)

    2009

  17. [26]

    J., Lombardo, A., Milana, S., Nai r, R

    Brida, D., Tomadin, A., Manzoni, C., Kim, Y. J., Lombardo, A., Milana, S., Nai r, R. R., Novoselov, K. S., Ferrari, A. C., Cerullo, G. et al. Ultrafast collinear scattering and carrier multiplication in graphene. Nature Communications 4, 1987 (2013)

    2013

  18. [27]

    W., Squier, J., R´ aksi, F., Forget, P

    Cavalleri, A., T´ oth, C., Siders, C. W., Squier, J., R´ aksi, F., Forget, P. & Kieffer, J. Femtosec- ond structural dynamics in VO 2 during an ultrafast solid-solid phase transition. Phys. Rev. Lett. 87, 237401 (2001)

    2001

  19. [28]

    R., Haddad, E., Leblanc, A., Gruson, V., Lassonde, P., Ibrahim, H., Chaillou, J., ´Emond, N., Otto, M

    Bionta, M. R., Haddad, E., Leblanc, A., Gruson, V., Lassonde, P., Ibrahim, H., Chaillou, J., ´Emond, N., Otto, M. R., Jim´ enez-Gal´ an, A., Silva, R. E. F., Ivanov, M., Siwick, B. J., Chaker, M. & L´ egar´ e, F. Tracking ultrafast solid-state dynamics using high h armonic spe...

    2021

  20. [29]

    & Kraus, P

    Nie, Z., Guery, L., Molinero, E., Juergens, P., Van Den Hooven, T., Wang, Y., Jimenez Galan, A., Planken, P., Silva, R. & Kraus, P. Following the nonthermal phase t ransition in niobium dioxide by time-resolved harmonic spectroscopy. Phys. Rev. Lett. 131, 243201 (2023). 21

    2023

  21. [30]

    & St¨ ahler, J

    Wegkamp, D. & St¨ ahler, J. Ultrafast dynamics during the photoinduc ed phase transition in VO2. Prog. Surf. Sci. 90, 464–502 (2015)

    2015

  22. [31]

    & Werner, P

    Murakami, Y., Eckstein, M. & Werner, P. High-harmonic generation in m ott insulators. Phys. Rev. Lett. 121, 057405 (2018)

    2018

  23. [32]

    V., Rubtsov, A

    Silva, R., Blinov, I. V., Rubtsov, A. N., Smirnova, O. & Ivanov, M. High-harmonic spec- troscopy of ultrafast many-body dynamics in strongly correlated system s. Nature Photonics 12, 266–270 (2018)

    2018

  24. [33]

    Valmispild, V., Gorelov, E., Eckstein, M., Lichtenstein, A., Aok i, H., Katsnelson, M., Ivanov, M. Y. & Smirnova, O. Sub-cycle multidimensional spectroscopy of str ongly correlated mate- rials. Nature Photonics 18, 432–439 (2024)

    2024

  25. [34]

    S., Liu, H., Ghimire, S

    Vampa, G., You, Y. S., Liu, H., Ghimire, S. & Reis, D. A. Observation of b ackward high- harmonic emission from solids. Opt. Express 26, 12210–12218 (2018)

    2018

  26. [35]

    & Tanaka, K

    Yoshikawa, N., Tamaya, T. & Tanaka, K. High-harmonic generation in graphene e nhanced by elliptically polarized light excitation. Science 356, 736–738 (2017)

    2017

  27. [36]

    J., Corkum, P

    Taucer, M., Hammond, T. J., Corkum, P. B., Vampa, G., Couture, C., Th ir´ e, N., Schmidt, B. E., L´ egar´ e, F., Selvi, H., Unsuree, N., Hamilton, B., Echtermeyer, T. J. & Denecke, M. A. Nonperturbative harmonic generation in graphene from intense midinfrar ed pulsed light. Ph...

    2017

  28. [37]

    Cha, S., Kim, M., Kim, Y., Choi, S., Kang, S., Kim, H., Yoon, S., Moon, G., Kim, T., Lee, Y. W. et al. Gate-tunable quantum pathways of high harmonic generation in graphene. Nature Communications 13, 6630 (2022)

    2022

  29. [38]

    K., Mkrtchian, G

    Avetissian, H. K., Mkrtchian, G. F. & Knorr, A. Efficient high-harmoni c generation in graphene with two-color laser field at orthogonal polarization. Phys. Rev. B 105, 195405 (2022)

    2022

  30. [39]

    Liu, C., Zheng, Y., Zeng, Z. & Li, R. Driving-laser ellipticity dep endence of high-order harmonic generation in graphene. Phys. Rev. A 97, 063412 (2018)

    2018

  31. [40]

    & Dixit, G

    Mrudul, M. & Dixit, G. High-harmonic generation from monolayer and bil ayer graphene. Physical Review B 103, 094308 (2021)

    2021

  32. [41]

    D., Zhu, T., Silva, F., Teichm ann, S., Massicotte, M., Koppens, F., Levitov, L

    Baudisch, M., Marini, A., Cox, J. D., Zhu, T., Silva, F., Teichm ann, S., Massicotte, M., Koppens, F., Levitov, L. S., Garcia de Abajo, F. J. & Biegert, J. Ultrafas t nonlinear optical response of Dirac fermions in graphene. Nature Communications 9, 1018 (2018). 22

    2018

  33. [42]

    & Kulander, K

    Gaarde, M., Antoine, P., L’Huillier, A., Schafer, K. & Kulander, K. M acroscopic studies of short-pulse high-order harmonic generation using the time-depende nt schr¨ odinger equation. Physical Review A 57, 4553 (1998)

    1998

  34. [43]

    Y., Villeneuve, D

    Dudovich, N., Smirnova, O., Levesque, J., Mairesse, Y., Ivanov, M. Y., Villeneuve, D. M. & Corkum, P. B. Measuring and controlling the birth of attosecond XUV pulse s. Nat. Phys. 2, 781–786 (2006)

    2006

  35. [44]

    J., Jim´ enez-Gal´ an,´A., Orenstein, G., Silva, R

    Uzan-Narovlansky, A. J., Jim´ enez-Gal´ an,´A., Orenstein, G., Silva, R. E., Arusi-Parpar, T., Shames, S., Bruner, B. D., Yan, B., Smirnova, O., Ivanov, M. et al. Observation of light-driven band structure via multiband high-harmonic spectroscopy. Nature Photonics 16, 428–432 (2022)

    2022

  36. [45]

    & K¨ artner , F

    Tritschler, T., M¨ ucke, O., Wegener, M., Morgner, U. & K¨ artner , F. Evidence for third- harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics. Phys. Rev. Lett. 90, 217404 (2003)

    2003

  37. [47]

    A., Hirori, H., Sanari, Y., Kanemitsu, Y

    Sato, S. A., Hirori, H., Sanari, Y., Kanemitsu, Y. & Rubio, A. High-order harmon ic generation in graphene: Nonlinear coupling of intraband and interband transitions. Phys. Rev. B 103, L041408 (2021)

    2021

  38. [48]

    R., Orlando, G., Klug, D

    Vampa, G., McDonald, C. R., Orlando, G., Klug, D. D., Corkum, P. B. & B rabec, T. Theo- retical analysis of high-harmonic generation in solids. Phys. Rev. Lett. 113, 073901 (2014)

    2014

  39. [49]

    M., Sato, S

    Sommer, A., Bothschafter, E. M., Sato, S. A., Jakubeit, C., Latka, T., R azskazovskaya, O., Fattahi, H., Jobst, M., Schweinberger, W., Shirvanyan, V., Yakovlev, V. S., Kienberger, R., Yabana, K., Karpowicz, N., Schultze, M. & Krausz, F. Attosecond nonlin ear polarization and l...

    2016

  40. [50]

    B., Franco, I

    Boolakee, T., Heide, C., Garz´ on-Ram ´ ırez, A., Weber, H. B., Franco, I. & Hommelhoff, P. Light-field control of real and virtual charge carriers. Nature 605, 251–255 (2022)

    2022

  41. [51]

    S., Lamprou, T., Arg¨ uel lo-Luengo, J., Tzallas, P., Ciappina, M

    Stammer, P., Rivera-Dean, J., Maxwell, A. S., Lamprou, T., Arg¨ uel lo-Luengo, J., Tzallas, P., Ciappina, M. F. & Lewenstein, M. Entanglement and squeezing of the opt ical field modes in high harmonic generation. Phys. Rev. Lett. 132, 143603 (2024)

    2024

  42. [52]

    H., Schulz, M

    Braatz, T., Zapolnova, E., Starosielec, S., Grguraˇ s, I., Golz, T., Prandolini, M., Buss, J. H., Schulz, M. & Riedel, R. 1 MHz - dual channel, CEP stable, few-cycle OPCPA at 800nm 23 and >1.7µm wavelength. In Schunemann, P. G. & Schepler, K. L. (eds.) Nonlinear Frequency Gene...

    2021

  43. [53]

    & Koch, S

    Golde, D., Meier, T. & Koch, S. W. High harmonics generated in semic onductor nanostruc- tures by the coupled dynamics of optical inter-and intraband excitati ons. Phys. Rev. B 77, 075330 (2008)

    2008

  44. [54]

    ) knife position Y-axis (!

    Luu, T. T. & W¨ orner, H. J. High-order harmonic generation in solids: A un ifying approach. Phys. Rev. B 94, 115164 (2016). 24 Supplementary Information: Two-color harmonic spectroscopy of ultrafast Dirac electron dynamics Zhaopin Chen, 1, 2, 3, ∗ Camilo Granados, 1, 4, 5, 6,...

    2016

  45. [55]

    Al-Naib, I., Sipe, J. E. & Dignam, M. M. High harmonic generation in undope d graphene: Interplay of inter- and intraband dynamics. Phys. Rev. B 90, 245423 (2014)

    2014

  46. [56]

    R., Orlando, G., Corkum, P

    Vampa, G., McDonald, C. R., Orlando, G., Corkum, P. B. & Brabec, T. Se miclassical analysis of high harmonic generation in bulk crystals. Phys. Rev. B 91, 064302 (2015)

    2015

  47. [57]

    Yu, C., Zhang, X., Jiang, S., Cao, X., Yuan, G., Wu, T., Bai, L. & Lu, R. Depe ndence of high-order-harmonic generation on dipole moment in SiO 2 crystals. Phys. Rev. A 94, 013846 (2016)

    2016

  48. [58]

    & Gaarde, M

    Yue, L. & Gaarde, M. B. Introduction to theory of high-harmonic generat ion in solids: tutorial. J. Opt. Soc. Am. B 39, 535–555 (2022)

    2022

  49. [59]

    J., Chae, S

    Kim, M., Kim, T., Galler, A., Kim, D., Chacon, A., Gong, X., Yang, Y., Fang, R., Watanabe, K., Taniguchi, T., Kim, B. J., Chae, S. H., Jo, M.-H., Rubio, A., Nuefeld , O. & Kim, J. Quantum interference and occupation control in high harmonic generation from monolayer WS2. Natur...

    2025

  50. [60]

    & Rubio, A

    Neufeld, O., H¨ ubener, H., Jotzu, G., De Giovannini, U. & Rubio, A. Band nonlinearity- enabled manipulation of Dirac nodes, Weyl cones, and valleytronics wit h intense linearly polarized light. Nano Lett. 23, 7568–7575 (2023)

    2023

  51. [61]

    & Neufeld, O

    Galler, A., Rubio, A. & Neufeld, O. Mapping light-dressed floquet b ands by highly nonlinear optical excitations and valley polarization. J. Phys. Chem. Lett. 14, 11298–11304 (2023)

    2023

  52. [62]

    & Kartashov, D

    Korolev, V., Lettau, T., Krishna, V., Croy, A., Zuerch, M., Spielman n, C., Waechtler, M., Peschel, U., Graefe, S., Soavi, G. & Kartashov, D. Unveiling the role of electron-phonon scat- tering in dephasing high-order harmonics in solids. arXiv preprint arXiv:2401.12929 (2024)

    2024 arXiv

  53. [63]

    A., Albareda, G., Rubio, A

    Lively, K., Sato, S. A., Albareda, G., Rubio, A. & Kelly, A. Revealing ul trafast phonon me- diated inter-valley scattering through transient absorption and high h armonic spectroscopies. Phys. Rev. Research 6, 013069 (2024)

    2024

  54. [64]

    B., Tate, J

    Gaarde, M. B., Tate, J. L. & Schafer, K. J. Macroscopic aspects of attosec ond pulse generation. J. Phys. B: At. Mol. Opt. Phys. 41, 132001 (2008)

    2008

  55. [65]

    & Lewenstein, M

    Salieres, P., L’Huillier, A., Antoine, P. & Lewenstein, M. Study of the spatial and temporal coherence of high-order harmonics. In Adv. At. Mol. Opt. Phys. , vol. 41, 83–142 (Elsevier, 1999). 24

    1999

  56. [66]

    Querry, M. R. Optical constants. Tech. Rep. (1985)

    1985

  57. [67]

    & Neufeld, O

    Uzner, E. & Neufeld, O. manuscript in preparation. 25

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