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arxiv: 2409.01033 · v1 · submitted 2024-09-02 · ⚛️ physics.optics · cond-mat.mtrl-sci· physics.atom-ph

Simulating strong-field electron-hole dynamics in solids probed by attosecond transient absorption spectroscopy

Stefano M. Cavaletto , Lars Bojer Madsen This is my paper

Pith reviewed 2026-05-23 21:28 UTC · model grok-4.3

classification ⚛️ physics.optics cond-mat.mtrl-sciphysics.atom-ph
keywords attosecond transient absorption spectroscopystrong-field dynamicsTDDFTsemiconductor Bloch equationsinterband couplingselectron-hole dynamicswide-bandgap solids
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The pith

Agreement between TDDFT and SBE calculations validates the SBE model for attosecond transient absorption in solids.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper compares two ways of computing how an intense few-femtosecond pulse drives electrons and holes across the bands of a model wide-bandgap solid while a delayed attosecond extreme-ultraviolet pulse records the absorption. One calculation uses time-dependent density functional theory on a finite cluster; the other uses semiconductor Bloch equations on an infinite crystal whose momentum-dependent bands and couplings are obtained in the parallel-transport structure gauge. Both methods produce nearly identical delay-dependent features in the resulting attosecond transient absorption spectra. Because the results match, the simpler Bloch-equation picture can be used to interpret the more detailed density-functional results in terms of specific interband couplings, thereby confirming that the Bloch model is reliable for this regime.

Core claim

The very good agreement between TDDFT and SBE-based results allows us to interpret the ab-initio TDDFT simulations in terms of SBEs' interband couplings, validating our SBE-based model and corroborating its conclusions.

What carries the argument

Interband couplings computed within the semiconductor Bloch equations from crystal-momentum-dependent energy bands in the parallel-transport structure gauge, which link the simulated dynamics to the observed time-delay-dependent absorption features.

If this is right

  • The semiconductor Bloch equations can be used to predict the measurable delay-dependent features in attosecond transient absorption spectra.
  • The ab-initio TDDFT dynamics acquire a transparent interpretation through the interband couplings of the Bloch model.
  • The validated model supplies a practical route from first-principles simulations to experimentally accessible signals in similar solids.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same cross-validation strategy could be applied to narrower-gap materials where excitonic or many-body effects become stronger.
  • Direct comparison of the predicted spectra against measured data on real crystals would test whether the chosen gauge and bands are sufficient.
  • Adding lattice vibrations to the Bloch model might produce additional delay-dependent signatures that could be checked experimentally.

Load-bearing premise

The model band structure and the parallel-transport gauge choice correctly represent the real material's interband couplings.

What would settle it

An experiment that records attosecond transient absorption spectra on the modeled material and finds that the delay-dependent spectral features differ substantially from the predictions of both the TDDFT and SBE calculations would falsify the validation.

Figures

Figures reproduced from arXiv: 2409.01033 by Lars Bojer Madsen, Stefano M. Cavaletto.

Figure 1
Figure 1. Figure 1: (a) KS potential VKS[{nGS(x)}](x) [Eq. (43)] for the GS density nGS(x) obtained by imaginary-time propagation of the TDKSE in the absence of external vector potentials, for a linear chain of Nat = 40 atoms with nuclear charge Z = 4, lattice constant a = 7 a.u., and softening parameter ϵ = 0.9 a.u. (b) Detail of the potential in panel (a) in the bulk of the finite-size solid. IV. MODEL OF SOLID In this sect… view at source ↗
Figure 2
Figure 2. Figure 2: Modulus square |ϕ˜GS,q(k)| 2 (displayed in logarith￾mic scale) of the Fourier transform ϕ˜GS,q(k) of the eigenstates ϕGS,q(x) of the GS KS Hamiltonian, as a function of their as￾sociated eigenenergies EGS,q, for a linear chain of Nat = 40 atoms with nuclear charge Z = 4, lattice constant a = 7 a.u., and softening parameter ϵ = 0.9 a.u. The inner VB v1, the more highly excited VB v2, and the CBs c1, c2, and… view at source ↗
Figure 3
Figure 3. Figure 3: displays the energy bands En,k for the two VBs and the first two CBs of the model, obtained by solving the eigenvalue problem of Eq. (53). The energy bands of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Interband couplings calculated by the parallel-transport procedure for the model of a solid with periodic boundary [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Static absorption spectrum of a broadband XUV [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Transient absorption spectrum for a peak strength [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Transient absorption spectrum for a peak strength [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
read the original abstract

We investigate the ultrafast electron dynamics of a model of a wide-bandgap material with inner, valence, and conduction bands excited by an intense few-femtosecond pump and monitored by a delayed attosecond extreme-ultraviolet probe pulse. Complementary computational methods are utilized and compared, based on the semiconductor Bloch equations (SBEs) and time-dependent density functional theory (TDDFT). TDDFT is employed to study a finite-size system, while the SBEs are utilized to investigate the corresponding solid with periodic boundary conditions imposed, with the crystal-momentum-dependent energy bands and interband couplings calculated in the parallel-transport structure gauge. The resulting strong-field electron dynamics are employed to predict experimentally accessible attosecond transient absorption spectroscopy (ATAS) signals as a function of the probe-pulse frequency and pump-probe interpulse delay. Both simulation protocols similarly capture the time-delay-dependent spectral features in the ATAS signals. The very good agreement between our TDDFT and SBE-based results allows us to interpret the ab-initio TDDFT simulations in terms of SBEs' interband couplings, validating our SBE-based model and corroborating its conclusions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript investigates ultrafast electron-hole dynamics in a model wide-bandgap solid (with inner, valence, and conduction bands) driven by an intense few-fs pump and probed by a delayed attosecond XUV pulse. It compares two independent methods: TDDFT simulations on a finite-size cluster and semiconductor Bloch equations (SBEs) on the corresponding periodic solid, where crystal-momentum-dependent bands and interband couplings are obtained in the parallel-transport structure gauge. Both approaches are used to compute attosecond transient absorption spectroscopy (ATAS) signals versus probe frequency and pump-probe delay; the resulting time-delay-dependent spectral features are reported to agree qualitatively. The authors conclude that this agreement validates the SBE model and permits interpretation of the TDDFT results in terms of the SBEs' interband couplings.

Significance. If the reported agreement is placed on a quantitative footing, the work supplies a concrete bridge between ab-initio TDDFT and gauge-based SBE descriptions of strong-field ATAS in solids. The structural independence of the two formalisms (finite versus periodic boundary conditions, distinct electronic-structure treatments) supplies non-circular support for the SBE interband-coupling picture, which is a useful interpretive tool for the community working on attosecond spectroscopy of solids.

major comments (1)
  1. [Abstract] Abstract: the central validation claim rests on the statement that the two methods 'similarly capture the time-delay-dependent spectral features' and exhibit 'very good agreement.' Because the comparison is presented only qualitatively, without reported overlap integrals, RMS differences, or error bars on the ATAS spectra, the strength of the evidence supporting model validation remains difficult to judge.
minor comments (1)
  1. The manuscript would benefit from an explicit statement of the model parameters (lattice constant, band gaps, pump and probe intensities, dephasing times) used in both TDDFT and SBE calculations so that the comparison can be reproduced.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation and the helpful suggestion regarding the strength of our validation claim. We respond to the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central validation claim rests on the statement that the two methods 'similarly capture the time-delay-dependent spectral features' and exhibit 'very good agreement.' Because the comparison is presented only qualitatively, without reported overlap integrals, RMS differences, or error bars on the ATAS spectra, the strength of the evidence supporting model validation remains difficult to judge.

    Authors: We agree that a quantitative measure would make the degree of agreement more transparent to readers. In the revised manuscript we will add root-mean-square differences between the TDDFT and SBE ATAS spectra (computed over the relevant probe-frequency and delay ranges) and will reference these values in the abstract and results section. This addition directly addresses the concern while preserving the manuscript's focus on the physical interpretation. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central claim rests on agreement between two structurally independent methods: ab-initio TDDFT applied to a finite-size system versus SBEs applied to the corresponding periodic solid, with crystal-momentum-dependent bands and interband couplings computed separately in the parallel-transport structure gauge. No equations reduce the ATAS predictions to quantities fitted from the same data, no self-citations are load-bearing for the validation step, and no ansatz or uniqueness result is smuggled in. The cross-method comparison constitutes independent support rather than a self-referential loop.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard domain assumptions of the two methods plus one gauge choice; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Parallel-transport structure gauge yields accurate crystal-momentum-dependent energy bands and interband couplings for the SBE model
    Invoked to connect the periodic solid calculation to the TDDFT results.

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Reference graph

Works this paper leans on

76 extracted references · 76 canonical work pages

  1. [1]

    Attosecond science based on high harmonic generation from gases and solids,

    J. Li, J. Lu, A. Chew, S. Han, J. Li, Y. Wu, H. Wang, S. Ghimire, and Z. Chang, “Attosecond science based on high harmonic generation from gases and solids,” Nature Commun. 11, 2748 (2020)

    work page 2020

  2. [2]

    Transient absorption spec- troscopy using high harmonic generation: a review of ultrafast X-ray dynamics in molecules and solids,

    R. Geneaux, H. J. B. Marroux, A. Guggenmos, D. M. Neumark, and S. R. Leone, “Transient absorption spec- troscopy using high harmonic generation: a review of ultrafast X-ray dynamics in molecules and solids,” Phil. Trans. R. Soc. A377, 20170463 (2019)

    work page 2019

  3. [3]

    Observation of high- order harmonic generation in a bulk crystal,

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

    work page 2011

  4. [4]

    Ultimate waveform reproducibility of extreme-ultraviolet pulses by high-harmonic generation in quartz,

    M. Garg, H. Y. Kim, and E. Goulielmakis, “Ultimate waveform reproducibility of extreme-ultraviolet pulses by high-harmonic generation in quartz,” Nature Photon.12, 291–296 (2018)

    work page 2018

  5. [5]

    Extreme ultraviolet high- harmonic spectroscopy of solids,

    T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, “Extreme ultraviolet high- harmonic spectroscopy of solids,” Nature (London)521, 498–502 (2015)

    work page 2015

  6. [6]

    All-Optical Reconstruction of Crystal Band Structure,

    G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-Optical Reconstruction of Crystal Band Structure,” Phys. Rev. Lett.115, 193603 (2015)

    work page 2015

  7. [7]

    Sub-cycle control of ter- ahertz high-harmonic generation by dynamical Bloch os- cillations,

    O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of ter- ahertz high-harmonic generation by dynamical Bloch os- cillations,” Nature Photon.8, 119–123 (2014)

    work page 2014

  8. [8]

    Strong-field perspective on high-harmonic radiation from bulk solids,

    T. Higuchi, M. I. Stockman, and P. Hommelhoff, “Strong-field perspective on high-harmonic radiation from bulk solids,” Phys. Rev. Lett.113, 213901 (2014)

    work page 2014

  9. [9]

    High-harmonic generation from Bloch electrons in solids,

    M. Wu, S. Ghimire, D. A Reis, K. J. Schafer, and M. B. Gaarde, “High-harmonic generation from Bloch electrons in solids,” Phys. Rev. A91, 043839 (2015)

    work page 2015

  10. [10]

    Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals,

    C. R. McDonald, G. Vampa, P. B. Corkum, and T. Brabec, “Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals,” Phys. Rev. A92, 033845 (2015)

    work page 2015

  11. [11]

    Real- time observation of interfering crystal electrons in high- harmonic generation,

    M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real- time observation of interfering crystal electrons in high- harmonic generation,” Nature (London)523, 572–575 (2015)

    work page 2015

  12. [12]

    All-optical reconstruction of crystal band structure,

    G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, “All-optical reconstruction of crystal band structure,” Phys. Rev. Lett.115, 193603 (2015)

    work page 2015

  13. [13]

    Solid-state harmonics beyond the atomic limit,

    G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature (London) 534, 520–523 (2016)

    work page 2016

  14. [14]

    Multi- petahertz electronic metrology,

    M. Garg, M. Zhan, T. T. Luu, H. Lakhotia, T. Kloster- mann, A. Guggenmos, and E. Goulielmakis, “Multi- petahertz electronic metrology,” Nature (London)538, 359–363 (2016)

    work page 2016

  15. [15]

    Optical-field-induced current in dielectrics,

    A. Schiffrin, T. Paasch-Colberg, N. Karpowicz, V. Apalkov, D. Gerster, S. Mühlbrandt, M. Korb- man, J. Reichert, M. Schultze, S. Holzner, J. V. Barth, R. Kienberger, R. Ernstorfer, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Optical-field-induced current in dielectrics,” Nature (London) 493, 70–74 (2013)

    work page 2013

  16. [16]

    Controlling dielectrics with the electric field of light,

    M. Schultze, E. M. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kien- berger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature (London)493, 75–78 (2013)

    work page 2013

  17. [17]

    Petahertz optical drive with wide-bandgap semiconductor,

    H. Mashiko, K. Oguri, T. Yamaguchi, A. Suda, and H. Gotoh, “Petahertz optical drive with wide-bandgap semiconductor,” Nature Phys.12, 741–745 (2016)

    work page 2016

  18. [18]

    Attosecond nonlinear polarization and light–matter energy transfer in solids,

    A. Sommer, E. M. Bothschafter, S. A. Sato, C. Jakubeit, T. Latka, O. Razskazovskaya, H. Fattahi, M. Jobst, W. Schweinberger, V. Shirvanyan, V. S. Yakovlev, R. Kienberger, K. Yabana, N. Karpowicz, M. Schultze, and F. Krausz, “Attosecond nonlinear polarization and light–matter energy transfer in solids,” Nature (London) 534, 86–90 (2016)

    work page 2016

  19. [19]

    Light-field-driven currents in graphene,

    T. Higuchi, C. Heide, K. Ullmann, H. B. Weber, and P. Hommelhoff, “Light-field-driven currents in graphene,” Nature (London)550, 224–228 (2017)

    work page 2017

  20. [20]

    Trackingultrafastsolid-state dynamics using high harmonic spectroscopy,

    M. R. Bionta, E. Haddad, A. Leblanc, V. Gruson, P. Las- sonde, H. Ibrahim, J. Chaillou, N. Émond, M.n R. Otto, Á.Jiménez-Galán, R.E.F.Silva, M.Ivanov, B.J.Siwick, M.Chaker, andF.Légaré,“Trackingultrafastsolid-state dynamics using high harmonic spectroscopy,” Phys. Rev. Res. 3, 023250 (2021)

    work page 2021

  21. [21]

    The speed limit of optoelectronics,

    M. Ossiander, K. Golyari, K. Scharl, L. Lehnert, F.Siegrist, J.P.Bürger, D.Zimin, J.A.Gessner, M.Wei- dman, I. Floss, V. Smejkal, S. Donsa, C. Lemell, F. Li- bisch, N. Karpowicz, J. Burgdörfer, F. Krausz, and M. Schultze, “The speed limit of optoelectronics,” Nature Commun. 13, 1620 (2022)

    work page 2022

  22. [22]

    Observation of Floquet-Bloch States on the Surface of a Topological Insulator,

    Y. H. Wang, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, “Observation of Floquet-Bloch States on the Surface of a Topological Insulator,” Science342, 453–457 (2013)

    work page 2013

  23. [23]

    Attosecond absorption and reflection spectroscopy of solids,

    N. Di Palo, G. Inzani, G. L. Dolso, M. Talarico, S. Bonetti, and M. Lucchini, “Attosecond absorption and reflection spectroscopy of solids,” APL Photonics9, 020901 (2024)

    work page 2024

  24. [24]

    Solidstate core-exciton dynamics in NaCl observed by tabletop at- tosecond four-wave mixing spectroscopy,

    J. D. Gaynor, A. P. Fidler, Y.-C. Lin, H.-T. Chang, M.Zuerch, D.M.Neumark, andS.R.Leone,“Solidstate core-exciton dynamics in NaCl observed by tabletop at- tosecond four-wave mixing spectroscopy,” Phys. Rev. B 103, 245140 (2021)

    work page 2021

  25. [25]

    Attosecond band-gap dynamics in silicon,

    M. Schultze, K. Ramasesha, C. D. Pemmaraju, S. A. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. J. Borja, D. Prendergast, K. Yabana, D. M. Neumark, and S. R. Leone, “Attosecond band-gap dynamics in silicon,” Sci- ence 346, 1348–1352 (2014)

    work page 2014

  26. [26]

    Attosecond dynamical Franz- Keldysh effect in polycrystalline diamond,

    M. Lucchini, S. A. Sato, A. Ludwig, J. Herrmann, M. Volkov, L. Kasmi, Y. Shinohara, K. Yabana, L. Gall- mann, and U. Keller, “Attosecond dynamical Franz- Keldysh effect in polycrystalline diamond,” Science353, 916–919 (2016)

    work page 2016

  27. [27]

    Tracking the insulator-to-metal phase transition in VO2 with few-femtosecond extreme UV transient absorption spectroscopy,

    M. F. Jager, C. Ott, P. M. Kraus, C. J. Kaplan, W. Pouse, R. E. Marvel, R. F. Haglund, D. M. Neu- mark, and S. R. Leone, “Tracking the insulator-to-metal phase transition in VO2 with few-femtosecond extreme UV transient absorption spectroscopy,” Proc. Natl. Acad. Sci. U.S.A.114, 9558–9563 (2017)

    work page 2017

  28. [28]

    Direct and simultaneous obser- vation of ultrafast electron and hole dynamics in germa- nium,

    M. Zürch, H.-T. Chang, L. J. Borja, P. M. Kraus, S. K. Cushing, A. Gandman, C. J. Kaplan, M. H. Oh, J. S. Prell, D. Prendergast, C. D. Pemmaraju, D. M. Neu- mark, and S. R. Leone, “Direct and simultaneous obser- vation of ultrafast electron and hole dynamics in germa- nium,” Nature Commun.8, 15734 (2017)

    work page 2017

  29. [29]

    Soft x-ray excitonics,

    A. Moulet, J. B. Bertrand, T. Klostermann, A. Guggen- mos, N. Karpowicz, and E. Goulielmakis, “Soft x-ray excitonics,” Science357, 1134–1138 (2017)

    work page 2017

  30. [30]

    Attosecond optical-field-enhanced carrier in- jection into the GaAs conduction band,

    F. Schlaepfer, M. Lucchini, S. A. Sato, M. Volkov, L. Kasmi, N. Hartmann, A. Rubio, L. Gallmann, and U. Keller, “Attosecond optical-field-enhanced carrier in- jection into the GaAs conduction band,” Nature Phys. 14, 560–564 (2018)

    work page 2018

  31. [31]

    Attosecond screening dynamics mediated by electron localization in transition metals,

    M. Volkov, S. A. Sato, F. Schlaepfer, L. Kasmi, N. Hart- 20 mann, M. Lucchini, L. Gallmann, A. Rubio, and U. Keller, “Attosecond screening dynamics mediated by electron localization in transition metals,” Nature Phys. 15, 1145–1149 (2019)

    work page 2019

  32. [32]

    Attosecond state-resolved carrier motion in quantum materials probed by soft x-ray XANES,

    B. Buades, A. Picón, E. Berger, I. León, N. Di Palo, S. L. Cousin, C. Cocchi, E. Pellegrin, J. H. Martin, S.MañasValero, E.Coronado, T.Danz, C.Draxl, M.Ue- moto, K. Yabana, M. Schultze, S. Wall, M. Zürch, and J. Biegert, “Attosecond state-resolved carrier motion in quantum materials probed by soft x-ray XANES,” Appl. Phys. Rev.8, 011408 (2021)

    work page 2021

  33. [33]

    Floquet-Bloch resonances in near- petahertz electroabsorption spectroscopy ofSiO2,

    M. Volkov, S. A. Sato, A. Niedermayr, A. Rubio, L. Gall- mann, and U. Keller, “Floquet-Bloch resonances in near- petahertz electroabsorption spectroscopy ofSiO2,” Phys. Rev. B107, 184304 (2023)

    work page 2023

  34. [34]

    Field-driven attosec- ond charge dynamics in germanium,

    G. Inzani, L. Adamska, A. Eskandari-asl, N. Di Palo, G. L. Dolso, B. Moio, L. J. D’Onofrio, A. Lamperti, A. Molle, R. Borrego-Varillas, M. Nisoli, S. Pittalis, C. A. Rozzi, A. Avella, and M. Lucchini, “Field-driven attosec- ond charge dynamics in germanium,” Nature Photon.17, 1059–1065 (2023)

    work page 2023

  35. [35]

    The physics of x-ray free-electron lasers,

    C. Pellegrini, A. Marinelli, and S. Reiche, “The physics of x-ray free-electron lasers,” Rev. Mod. Phys.88, 015006 (2016)

    work page 2016

  36. [36]

    Tunable isolated attosec- ond X-ray pulses with gigawatt peak power from a free- electron laser,

    J. Duris, S. Li, T. Driver, E. G. Champenois, J. P. MacArthur, A. A. Lutman, Z. Zhang, P. Rosenberger, J. W. Aldrich, R. Coffee, G. Coslovich, F.-J. Decker, J. M. Glownia, G. Hartmann, W. Helml, A. Kamalov, J. Knurr, J. Krzywinski, M.-F. Lin, J. P. Marangos, M. Nantel, A. Natan, J. T. O’Neal, N. Shivaram, P. Wal- ter, A. L. Wang, J. J. Welch, T. J. A. Wol...

    work page 2020

  37. [37]

    Single- and two-color attosecond hard x-ray free-electron laser pulses with nonlinear compression,

    A. Malyzhenkov, Y. P. Arbelo, P. Craievich, P. Dijkstal, E. Ferrari, S. Reiche, T. Schietinger, P. Juranić, and E. Prat, “Single- and two-color attosecond hard x-ray free-electron laser pulses with nonlinear compression,” Phys. Rev. Research2, 042018 (2020)

    work page 2020

  38. [38]

    Experimental demonstration of attosec- ond pump-probe spectroscopy with an x-ray free-electron laser,

    Z. Guo, T. Driver, S. Beauvarlet, D. Cesar, J. Duris, P. L. Franz, O. Alexander, D. Bohler, C. Bostedt, V. Aver- bukh, X. Cheng, L. F. DiMauro, G. Doumy, R. Forbes, O. Gessner, J. M. Glownia, E. Isele, A. Kamalov, K. A. Larsen, S. Li, X. Li, M.-F. Lin, G. A. McCracken, R. Obaid, J. T. O’Neal, R. R. Robles, D. Rolles, M. Ru- berti, A.Rudenko, D.S.Slaughter...

    work page 2024

  39. [39]

    Density-functional the- ory for time-dependent systems,

    Erich Runge and E. K. U. Gross, “Density-functional the- ory for time-dependent systems,” Phys. Rev. Lett.52, 997–1000 (1984)

    work page 1984

  40. [40]

    C. A. Ullrich,Time-Dependent Density-Functional The- ory: Concepts and Applications (Oxford University Press, Oxford, 2011)

    work page 2011

  41. [41]

    Marques, N

    M. Marques, N. T. Maitra, F. M. S. Nogueira, E. K. U. Gross, and A. Rubio, eds., Fundamentals of time- dependent density functional theory , Lecture notes in physics No. Vol. 837 (Springer, Berlin Heidelberg New York, 2012)

    work page 2012

  42. [42]

    Impact of the electronic band structure in high-harmonic generation spectra of solids,

    N. Tancogne-Dejean, O. D. Mücke, F. X. Kärtner, and A. Rubio, “Impact of the electronic band structure in high-harmonic generation spectra of solids,” Phys. Rev. Lett. 118, 087403 (2017)

    work page 2017

  43. [43]

    Ab initio multiscale simulation of high-order harmonic generation in solids,

    I. Floss, C. Lemell, G. Wachter, V. Smejkal, S. A. Sato, X.-M. Tong, K. Yabana, and J. Burgdörfer, “Ab initio multiscale simulation of high-order harmonic generation in solids,” Phys. Rev. A97, 011401 (2018)

    work page 2018

  44. [44]

    Finite- system effects on high-order harmonic generation: From atoms to solids,

    K. K. Hansen, D. Bauer, and L. B. Madsen, “Finite- system effects on high-order harmonic generation: From atoms to solids,” Phys. Rev. A97, 043424 (2018)

    work page 2018

  45. [45]

    Enhanced high-orderharmonicgenerationindonor-dopedband-gap materials,

    C. Yu, K. K. Hansen, and L. B. Madsen, “Enhanced high-orderharmonicgenerationindonor-dopedband-gap materials,” Phys. Rev. A99, 013435 (2019)

    work page 2019

  46. [46]

    High-order harmonic generation in imperfect crystals,

    C. Yu, K. K. Hansen, and L. B. Madsen, “High-order harmonic generation in imperfect crystals,” Phys. Rev. A 99, 063408 (2019)

    work page 2019

  47. [47]

    High-order harmonic generation in solid slabs beyond the single- active-electron approximation,

    K. K. Hansen, T. Deffge, and D. Bauer, “High-order harmonic generation in solid slabs beyond the single- active-electron approximation,” Phys. Rev. A96, 053418 (2017)

    work page 2017

  48. [48]

    High-Harmonic Genera- tion in Solids with and without Topological Edge States,

    D. Bauer and K. K. Hansen, “High-Harmonic Genera- tion in Solids with and without Topological Edge States,” Phys. Rev. Lett.120, 177401 (2018)

    work page 2018

  49. [49]

    Ul- trafast modification of hubbard u in a strongly corre- lated material: Ab initio high-harmonic generation in nio,

    N. Tancogne-Dejean, M. A. Sentef, and A. Rubio, “Ul- trafast modification of hubbard u in a strongly corre- lated material: Ab initio high-harmonic generation in nio,” Phys. Rev. Lett.121, 097402 (2018)

    work page 2018

  50. [50]

    Effect of spin-orbit coupling on the high harmonics from the topological Dirac semimetal Na3Bi,

    N. Tancogne-Dejean, F. G. Eich, and A. Rubio, “Effect of spin-orbit coupling on the high harmonics from the topological Dirac semimetal Na3Bi,” npj Comput. Mater. 8, 145 (2022)

    work page 2022

  51. [51]

    Are There Universal Signa- tures of Topological Phases in High-Harmonic Genera- tion? Probably Not

    O. Neufeld, N. Tancogne-Dejean, H. Hübener, U. De Gio- vannini, and A. Rubio, “Are There Universal Signa- tures of Topological Phases in High-Harmonic Genera- tion? Probably Not.” Phys. Rev. X13, 031011 (2023)

    work page 2023

  52. [52]

    Meier, P

    T. Meier, P. Thomas, and S. W. Koch, Coherent semiconductor optics: from basic concepts to nanostruc- ture applications (Springer, Berlin Heidelberg New York, 2007)

    work page 2007

  53. [53]

    Attosecond x-ray transient absorption in condensed-matter: a core-state- resolved Bloch model,

    A. Picón, L. Plaja, and J. Biegert, “Attosecond x-ray transient absorption in condensed-matter: a core-state- resolved Bloch model,” New J. Phys.21, 043029 (2019)

    work page 2019

  54. [54]

    Theoretical Approach for Electron Dy- namics and Ultrafast Spectroscopy (EDUS),

    G. Cistaro, M. Malakhov, J. J. Esteve-Paredes, A. J. Uría-Álvarez, R. E. F. Silva, F. Martín, J. J. Palacios, and A. Picón, “Theoretical Approach for Electron Dy- namics and Ultrafast Spectroscopy (EDUS),” J. Chem. Theory Comput.19, 333–348 (2023)

    work page 2023

  55. [55]

    Attosecond transient-absorption spectroscopy in one- dimensional periodic crystals,

    M. Du, C. Liu, Y. Zheng, Z. Zeng, and R. Li, “Attosecond transient-absorption spectroscopy in one- dimensional periodic crystals,” Phys. Rev. A100, 043840 (2019)

    work page 2019

  56. [56]

    Fishbone resonance structure in the attosecond transient absorption spectrum of graphene,

    F. Dong and J. Liu, “Fishbone resonance structure in the attosecond transient absorption spectrum of graphene,” Phys. Rev. A106, 063107 (2022)

    work page 2022

  57. [57]

    Contribution of Floquet-Bloch states to high-order harmonic generation in solids,

    J.-Z. Jin, H. Liang, X.-R. Xiao, M.-X. Wang, S.-G. Chen, X.-Y. Wu, Q. Gong, and L.-Y. Peng, “Contribution of Floquet-Bloch states to high-order harmonic generation in solids,” Phys. Rev. A100, 013412 (2019)

    work page 2019

  58. [58]

    Acceleration of Electrons in a Crystal Lattice,

    W. V. Houston, “Acceleration of Electrons in a Crystal Lattice,” Phys. Rev.57, 184–186 (1940)

    work page 1940

  59. [59]

    Time evolution of Bloch electrons in a homogeneous electric field,

    J. B. Krieger and G. J. Iafrate, “Time evolution of Bloch electrons in a homogeneous electric field,” Phys. Rev. B 21 33, 5494–5500 (1986)

    work page 1986

  60. [60]

    PhaseinvarianceofthesemiconductorBlochequations,

    J. Li, X. Zhang, S. Fu, Y. Feng, B. Hu, and H. Du, “PhaseinvarianceofthesemiconductorBlochequations,” Phys. Rev. A100, 043404 (2019)

    work page 2019

  61. [61]

    Smooth periodic gauge satisfying crystal symmetry and periodicity to study high-harmonic generation in solids,

    S.Jiang, C.Yu, J.Chen, Y.Huang, R.Lu, andC.D.Lin, “Smooth periodic gauge satisfying crystal symmetry and periodicity to study high-harmonic generation in solids,” Phys. Rev. B102, 155201 (2020)

    work page 2020

  62. [62]

    Role of the transition dipole amplitude and phase on the generation of odd and even high-order harmonics in crystals,

    S. Jiang, J. Chen, H. Wei, C. Yu, R. Lu, and C. D. Lin, “Role of the transition dipole amplitude and phase on the generation of odd and even high-order harmonics in crystals,” Phys. Rev. Lett.120, 253201 (2018)

    work page 2018

  63. [63]

    Highharmonic generation in crystals using maximally localized Wannier functions,

    R.E.F.Silva, F.Martín, andM.Ivanov,“Highharmonic generation in crystals using maximally localized Wannier functions,” Phys. Rev. B100, 195201 (2019)

    work page 2019

  64. [64]

    Structure gauges and laser gauges for the semiconductor Bloch equations in high- order harmonic generation in solids,

    L. Yue and M. B. Gaarde, “Structure gauges and laser gauges for the semiconductor Bloch equations in high- order harmonic generation in solids,” Phys. Rev. A101, 053411 (2020)

    work page 2020

  65. [65]

    Introduction to theory of high-harmonic generation in solids: tutorial,

    L. Yue and M. B. Gaarde, “Introduction to theory of high-harmonic generation in solids: tutorial,” J. Opt. Soc. Am. B39, 535–555 (2022)

    work page 2022

  66. [66]

    Formalisms of Band Theory,

    E. I. Blount, “Formalisms of Band Theory,” inSolid State Physics, Vol. 13 (Elsevier, Amsterdam, 1962) pp. 305– 373

    work page 1962

  67. [67]

    N. W. Ashcroft and N. D. Mermin,Solid state physics (Holt, Rinehart and Winston, New York, 1976)

    work page 1976

  68. [68]

    Vanderbilt,Berry Phases in Electronic Structure The- ory: Electric Polarization, Orbital Magnetization and Topological Insulators, 1st ed

    D. Vanderbilt,Berry Phases in Electronic Structure The- ory: Electric Polarization, Orbital Magnetization and Topological Insulators, 1st ed. (Cambridge University Press, Cambridge, 2018)

    work page 2018

  69. [69]

    Edge- state-induced correlation effects in two-color pump-probe high-order harmonic generation,

    S. V. B. Jensen, H. Iravani, and L. B. Madsen, “Edge- state-induced correlation effects in two-color pump-probe high-order harmonic generation,” Phys. Rev. A 103, 053121 (2021)

    work page 2021

  70. [70]

    QPROP: A Schrödinger-solver for intense laser-atom interaction,

    D. Bauer and P. Koval, “QPROP: A Schrödinger-solver for intense laser-atom interaction,” Comp. Phys. Com- mun. 174, 396–421 (2006)

    work page 2006

  71. [71]

    Dependence of high-order-harmonic generationondipolemomentin Sio2 crystals,

    C. Yu, X. Zhang, S. Jiang, X. Cao, G. Yuan, T. Wu, L. Bai, and R. Lu, “Dependence of high-order-harmonic generationondipolemomentin Sio2 crystals,” Phys.Rev. A 94, 013846 (2016)

    work page 2016

  72. [72]

    Crystal- momentum-resolved contributions to multiple plateaus of high-order harmonic generation from band-gap ma- terials,

    C. Yu, H. Iravani, and L. B. Madsen, “Crystal- momentum-resolved contributions to multiple plateaus of high-order harmonic generation from band-gap ma- terials,” Phys. Rev. A102, 033105 (2020)

    work page 2020

  73. [73]

    Nuclear- motion effects in attosecond transient-absorption spec- troscopy of molecules,

    J. E. Bækhøj, L. Yue, and L. B. Madsen, “Nuclear- motion effects in attosecond transient-absorption spec- troscopy of molecules,” Phys. Rev. A91, 043408 (2015)

    work page 2015

  74. [74]

    Transient absorption and reshaping of ultrafast xuv light by laser-dressed helium,

    M. B. Gaarde, C. Buth, J. L. Tate, and K. J. Schafer, “Transient absorption and reshaping of ultrafast xuv light by laser-dressed helium,” Phys. Rev. A83, 013419 (2011)

    work page 2011

  75. [75]

    Theory of attosecond transient absorption spectroscopy of strong-field-generated ions,

    R. Santra, V. S. Yakovlev, T. Pfeifer, and Z.-H. Loh, “Theory of attosecond transient absorption spectroscopy of strong-field-generated ions,” Phys. Rev. A83, 033405 (2011)

    work page 2011

  76. [76]

    Haug and S

    H. Haug and S. W. Koch,Quantum Theory of the Opti- cal and Electronic Properties of Semiconductors , 5th ed. (World Scientific, Singapore, 2009)

    work page 2009