Pith. sign in

REVIEW 2 major objections 5 minor 55 references

Relaxation of electrons in quantum-confined states in Pb/Si(111) thin films from master equation with first-principles-derived rates

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read In atomically thin lead films on silicon, hot electrons near 0.3 eV above the Fermi level relax through a phonon bottleneck, while one surface phonon mode absorbs most of the energy.

desk verdict A credible DFT-informed master-equation study of hot-electron relaxation in Pb/Si(111) films; the new dynamical results are the 0.3 eV phonon bottleneck and mode-selective phonon heating, but the bottleneck position rests on a bulk-Pb e-e rate that gets no sensitivity analysis. read the letter →

arxiv 1908.06119 v3 pith:HDEDDROZ submitted 2019-08-16 cond-mat.mes-hall

Peter Kratzer , Maedeh Zahedifar This is my paper · ORCID
classification cond-mat.mes-hall PACS 71.38.-k73.21.Fg79.60.-i
keywords electronrelaxationdynamicsquantumwellstatesPb/Si(111)thinfilmselectron-phononscatteringelectron-electronphononbottleneckmasterequationdeformationpotentialtheory
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks which scattering mechanism controls how fast hot electrons cool in atomically thin lead films on silicon. It builds a master equation for the occupations of the confined electron states, with electron-phonon rates from density functional theory and electron-electron rates from a GW self-energy calculation. The simulation shows that above 0.5 eV electron-electron scattering dominates and sets lifetimes near 20 to 100 fs, matching time-resolved photoemission experiments. Below about 0.3 eV the electron-phonon channel takes over, producing a phonon bottleneck: excited electrons pile up near 0.3 eV and decay slowly by emitting phonons. The energy flow into the lattice is strongly mode-selective, with one surface phonon mode receiving the largest share.

What carries the argument

The load-bearing object is a kinetic master equation for the electronic occupation numbers, $\frac{d}{dt} f_{nk} = \Gamma^{\mathrm{in}}_{nk}(1-f_{nk}) - \Gamma^{\mathrm{out}}_{nk} f_{nk}$, with each rate split into electron-electron and electron-phonon parts. The electron-phonon rates are computed by Fermi's golden rule using deformation potentials from density functional theory, with a deformation potential that is taken independent of phonon wave vector $\mathbf{Q}$ and overlap integrals between confined wave functions. The electron-electron scattering-out rate is obtained from a GW self-energy calculation for bulk lead, fitted to the Fermi-liquid form $\Gamma^{\mathrm{out,(ee)}}_{nk} = (\varepsilon_{nk}-E_F)^2 / [30\,\mathrm{fs}\,(\mathrm{eV})^2]$, while the scattering-in term uses a stationary secondary-electron distribution $\Phi(x)=x/\cosh^2(x/2)$. The phonons are described as heat baths, with a separate bath for each high-frequency surface mode and a common bath for lower-frequency modes, coupled on a 30 ps mode-conversion time scale. This combination turns the atomistic input into directly comparable lifetimes and per-mode phonon excitation curves.

What would settle it

Compute the electron-electron self-energy for the confined Pb/Si(111) slab directly instead of using bulk lead, then rerun the master equation; if the pile-up near 0.3 eV disappears or a different phonon mode dominates, the bottleneck claim fails. Alternatively, a time-resolved two-photon photoemission experiment with sensitivity down to 0.3 eV could look directly for the predicted delayed population.

Watch

Extended reading notes

Core claim

The paper's central discovery is that electron-phonon scattering, although weak compared to electron-electron scattering for highly excited electrons, becomes the controlling relaxation channel near 0.3 eV above the Fermi level and is strongly phonon-mode-specific. In both 4- and 5-monolayer Pb films on Si(111), the master-equation simulation produces a pile-up of electrons around 0.3 eV, interpreted as a phonon bottleneck caused by the discrete, well-separated quantum-well states. The energy deposited into the lattice goes mainly into one high-frequency surface phonon mode, at 2.26 THz in the 4 ML film and at 2.03 THz in the 5 ML film, the latter matching a measured 2.0 THz oscillation of the quantum-well energy. Simulated lifetimes of 101 fs and 21 fs for the 0.58 and 1.21 eV peaks are in reasonable agreement with the experimentally observed 115 and 10 fs values. The paper concludes that the usual neglect of electron-phonon scattering in analyzing these experiments is justified at high energy but not at low energy, and that non-thermal phonon distributions can persist for several picoseconds.

Load-bearing premise

The electron-electron scattering rate used in the simulation is carried over from a calculation for bulk lead, not for the confined film itself; if the film's confinement or its contact with the silicon substrate changes how electrons screen each other, the high-energy part of the result would need to be revised.

Editorial extensions

If this is right

  • Above roughly 0.5 eV, electron-electron scattering sets the relaxation times and electron-phonon scattering can be neglected, so two-temperature models that ignore the phonon channel remain valid for highly excited electrons.
  • Below roughly 0.3 eV the phonon channel dominates, so relaxation in these films cannot be described by a single electron-phonon coupling constant from bulk Eliashberg theory; the discrete level structure creates a bottleneck.
  • The phonon system itself stays out of thermal equilibrium for several picoseconds, with non-thermal occupation concentrated in surface modes; this should be observable in time-resolved diffraction and reflects a general feature of hot-carrier relaxation in nanostructures.
  • The simulated lifetimes for the main quantum-well states match experimental values within the expected errors, indicating that the parameter-free DFT-based master-equation route can predict lifetime trends across film thicknesses.
  • Mode selectivity is stronger for even-layer (4 ML) films than odd-layer (5 ML) films, correlating with larger deformation potentials and faster electron-phonon decay in the thinner film.

Reading between the lines

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

  • The paper does not test capping or substrate substitution; a layer that suppresses the 2.0-2.3 THz surface modes should lengthen the low-energy lifetimes, which would isolate the mode-specificity claim.
  • The implicit bottleneck criterion is that the electronic level spacing exceeds the largest phonon energy; the same master-equation machinery applied to other confined metals with wider or narrower spacings would predict where pile-ups should form.
  • Since the 0.3 eV pile-up lies below the probe window of the original photoemission experiments, a dedicated low-energy two-photon photoemission measurement is the cleanest independent check.
  • The persistent non-thermal phonon population suggests that repetitive optical pumping could selectively heat individual surface modes, making phonon-mode engineering in ultrathin films a testable prospect.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper presents a master-equation model for the relaxation of excited electrons in 4 and 5 monolayer Pb films on Si(111), combining first-principles DFT-derived electron-phonon rates (deformation-potential approximation) with an electron-electron scattering rate fitted to a GW calculation of bulk Pb. The model reproduces the experimentally observed peak energies and lifetimes of quantum well states, predicts a phonon bottleneck (population pile-up around 0.3 eV) where electron-phonon scattering becomes comparable to electron-electron scattering, and identifies a strongly mode-selective energy transfer to a specific surface phonon mode (2.26 THz for 4 ML, 2.03 THz for 5 ML, the latter matching a measured 2.0±0.1 THz coherent phonon). The dynamics are followed by numerically integrating the rate equations on a fine k-grid.

Significance. The work is a valuable attempt to disentangle e-e and e-ph contributions to ultrafast relaxation in a confined metal with a realistic band structure. Its main strengths are the first-principles derivation of e-ph matrix elements, the careful Brillouin-zone integration scheme, and the quantitative comparison with time-resolved two-photon photoemission lifetimes. The predicted phonon bottleneck at ~0.3 eV and the mode-selective phonon emission are falsifiable predictions. However, the e-e channel is imported from bulk Pb without uncertainty quantification, and the e-ph rates rest on approximations (constant deformation potential, no hole-phonon scattering) that are not quantified. If the bulk-derived e-e rate is significantly modified by confinement, the 0.3 eV crossover could shift or disappear, so the central claim is not yet robust.

major comments (2)
  1. [Section III B, Eq. (9)] The e-e scattering rate is fitted to a GW self-energy of bulk Pb (α=0.022 eV^-1) and inserted into the master equation for a 4–5 ML Pb/Si(111) film. The 0.3 eV 'phonon bottleneck' is defined by the crossover between this rate and the e-ph rates (Section III D). A confinement-induced enhancement of the e-e rate by a factor of about two—not implausible for quasi-2D screening in a 5–10 Å film—would reduce the e-e lifetime at 0.3 eV from ~300 fs to ~150–170 fs, making e-e dominate and erasing the pile-up in Fig. 3. Since no error bar is given for α and no sensitivity analysis is performed, the headline bottleneck claim is not yet distinguished from a consequence of the bulk-Pb approximation. Please add a robustness analysis (varying α, or computing the e-e rate for the confined slab) and state explicitly how the crossover energy depends on α.
  2. [Section II, Eq. (8) and hole treatment] The e-ph matrix elements neglect the Q-dependence of the deformation potential and retain only the constant term D_{nk,I}, and the paper excludes e-ph scattering for holes (Section II: 'only Coulomb scattering ... will be considered among the holes'). Both approximations affect the absolute e-ph rates and the energy transfer to phonon modes shown in Fig. 5, and hence also the precise location of the e-e/e-ph crossover. The paper should quantify the sensitivity of the 0.3 eV pile-up and the mode-selective phonon distribution to these approximations, e.g., by evaluating a few Q-dependent matrix elements or by adding a representative hole-phonon coupling. Without such quantification, the robustness of the central predictions remains unclear.
minor comments (5)
  1. [Section II and Conclusion] The approach is described as 'parameter-free' in several places (e.g., Section II and Conclusion), but the e-e rate α (Eq. 9), the electronic temperature T_el, and the bath time constants τ_conv and τ_sub (Appendix B) are empirical inputs. Please rephrase to 'first-principles-derived e-ph rates' and list the external parameters explicitly.
  2. [Figure 2(b) caption] The caption states that circles show lifetimes for 4 ML and 5 ML films without distinguishing the two thicknesses; please add separate symbols or a legend.
  3. [Section III A and Introduction] There are typos: 'under the sole effect' should be 'under the sole effect', and 'detailled' in the Introduction should be 'detailed'.
  4. [Figure 3] The 'phonon bottleneck' pile-up is very small and only visible in the inset; consider enlarging the inset or plotting the low-energy region on a linear y-scale to better display the shoulder.
  5. [Appendix B] The value τ_conv = 30 ps is taken from a simulation of a monolayer Pb/Si(111) (Ref. 54) but is applied to 4–5 ML films; please justify the transfer or discuss its sensitivity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the phonon bottleneck and mode-selective heating emerge from a master-equation calculation using independently fitted and DFT-derived rates.

full rationale

The paper's central claims, the 0.3 eV phonon bottleneck and the mode-selective excitation of specific surface phonon modes, are emergent results of numerically solving a master equation, not restatements of the input rates. The electron-phonon rates are obtained from first-principles DFT deformation potentials, band structures, and phonon modes (from the authors' earlier Ref. 14), which are parameter-free and do not presuppose the bottleneck phenomenon. The electron-electron rate in Eq. (9) is independently fitted to a GW calculation of bulk Pb, with the fitted coefficient alpha = 0.022 eV^-1 in agreement with earlier independent GW work (Ref. 41); it is an input modeling the e-e channel, not a fitted surrogate for the predicted bottleneck. The bottleneck appears because the e-e lifetime grows above 300 fs below about 0.33 eV while the computed e-ph lifetime is about 350 fs near 0.46 eV, leading to a crossover; this crossover is a quantitative consequence of combining a fitted bulk-derived e-e rate with computed e-ph rates, not a circular reduction. The mode-selective phonon heating is compared with an external experimental frequency (2.0 +/- 0.1 THz from Ref. 47), and the QWS lifetimes are compared with independent two-photon photoemission data (Ref. 11), providing external checks. The authors' statement that the approach is 'parameter-free' is an overstatement because Eq. (9) contains a fitted coefficient and the electronic temperature Tel = 650 K is chosen, but this is a correctness/characterization issue, not a circularity. No equation or claim reduces by construction to its own input, and no load-bearing uniqueness or ansatz is imported solely from the authors' prior work.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The model is first-principles-informed but not fully parameter-free. It draws band structures, phonons, and deformation potentials from the authors' prior DFT work (Ref. 14), fits the e-e rate to a bulk Pb GW self-energy, and imports phonon-bath timescales from the literature. These inputs are all stated, but their combined uncertainty is not propagated into the reported lifetimes.

free parameters (7)
  • α (e-e rate coefficient) = 0.022 (eV)^-1
    Fitted to the imaginary part of the GW self-energy of bulk Pb in Section III B; enters the master equation through eq. (9) as Γ=(ε-EF)^2/[30 fs (eV)^2].
  • Tel (electronic temperature) = 650 K
    Chosen in Section III B to represent the secondary-electron distribution generated by a 0.1 eV deposited energy pulse; used in Φ(x)=x/cosh^2(x/2).
  • τconv (optical to acoustic phonon conversion time) = 30 ps
    Adopted from prior molecular dynamics (Ref. 54) in Appendix B; couples each optical-mode bath to the acoustic bath.
  • τsub (Pb film to Si substrate equilibration time) = 160 ps
    Adopted from Witte et al. (Ref. 55) in Appendix B; acts as heat sink in eq. (B2).
  • t_ee_off (time when e-e scattering is disabled) = 6 fs
    Chosen in Section III C as 'somewhat arbitrarily chosen'; used to isolate e-ph relaxation rates for the circular-symbol curves in Fig. 4.
  • Phonon bath cutoff frequency = 2 THz
    Defines the split between six individual optical-mode baths and one acoustic bath (Appendix B); influences which modes can appear to be selectively excited.
  • Deposited excitation energy Edep = 0.1 eV per supercell (3.7 µJ/cm^2)
    Sets A0 in eq. (10) and Tel via the electronic heat capacity; matches the experimental pump fluence of Ref. 11.
assumptions (6)
  • domain assumption Kohn-Sham eigenvalues from GGA-PBE are used as the quasiparticle energies εnk in the master equation.
    Section II states the electronic single-particle energies are taken to be the Kohn-Sham eigenvalues from PBE. No GW self-energy correction is applied to the slab band structure.
  • domain assumption Electron-electron scattering in the thin film is the same as in bulk Pb.
    Section III B: 'The self-energy Σ is obtained from a GW calculation of bulk Pb.' This ignores confinement and substrate screening changes to the Coulomb interaction.
  • domain assumption Deformation potentials are independent of phonon wave vector Q and optical phonon dispersion is negligible.
    Eq. (8) and Appendix A replace D_{nk,IQ} by D_{nk,I} and Ω_IQ by Ω_I0; stated as justified by the large supercell and small Brillouin zone.
  • standard math Markov and second-order Born approximations are valid for the electron dynamics.
    Used to derive the master equation (eq. 3) from the density matrix; standard for weak coupling, but requires fast loss of coherence.
  • ad hoc to paper The scattering-in term for e-e interaction factorizes as Γ_in = Φ(x)N(t) with Φ from a stationary Boltzmann solution.
    Section III B assumes this factorization for computational convenience and sets Φ according to Ref. 5; energy conservation fixes N(t).
  • ad hoc to paper Holes do not scatter via electron-phonon interaction.
    Section II: 'the hole states are treated in less detail, and only Coulomb scattering, as described in Section III B, will be considered among the holes.' This truncation could affect the phonon energy flow but is not quantified.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Relaxation of electrons in quantum-confined states in Pb/Si(111) thin films from master equation with first-principles-derived rates." pith.science (2026). https://pith.science/paper/HDEDDROZ

@misc{pith2026190806119,
  author       = {Pith},
  title        = {Pith review of: Relaxation of electrons in quantum-confined states in Pb/Si(111) thin films from master equation with first-principles-derived rates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HDEDDROZ}},
  note         = {Machine review of arXiv:1908.06119}
}
read the original abstract

Atomically thin films of Pb on Si(111) provide an experimentally tunable system comprising a highly structured electronic density of states. The lifetime of excited electrons in these states is limited by both electron-electron (e-e) and electron-phonon (e-ph) scattering. We employ the description by a master equation for the electronic occupation numbers to analyze the relative importance of both scattering mechanisms. The electronic and phononic band structures, as well as the matrix elements for electron-phonon coupling within deformation potential theory were obtained from density functional calculations, thus taking into account quantum confinement effects. For the relaxation dynamics, the contribution of impact ionization processes to the lifetime is estimated from the imaginary part of the electronic self-energy calculated in the GW approximation. By numerically solving rate equations for the occupations of the Pb-derived electronic states coupled to a phononic heat bath, we are able to follow the distribution of the electronic excitation energy to the various modes of Pb lattice vibrations. While e-e scattering is the dominant relaxation mechanism, we demonstrate that the e-ph scattering is highly phonon-mode-specific, with a large contribution from surface phonons. At electron energies of about 0.3 eV above the Fermi surface, a 'phonon bottleneck' characteristic of relaxation in nanostructures with well-separated electronic states is observed. The time scales extracted from the simulations are compared to data from pump-probe experiments using time-resolved two-photon photoemission.

Figures

Figures reproduced from arXiv: 1908.06119 by the authors.

Figure 1
Figure 1. FIG. 1. Atomic structure and electronic bands (dashed lines) in a selected energy range above the Fermi energy (horizontal [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. a) Decay of the population in a single quantum well [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Electronic excitation spectra (thick black line) after [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Relaxation of the population at various electronic [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Temporal evolution of the energy in the highest-lying [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The figure illustrates schematically how energy conservation is imposed when evaluating Brillouin zone integrals. The [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

55 extracted references · 48 canonical work pages

  1. [1]

    author author W. S. \ Fann , author R. Storz , author H. W. K. \ Tom , \ and\ author J. Bokor ,\ @noop journal journal Phys. Rev. B \ volume 46 ,\ pages 13592 ( year 1992 ) NoStop

    work page 1992

  2. [2]

    author author R. H. M. \ Groeneveld , author R. Sprik , \ and\ author A. Lagendijk ,\ @noop journal journal Phys. Rev. B \ volume 51 ,\ pages 11433 ( year 1995 ) NoStop

    work page 1995

  3. [3]

    author author P. B. \ Allen ,\ @noop journal journal Phys. Rev. Lett. \ volume 59 ,\ pages 1460 ( year 1987 ) NoStop

    work page 1987

  4. [4]

    Lisowski , author P

    author author M. Lisowski , author P. A. \ Loukakos , author U. Bovensiepen , author J. St \"a hler , author G. Gahl , \ and\ author M. Wolf ,\ DOI: 10.1007/s00339-003-2301-7 journal journal Appl. Phys. A \ volume 78 ,\ pages 165 ( year 2004 ) NoStop

    work page doi:10.1007/s00339-003-2301-7

  5. [5]

    author author V. V. \ Baranov \ and\ author V. V. \ Kabanov ,\ @noop journal journal Phys. Rev. B \ volume 89 ,\ pages 125102 ( year 2014 ) NoStop

    work page 2014

  6. [6]

    u kermann , author P. Zhou , author I. Avigo , author H. Pfn \

    author author A. S. \ Syed , author V. M. \ Trontl , author M. Ligges , author S. Sakong , author P. Kratzer , author D. L \"u kermann , author P. Zhou , author I. Avigo , author H. Pfn \"u r , author C. Tegenkamp , \ and\ author U. Bovensiepen ,\ 10.1103/PhysRevB.92.134301 journal journal Phys. Rev. B \ volume 92 ,\ pages 134301 ( year 2015 ) NoStop

    work page doi:10.1103/physrevb.92.134301

  7. [7]

    Zhang , author P

    author author T. Zhang , author P. Chen , author W.-J. \ Li , author Y.-J. \ Sun , author G. Wang , author X.-G. \ Zhu , author K. He , author L. Wang , author X. Ma , author X. Chen , author Y. Wang , author Y. Liu , author H.-Q. \ Lin , author J.-F. \ Jia , \ and\ author Q.-K. \ Xue ,\ @noop journal journal Nature Physics \ volume 6 ,\ pages 104 ( year ...

    work page 2010

  8. [8]

    Hofmann , author I

    author author P. Hofmann , author I. Y. \ Sklyadneva , author E. D. L. \ Rienks , \ and\ author E. V. \ Chulkov ,\ @noop journal journal New J. Phys. \ volume 11 ,\ pages 125005 ( year 2009 ) NoStop

    work page 2009

Show all 55 references
  1. [9]

    \ Zhang , author J.-F

    author author Y.-F. \ Zhang , author J.-F. \ Jia , author T.-Z. \ Han , author Z. Tang , author Q.-T. \ Shen , author Y. Guo , author Z. Q. \ Qiu , \ and\ author Q.-K. \ Xue ,\ @noop journal journal Phys. Rev. Lett. \ volume 95 ,\ pages 096802 ( year 2005 ) NoStop

    2005

  2. [10]

    author author M. H. \ Upton , author C. M. \ Wei , author M. Y. \ Chou , author T. Miller , \ and\ author T.-C. \ Chiang ,\ @noop journal journal Phys. Rev. Lett. \ volume 93 ,\ pages 026802 ( year 2004 ) NoStop

    2004

  3. [11]

    author author P. S. \ Kirchmann , author L. Rettig , author X. Zubizarreta , author V. M. \ Silkin , author E. V. \ Chulkov , \ and\ author U. Bovensiepen ,\ 10.1038/nphys1735 journal journal Nature Physics \ volume 6 ,\ pages 782 ( year 2010 ) NoStop

    doi

  4. [12]

    author author P. M. \ Echenique , author R. Berndt , author E. V. \ Chulkov , author T. Fauster , author A. Goldmann , \ and\ author U. H\"ofer ,\ https://doi.org/10.1016/j.surfrep.2004.02.002 journal journal Surf. Sci. Rep. \ volume 52 ,\ pages 219 ( year 2004 ) NoStop

    2004 doi

  5. [13]

    author author E. V. \ Chulkov , author A. G. \ Borisov , author J. P. \ Gauyacq , author D. S\'anchez , author V. M. \ Silkin , author V. P. \ Zhukov , \ and\ author P. M. \ Echenique ,\ 10.1021/cr050166o journal journal Chemical Reviews \ volume 106 ,\ pages 4160 ( year 2006 ) NoStop

    doi

  6. [14]

    Zahedifar \ and\ author P

    author author M. Zahedifar \ and\ author P. Kratzer ,\ 10.1103/PhysRevB.96.115442 journal journal Phys. Rev. B \ volume 96 ,\ pages 115442 ( year 2017 ) NoStop

    2017 doi

  7. [15]

    Giustino ,\ @noop journal journal Rev

    author author F. Giustino ,\ @noop journal journal Rev. Mod. Phys. \ volume 89 ,\ pages 015003 ( year 2017 ) NoStop

    2017

  8. [16]

    Bernardi , author D

    author author M. Bernardi , author D. Vigil-Fowler , author J. Lischner , author J. B. \ Neaton , \ and\ author S. G. \ Louie ,\ @noop journal journal Phys. Rev. Lett. \ volume 112 ,\ pages 257402 ( year 2014 ) NoStop

    2014

  9. [17]

    author author V. A. \ Jhalani , author J.-J. \ Zhou , \ and\ author M. Bernardi ,\ 10.1021/acs.nanolett.7b02212 journal journal Nano Lett. \ volume 17 ,\ pages 5012 ( year 2017 ) NoStop

    2017 doi

  10. [18]

    Maldonado , author K

    author author P. Maldonado , author K. Carva , author M. Flammer , \ and\ author P. M. \ Oppeneer ,\ @noop journal journal Phys. Rev. B \ volume 96 ,\ pages 174439 ( year 2017 ) NoStop

    2017

  11. [19]

    \ Chan , author C

    author author T.-L. \ Chan , author C. Z. \ Wang , author M. Hupalo , author M. C. \ Tringides , author Z.-Y. \ Lu , \ and\ author K. M. \ Ho ,\ @noop journal journal Phys. Rev. B \ volume 68 ,\ pages 045410 ( year 2003 ) NoStop

    2003

  12. [20]

    Yakes , author V

    author author M. Yakes , author V. Yeh , author M. Hupalo , \ and\ author M. C. \ Tringides ,\ 10.1063/1.2724910 journal journal Phys. Rev. B \ volume 69 ,\ pages 224103 ( year 2004 ) NoStop

    2004 doi

  13. [21]

    Souto-Casares , author T.-L

    author author J. Souto-Casares , author T.-L. \ Chan , author J. R. \ Chelikowsky , author K.-M. \ Ho , author C.-Z. \ Wang , \ and\ author S. B. \ Zhang ,\ @noop journal journal Phys. Rev. B \ volume 92 ,\ pages 094103 ( year 2015 ) NoStop

    2015

  14. [22]

    author author A. V. \ Akimov \ and\ author O. V. \ Prezhdo ,\ 10.1021/ct400641n journal journal J. Chem. Theory Comput. \ volume 9 ,\ pages 4959 ( year 2013 ) NoStop

    2013 doi

  15. [23]

    author author A. V. \ Akimov \ and\ author O. V. \ Prezhdo ,\ 10.1021/ct400934c journal journal J. Chem. Theory Comput. \ volume 10 ,\ pages 789 ( year 2014 ) NoStop

    2014 doi

  16. [24]

    Zheng , author W

    author author Q. Zheng , author W. A. \ Saidi , author Y. Xie , author Z. Lan , author O. V. \ Prezhdo , author H. Petek , \ and\ author J. Zhao ,\ 10.1021/acs.nanolett.7b03429 journal journal Nano Lett. \ volume 17 ,\ pages 6435 ( year 2017 ) NoStop

    doi

  17. [25]

    Kira , author F

    author author M. Kira , author F. Jahnke , author W. Hoyer , \ and\ author S. W. \ Koch ,\ @noop journal journal Prog. Quantum Electronics \ volume 23 ,\ pages 189 ( year 1999 ) NoStop

    1999

  18. [26]

    Haug \ and\ author S

    author author H. Haug \ and\ author S. W. \ Koch ,\ @noop title Quantum Theory of the Optical and Electronic Properties of Semiconductors ,\ edition 5th \ ed.\ ( publisher World Scientific ,\ address Singapore ,\ year 2009 ) NoStop

    2009

  19. [27]

    Malic , author T

    author author E. Malic , author T. Winzer , author E. Bobkin , \ and\ author A. Knorr ,\ @noop journal journal Phys. Rev. B \ volume 84 ,\ pages 205406 ( year 2011 ) NoStop

    2011

  20. [28]

    Kresse \ and\ author J

    author author G. Kresse \ and\ author J. Furthm \"u ller ,\ @noop journal journal Phys. Rev. B \ volume 54 ,\ pages 11169 ( year 1996 ) NoStop

    1996

  21. [29]

    author author J. P. \ Perdew , author K. Burke , \ and\ author M. Ernzerhof ,\ @noop journal journal Phys. Rev. Lett. \ volume 77 ,\ pages 3865 ( year 1996 ) NoStop

    1996

  22. [30]

    Togo \ and\ author I

    author author A. Togo \ and\ author I. Tanaka ,\ @noop journal journal Scr. Mater. \ volume 108 ,\ pages 1 ( year 2015 ) NoStop

    2015

  23. [31]

    Sandhofer , author I

    author author M. Sandhofer , author I. Sklyadneva , author V. Sharma , author V. M. \ Trontl , author P. Zhou , author M. Ligges , author R. Heid , author K.-P. \ Bohnen , author E. Chulkov , \ and\ author U. Bovensiepen ,\ @noop journal journal J. Elec. Spec. Relat. Phen. \ v...

    2014

  24. [32]

    Rossi \ and\ author T

    author author F. Rossi \ and\ author T. Kuhn ,\ @noop journal journal Rev. Mod. Phys. \ volume 74 ,\ pages 895 ( year 2002 ) NoStop

    2002

  25. [33]

    B\"ucking , author P

    author author N. B\"ucking , author P. Kratzer , author M. Scheffler , \ and\ author A. Knorr ,\ 10.1103/PhysRevB.77.233305 journal journal Phys. Rev. B \ volume 77 ,\ pages 233305 ( year 2008 ) NoStop

    2008 doi

  26. [34]

    Richter , author A

    author author M. Richter , author A. Carmele , author S. Butscher , author N. B\"ucking , author F. Milde , author P. Kratzer , author M. Scheffler , \ and\ author A. Knorr ,\ 10.1063/1.3117236 journal journal Journal of Applied Physics \ volume 105 ,\ pages 122409 ( year 2009...

    doi

  27. [35]

    Richter , author S

    author author M. Richter , author S. Butscher , author N. B\"ucking , author F. Milde , author C. Weber , author P. Kratzer , author M. Scheffler , \ and\ author A. Knorr ,\ title Theory of ultrafast dynamics of electron-phonon interactions in two dimensional electron gases: S...

    doi

  28. [36]

    Ueba \ and\ author B

    author author H. Ueba \ and\ author B. Gumhalter ,\ 10.1016/j.progsurf.200703.002 journal journal Prog. Surf. Sci. \ volume 82 ,\ pages 193 ( year 2007 ) NoStop

    2007 doi

  29. [37]

    author author T. Kuhn ,\ title Density matrix theory of coherent ultrafast dynamics , \ in\ @noop booktitle Theory of transport properties of semiconductor nanostructures ,\ series and number Electronic Materials 4 ,\ editor edited by\ editor E. Sch \"o ll \ ( publisher Chapma...

    1998

  30. [38]

    Resta ,\ 10.1103/PhysRevB.44.11035 journal journal Phys

    author author R. Resta ,\ 10.1103/PhysRevB.44.11035 journal journal Phys. Rev. B \ volume 44 ,\ pages 11035 ( year 1991 ) NoStop

    1991 doi

  31. [39]

    Ladst \"a dter , author U

    author author F. Ladst \"a dter , author U. Hohenester , author P. Puschnig , \ and\ author C. Ambrosch-Draxl ,\ @noop journal journal Phys. Rev. B \ volume 70 ,\ pages 235125 ( year 2004 ) NoStop

    2004

  32. [40]

    Shishkin \ and\ author G

    author author M. Shishkin \ and\ author G. Kresse ,\ @noop journal journal Phys. Rev. B \ volume 74 ,\ pages 035101 ( year 2006 ) NoStop

    2006

  33. [41]

    author author I. P. \ Hong , author C. Brun , author F. Patthey , author I. Y. \ Sklyadneva , author X. Zubizarreta , author R. Heid , author V. M. \ Silkin , author P. M. \ Echenique , author K. P. \ Bohnen , author E. V. \ Chulkov , \ and\ author W.-D. \ Schneider ,\ @noop j...

    2009

  34. [42]

    Gajdo s s , author K

    author author M. Gajdo s s , author K. Hummer , author G. Kresse , author J. Furthm \"u ller , \ and\ author F. Bechstedt ,\ 10.1103/PhysRevB.73.045112 journal journal Phys. Rev. B \ volume 73 ,\ pages 045112 ( year 2006 ) NoStop

    2006 doi

  35. [43]

    note The dipole matrix elements are delivered by the VASP code using the keyword LOPTICS NoStop

  36. [44]

    Heitz , author H

    author author T. Heitz , author H. Born , author F. Guffarth , author O. Stier , author A. Schliwa , author A. Hoffmann , \ and\ author D. Bimberg ,\ @noop journal journal Phys. Rev. B \ volume 64 ,\ pages 241305(R) ( year 2001 ) NoStop

    2001

  37. [45]

    Jia , author J

    author author X. Jia , author J. Jiang , author Y. Zhang , author J. Qiu , author S. Wang , author Z. Chen , author N. Yuan , \ and\ author J. Ding ,\ 10.1063/1.5021679 journal journal Appl. Phys. Lett. \ volume 112 ,\ pages 143903 ( year 2018 ) ,\ http://arxiv.org/abs/https:/...

    doi

  38. [46]

    fig:esume

    note In our simulations, we explicitly allowed for the possibility of conversion between different vibrational modes (see appendix), but it should be noted that vibrational coupling takes place on a much longer time scale of at least 30 ps and is hardly relevant for the observ...

  39. [47]

    Rettig , author P

    author author L. Rettig , author P. S. \ Kirchmann , \ and\ author U. Bovensiepen ,\ 10.1088/1367-2630/14/2/023047 journal journal New J. Phys. \ volume 14 ,\ pages 023047 ( year 2012 ) NoStop

    2012 doi

  40. [48]

    author author S. D. \ Brorson , author A. Kazeroonian , author J. S. \ Moodera , author D. W. \ Face , author T. K. \ Cheng , author E. P. \ Ippen , author M. S. \ Dresselhaus , \ and\ author G. Dresselhaus ,\ @noop journal journal Phys. Rev. Lett. \ volume 64 ,\ pages 2172 ( ...

    1990

  41. [49]

    Zhou , author C

    author author P. Zhou , author C. Streub \"u hr , author A. Kalus , author T. Frigge , author S. Wall , author A. Hanisch-Blicharski , author M. Kammler , author M. Ligges , author U. Bovensiepen , author D. von der Linde , \ and\ author M. Horn-von Hoegen ,\ 10.105/epjconf/20...

  42. [50]

    Waldecker , author R

    author author L. Waldecker , author R. Bertoni , , author R. Ernstorfer , \ and\ author J. Vorberger ,\ @noop journal journal Phys. Rev. X \ volume 6 ,\ pages 021003 ( year 2016 ) NoStop

    2016

  43. [51]

    Maldonado , author T

    author author P. Maldonado , author T. Chase , author A. H. \ Reid , author X. Shen , author R. K. \ Li , author K. Carva , author T. Payer , author M. Horn von Hoegen , author K. Sokolowski-Tinten , author X. J. \ Wang , author P. M. \ Oppeneer , \ and\ author H. A. \ D \"u r...

    2019 arXiv

  44. [52]

    Sadasivam , author M

    author author S. Sadasivam , author M. K. Y. \ Chan , \ and\ author P. Darancet ,\ @noop journal journal Phys. Rev. Lett. \ volume 119 ,\ pages 136602 ( year 2017 ) NoStop

    2017

  45. [53]

    author author E. B. \ Ramayya , author D. Vasileska , author S. M. \ Goodnick , \ and\ author I. Knezevic ,\ @noop journal journal J. Appl. Phys. \ volume 104 ,\ pages 063711 ( year 2008 ) NoStop

    2008

  46. [54]

    Sakong , author P

    author author S. Sakong , author P. Kratzer , author S. Wall , author A. Kalus , \ and\ author M. Horn-von Hoegen ,\ 10.1103/PhysRevB.88.115419 journal journal Phys. Rev. B \ volume 88 ,\ pages 115419 ( year 2013 ) NoStop

    2013 doi

  47. [55]

    Witte , author T

    author author T. Witte , author T. Frigge , author B. Hafke , author B. Krenzer , \ and\ author M. Horn-von Hoegen ,\ 10.1063/1.4986509 journal journal Appl. Phys. Lett. \ volume 110 ,\ pages 243103 ( year 2017 ) NoStop

    2017 doi

Pith tools

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