pith. sign in

arxiv: 2604.06897 · v1 · submitted 2026-04-08 · ❄️ cond-mat.mes-hall

Excitonic Mott transition without population inversion

Oleg Dogadov , Armando Genco , Allison R. Cadore , James A. Kerfoot , Evgeny M. Alexeev , Osman Balci , Chiara Trovatello , Kenji Watanabe
show 7 more authors
Takashi Taniguchi Seth Ariel Tongay Andrea C. Ferrari Giulio Cerullo Stefano Dal Conte Gianluca Stefanucci Enrico Perfetto
This is my paper

Pith reviewed 2026-05-10 17:16 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords excitonic Mott transitionultrafast spectroscopymonolayer transition metal dichalcogenidenonthermal carriersdynamical Coulomb screeningexciton dissociationoptical gain
0
0 comments X

The pith

The excitonic Mott transition quenches semiconductor resonances without requiring population inversion under ultrafast excitation.

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

The paper demonstrates that the excitonic Mott transition can fully dissociate excitons in a monolayer semiconductor even when population inversion and optical gain remain absent. Experiments using femtosecond pump-probe spectroscopy on a transition metal dichalcogenide monolayer show the excitonic resonance vanishing within roughly 100 fs across a wide fluence range. Real-time ab initio simulations trace this outcome to the combined action of strongly nonthermal carrier distributions and time-dependent changes in Coulomb screening. A reader would care because the standard textbook connection between high-density exciton ionization, inversion, and gain breaks down in non-equilibrium conditions, implying new control mechanisms for dense optical responses.

Core claim

Femtosecond pump-probe measurements drive a monolayer transition metal dichalcogenide into a dense photoexcited state where the excitonic resonance quenches completely within approximately 100 fs, yet optical gain stays absent at all explored fluences. Real-time ab initio simulations establish that the excitonic Mott transition proceeds through the interplay of strongly nonthermal carrier populations and nonequilibrium dynamical screening of the Coulomb interaction. This agreement identifies a distinct ultrafast route to exciton ionization that operates outside quasi-equilibrium assumptions and shows population inversion is not a universal prerequisite.

What carries the argument

The interplay of strongly nonthermal carrier populations and nonequilibrium dynamical screening of the Coulomb interaction, which together produce the excitonic Mott transition.

If this is right

  • Exciton ionization can occur on sub-100 fs timescales without the carrier distribution reaching inversion.
  • The absence of optical gain does not rule out the excitonic Mott transition when excitation is strongly non-equilibrium.
  • Real-time ab initio calculations quantitatively predict nonequilibrium screening and population effects in two-dimensional semiconductors.
  • Quasi-equilibrium models of high-density optical response must be extended to capture ultrafast nonthermal pathways.

Where Pith is reading between the lines

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

  • The same non-equilibrium route could appear in other excitonic platforms such as quantum wells, suggesting targeted pump-probe tests at varying excitation durations.
  • Ultrafast optoelectronic switches might exploit this transition for rapid modulation at lower carrier densities than inversion-based designs require.
  • Engineering the dielectric environment to alter dynamical screening offers an independent handle on the transition threshold beyond carrier density alone.

Load-bearing premise

The observed quenching of the excitonic resonance is produced specifically by the excitonic Mott transition rather than by other ultrafast many-body processes, and the simulations reproduce the non-equilibrium dynamics without adjustable parameters.

What would settle it

Direct time-resolved measurement of carrier occupation numbers that reveals population inversion precisely when the resonance quenches, or a clear discrepancy between measured spectra and the parameter-free simulations, would show the transition identification is incorrect.

read the original abstract

Exciton dissociation via the excitonic Mott transition (EMT) governs the high-density optical response of semiconductors and sets fundamental limits for optoelectronic devices. The EMT is conventionally linked to the onset of population inversion and the emergence of optical gain. Here, we demonstrate that this paradigm can break down under ultrafast non-equilibrium excitation. Using femtosecond pump-probe optical spectroscopy, we drive a monolayer transition metal dichalcogenide into a dense photoexcited state in which the excitonic resonance is completely quenched within ~100 fs, while the optical gain is entirely absent across the explored fluence range. State-of-the-art real-time ab initio simulations reveal that the EMT is governed by an interplay of strongly nonthermal carrier populations and nonequilibrium dynamical screening of the Coulomb interaction. The quantitative agreement between theory and experiment identifies a distinct, ultrafast pathway to exciton ionization beyond quasi-equilibrium descriptions and demonstrates that population inversion is not a universal prerequisite for the EMT.

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

2 major / 2 minor

Summary. The paper reports femtosecond pump-probe optical spectroscopy on a monolayer transition metal dichalcogenide in which the excitonic resonance is completely quenched within ~100 fs under dense photoexcitation, with no optical gain observed across the fluence range. Real-time ab initio simulations attribute the quenching to an excitonic Mott transition (EMT) driven by strongly nonthermal carrier populations and nonequilibrium dynamical screening of the Coulomb interaction, concluding that population inversion is not a universal prerequisite for the EMT.

Significance. If the identification of the observed quenching specifically as the EMT holds, the result would demonstrate a distinct ultrafast, non-equilibrium pathway to exciton ionization that challenges the conventional quasi-equilibrium link between the EMT and population inversion. The quantitative agreement between experiment and parameter-free ab initio simulations is a notable strength, with potential implications for high-density exciton physics and ultrafast optoelectronics in 2D materials.

major comments (2)
  1. The central identification of the ~100 fs quenching as the EMT (rather than transient bandgap renormalization, phase-space filling, or intervalley scattering) rests on the absence of gain plus simulation agreement, but the manuscript does not report an explicit verification that the simulated carrier density exceeds the equilibrium Mott density for the material or that the exciton binding energy is driven to zero.
  2. In the non-equilibrium carrier distributions accessed here, the absence of optical gain does not rigorously exclude local inversion or chemical-potential conditions that could still produce gain in a quasi-equilibrium picture; a quantitative analysis of the occupation functions and possible gain thresholds would strengthen the claim that inversion is absent.
minor comments (2)
  1. The fluence range and corresponding estimated carrier densities should be stated explicitly in the main text or a table to allow direct comparison with literature Mott densities.
  2. Figure captions and simulation details could clarify which quantities are computed from first principles versus any post-processing or fitting.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of our work and for the constructive comments, which have helped us improve the clarity and rigor of the manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [—] The central identification of the ~100 fs quenching as the EMT (rather than transient bandgap renormalization, phase-space filling, or intervalley scattering) rests on the absence of gain plus simulation agreement, but the manuscript does not report an explicit verification that the simulated carrier density exceeds the equilibrium Mott density for the material or that the exciton binding energy is driven to zero.

    Authors: We agree that an explicit verification strengthens the identification of the EMT. In the revised manuscript we have added a new panel to Figure 4 showing the time evolution of the exciton binding energy extracted directly from the ab initio simulations; the binding energy drops to zero within ~100 fs at the densities reached. We also include a direct comparison of the simulated photoexcited carrier density (peaking above 4×10^13 cm^{-2}) to the equilibrium Mott density reported for monolayer TMDs (~1–2×10^13 cm^{-2}), confirming the threshold is exceeded. These additions distinguish the EMT from competing mechanisms such as bandgap renormalization, which is already self-consistently included in the real-time TDDFT treatment. revision: yes

  2. Referee: [—] In the non-equilibrium carrier distributions accessed here, the absence of optical gain does not rigorously exclude local inversion or chemical-potential conditions that could still produce gain in a quasi-equilibrium picture; a quantitative analysis of the occupation functions and possible gain thresholds would strengthen the claim that inversion is absent.

    Authors: We appreciate this caveat on non-equilibrium interpretations. We have added a quantitative analysis in the revised Supplementary Information (new Section S5) that extracts the time-dependent occupation functions from the simulations and computes the corresponding quasi-Fermi levels. At the relevant times, the electron and hole chemical potentials do not satisfy the inversion condition relative to the dynamically screened bandgap. For comparison, we also evaluate the optical response assuming a quasi-equilibrium Fermi-Dirac distribution at the same instantaneous density and temperature; this quasi-equilibrium case does predict gain, whereas the actual non-equilibrium occupations do not. A brief discussion of these results has been inserted in the main text near the end of Section III. revision: yes

Circularity Check

0 steps flagged

No circularity: central claim rests on independent pump-probe data and real-time ab initio simulations

full rationale

The paper's derivation chain consists of (i) experimental observation of complete excitonic resonance quenching within ~100 fs without optical gain, and (ii) comparison to state-of-the-art real-time ab initio simulations that incorporate nonthermal carrier populations and nonequilibrium dynamical screening. Neither step defines the target result (EMT without inversion) in terms of itself, fits a parameter to the outcome being predicted, or reduces the load-bearing argument to a self-citation whose validity is presupposed by the present work. The quantitative agreement is presented as external validation rather than a tautology. The manuscript is therefore self-contained against external benchmarks of ultrafast spectroscopy and computational many-body methods; no load-bearing step collapses by construction to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit list of free parameters or axioms; simulations are described as state-of-the-art real-time ab initio but without disclosed fitting details or background assumptions.

pith-pipeline@v0.9.0 · 5519 in / 1140 out tokens · 41140 ms · 2026-05-10T17:16:10.380419+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

60 extracted references · 60 canonical work pages

  1. [1]

    Brinkman, W. F. & Rice, T. M. Electron-hole liquids in semiconductors.Phys. Rev. B7, 1508–1523 (1973). URL https://link.aps.org/doi/10.1103/PhysRevB. 7.1508

    work page doi:10.1103/physrevb 1973

  2. [2]

    Mott, N. F. Metal-insulator transition.Rev. Mod. Phys.40, 677–683 (1968)

    work page 1968

  3. [3]

    Wang, G.et al.Colloquium: Excitons in atomically thin transition metal dichalco- genides.Rev. Mod. Phys.90, 021001 (2018). URL https://link.aps.org/doi/10. 18 1103/RevModPhys.90.021001

    work page 2018

  4. [4]

    & Deveaud, B

    Kappei, L., Szczytko, J., Morier-Genoud, F. & Deveaud, B. Direct observa- tion of the mott transition in an optically excited semiconductor quantum well. Phys. Rev. Lett.94, 147403 (2005). URL https://link.aps.org/doi/10.1103/ PhysRevLett.94.147403

    work page 2005

  5. [5]

    M., Rigosi, A

    Chernikov, A., Ruppert, C., Hill, H. M., Rigosi, A. F. & Heinz, T. F. Popula- tion inversion and giant bandgap renormalization in atomically thin WS 2 layers. Nature Photonics9, 466–470 (2015)

    work page 2015

  6. [6]

    & Kuwata-Gonokami, M

    Nagai, M. & Kuwata-Gonokami, M. Electron–hole liquid formation by exci- ton and biexciton resonant excitation in cucl.Journal of Luminescence 100, 233–242 (2002). URL https://www.sciencedirect.com/science/article/pii/ S0022231302004428

    work page 2002

  7. [7]

    & Gibbs, H

    Koch, S., Kira, M., Khitrova, G. & Gibbs, H. Semiconductor exci- tons in new light.Nature Materials5, 523 – 531 (2006). URL https://www.scopus.com/inward/record.uri?eid=2-s2.0-33745587349&doi=10. 1038%2fnmat1658&partnerID=40&md5=821aa952700693b603ff98e77a483ce6

    work page 2006

  8. [8]

    & Chemla, D

    Kaindl, R., Carnahan, M., H¨ agele, D., L¨ ovenich, R. & Chemla, D. Ultra- fast terahertz probes of transient conducting and insulating phases in an electron-hole gas.Nature423, 734 – 738 (2003). URL https: //www.scopus.com/inward/record.uri?eid=2-s2.0-0038341624&doi=10.1038% 2fnature01676&partnerID=40&md5=2d923f545e5073c2dc36982ba7541b28

    work page 2003

  9. [9]

    & Shimano, R

    Suzuki, T. & Shimano, R. Exciton mott transition in si revealed by terahertz spectroscopy.Physical Review Letters109(2012). 19

    work page 2012

  10. [10]

    & Koch, S.Quantum Theory Of The Optical And Electronic Properties Of Semiconductors (5th Edition)(World Scientific Publishing Company, 2009)

    Haug, H. & Koch, S.Quantum Theory Of The Optical And Electronic Properties Of Semiconductors (5th Edition)(World Scientific Publishing Company, 2009)

    work page 2009

  11. [11]

    & Yoshioka, T

    Asano, K. & Yoshioka, T. Exciton–mott physics in two-dimensional electron–hole systems: Phase diagram and single-particle spectra.Journal of the Physical Society of Japan83, 084702 (2014). URL https://doi.org/10.7566/JPSJ.83. 084702

    work page doi:10.7566/jpsj.83 2014

  12. [12]

    Semkat, D.et al.Ionization equilibrium in an excited semiconductor: Mott tran- sition versus bose-einstein condensation.Phys. Rev. B80, 155201 (2009). URL https://link.aps.org/doi/10.1103/PhysRevB.80.155201

    work page doi:10.1103/physrevb.80.155201 2009

  13. [13]

    Commun.8, 1166 (2017)

    Steinhoff, A.et al.Exciton fission in monolayer transition metal dichalcogenide semiconductors.Nat. Commun.8, 1166 (2017). URL https://doi.org/10.1038/ s41467-017-01298-6

    work page 2017

  14. [14]

    Hutter, G

    Das Sarma, S. & Wang, D. W. Many-body renormalization of semiconductor quantum wire excitons: Absorption, gain, binding, and unbinding.Phys. Rev. Lett.84, 2010–2013 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett. 84.2010

    work page doi:10.1103/physrevlett 2010

  15. [15]

    & Koch, S

    Meckbach, L., Stroucken, T. & Koch, S. W. Giant excitation induced bandgap renormalization in tmdc monolayers.Applied Physics Letters112, 061104 (2018). URL https://doi.org/10.1063/1.5017069

    work page doi:10.1063/1.5017069 2018

  16. [16]

    Meckbach, L.et al.Ultrafast band-gap renormalization and build-up of optical gain in monolayer MoTe2.Phys. Rev. B101, 075401 (2020). URL https://link. aps.org/doi/10.1103/PhysRevB.101.075401

    work page doi:10.1103/physrevb.101.075401 2020

  17. [17]

    Xu, Y.et al.Room-Temperature Amplified Spontaneous Emission in Two- Dimensional WS2 beyond Exciton Mott Transition.Phys. Rev. Lett.134, 066904 20 (2025). URL https://link.aps.org/doi/10.1103/PhysRevLett.134.066904

    work page doi:10.1103/physrevlett.134.066904 2025

  18. [18]

    & van Leeuwen, R.Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction(Cambridge University Press, 2013)

    Stefanucci, G. & van Leeuwen, R.Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction(Cambridge University Press, 2013)

    work page 2013

  19. [20]

    Real-Time G W : Toward anAb InitioDe- scription of the Ultrafast Carrier and Exciton Dynamics in Two-Dimensional Materials

    Perfetto, E., Pavlyukh, Y. & Stefanucci, G. Real-time GW: Toward an ab ini- tio description of the ultrafast carrier and exciton dynamics in two-dimensional materials.Phys. Rev. Lett.128, 016801 (2022). URL https://link.aps.org/doi/ 10.1103/PhysRevLett.128.016801

    work page doi:10.1103/physrevlett.128.016801 2022

  20. [21]

    & Stefanucci, G

    Perfetto, E. & Stefanucci, G. Real-Time GW-Ehrenfest-Fan-Migdal Method for Nonequilibrium 2D Materials.Nano Letters23, 7029–7036 (2023). URL https: //doi.org/10.1021/acs.nanolett.3c01772

    work page doi:10.1021/acs.nanolett.3c01772 2023

  21. [22]

    Reich, S.et al.Resonant raman scattering in cubic and hexagonal boron nitride.Phys. Rev. B71, 205201 (2005). URL https://link.aps.org/doi/10.1103/ PhysRevB.71.205201

    work page 2005

  22. [23]

    URL https://doi.org/10.1038/ s41467-018-05632-4

    Barbone, M.et al.Charge-tuneable biexciton complexes in monolayer WSe2.Nature Communications9, 3721 (2018). URL https://doi.org/10.1038/ s41467-018-05632-4

    work page 2018

  23. [24]

    Genco, A.et al.Ultrafast Exciton and Trion Dynamics in High-Quality Encapsulated MoS2 Monolayers.physica status solidi (b)260, 2200376 (2023). 21

    work page 2023

  24. [25]

    & Perfetto, E

    Stefanucci, G. & Perfetto, E. Semiconductor electron-phonon equations: A rung above Boltzmann in the many-body ladder.SciPost Phys.16, 073 (2024). URL https://scipost.org/10.21468/SciPostPhys.16.3.073

    work page doi:10.21468/scipostphys.16.3.073 2024

  25. [26]

    & Bechstedt, F.Spontaneous Emission from Semi- conductors After Ultrafast Pulse Excitation: Theory and Simulation, 139–192 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2004)

    Hannewald, K., Glutsch, S. & Bechstedt, F.Spontaneous Emission from Semi- conductors After Ultrafast Pulse Excitation: Theory and Simulation, 139–192 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2004). URL https://doi.org/10. 1007/978-3-540-44879-2 4

    work page 2004

  26. [27]

    & Koch, S

    Kira, M. & Koch, S. Many-body correlations and excitonic effects in semicon- ductor spectroscopy.Progress in Quantum Electronics30, 155–296 (2006). URL https://www.sciencedirect.com/science/article/pii/S0079672706000280

    work page 2006

  27. [29]

    & Stefanucci, G

    Perfetto, E., Sangalli, D., Marini, A. & Stefanucci, G. First-principles approach to excitons in time-resolved and angle-resolved photoemission spectra.Phys. Rev. B 94, 245303 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.245303

    work page doi:10.1103/physrevb.94.245303 2016

  28. [30]

    & Malic, E

    Perea-Caus´ ın, R., Brem, S. & Malic, E. Microscopic modeling of pump–probe spectroscopy and population inversion in transition metal dichalcogenides.phys- ica status solidi (b)257, 2000223 (2020)

    work page 2020

  29. [31]

    Lohof, F.et al.Prospects and limitations of transition metal dichalcogenide laser gain materials.Nano Letters19, 210–217 (2019)

    work page 2019

  30. [32]

    Mad´ eo, J.et al.Directly visualizing the momentum forbidden dark exci- tons and their dynamics in atomically thin semiconductors.arXiv preprint arXiv:2005.00241(2020). 22

    work page arXiv 2005

  31. [33]

    Pogna, E. A. A.et al.Photo-Induced Bandgap Renormalization Governs the Ultrafast Response of Single-Layer MoS2.ACS Nano10, 1182–1188 (2016)

    work page 2016

  32. [34]

    J.et al.Observation of Exciton Redshift–Blueshift Crossover in Monolayer WS2.Nano Letters17, 4210–4216 (2017)

    Sie, E. J.et al.Observation of Exciton Redshift–Blueshift Crossover in Monolayer WS2.Nano Letters17, 4210–4216 (2017)

    work page 2017

  33. [35]

    D., Hanbicki, A

    Cunningham, P. D., Hanbicki, A. T., Reinecke, T. L., McCreary, K. M. & Jonker, B. T. Resonant optical Stark effect in monolayer WS 2.Nature Communications 10, 5539 (2019)

    work page 2019

  34. [36]

    Trovatello, C.et al.Disentangling Many-Body Effects in the Coherent Optical Response of 2D Semiconductors.Nano Letters22, 5322–5329 (2022)

    work page 2022

  35. [37]

    Dynamic screening of quasiparticles in WS2 monolayers.Phys

    Calati, Stefano and Li, Qiuyang and Zhu, Xiaoyang and St¨ ahler, Julia. Dynamic screening of quasiparticles in WS2 monolayers.Phys. Rev. B107, 115404 (2023)

    work page 2023

  36. [38]

    URL https://doi.org/10.1021/nl071168m

    Casiraghi, C.et al.Rayleigh imaging of graphene and graphene layers.Nano Letters7, 2711–2717 (2007). URL https://doi.org/10.1021/nl071168m. PMID: 17713959

    work page doi:10.1021/nl071168m 2007

  37. [39]

    Flux method growth of bulk MoS2 single crystals and their application as a saturable absorber.CrystEngComm17, 4026–4032 (2015)

    Zhang, Xixia and Lou, Fei and Li, Chunlong and Zhang, Xiang and Jia, Ning and Yu, Tongtong and He, Jingliang and Zhang, Baitao and Xia, Haibing and Wang, Shanpeng and Tao, Xutang. Flux method growth of bulk MoS2 single crystals and their application as a saturable absorber.CrystEngComm17, 4026–4032 (2015)

    work page 2015

  38. [40]

    G.et al.Cleaning interfaces in layered materials heterostruc- tures.Nature Communications9, 5387 (2018)

    Purdie, D. G.et al.Cleaning interfaces in layered materials heterostruc- tures.Nature Communications9, 5387 (2018). URL https://doi.org/10.1038/ s41467-018-07558-3

    work page 2018

  39. [41]

    & Watanabe, K

    Taniguchi, T. & Watanabe, K. Synthesis of high-purity boron nitride single crystals under high pressure by using ba–bn solvent.Journal of Crystal Growth 23 303, 525–529 (2007). URL https://www.sciencedirect.com/science/article/pii/ S0022024807000486

    work page 2007

  40. [42]

    Hecht, E.Optics(Pearson, 2017)

    work page 2017

  41. [43]

    Ivchenko, E.Optical Spectroscopy of Semiconductor Nanostructures(Alpha Science, 2005)

    work page 2005

  42. [44]

    Kuzmenko, A. B. Kramers–Kronig constrained variational analysis of optical spectra.Review of Scientific Instruments76, 083108 (2005)

    work page 2005

  43. [45]

    Ashoka, A.et al.Extracting quantitative dielectric properties from pump-probe spectroscopy.Nature Communications13, 1437 (2022)

    work page 2022

  44. [46]

    G1-G2 scheme: Dramatic acceleration of nonequilibrium Green functions simulations within the Hartree-Fock generalized Kadanoff-Baym ansatz.Phys

    Joost, Jan-Philip and Schl¨ unzen, Niclas and Bonitz, Michael. G1-G2 scheme: Dramatic acceleration of nonequilibrium Green functions simulations within the Hartree-Fock generalized Kadanoff-Baym ansatz.Phys. Rev. B101, 245101 (2020). URL https://link.aps.org/doi/10.1103/PhysRevB.101.245101

    work page doi:10.1103/physrevb.101.245101 2020

  45. [47]

    & Bonitz, M

    Schl¨ unzen, N., Joost, J.-P. & Bonitz, M. Achieving the scaling limit for nonequi- librium green functions simulations.Phys. Rev. Lett.124, 076601 (2020). URL https://link.aps.org/doi/10.1103/PhysRevLett.124.076601

    work page doi:10.1103/physrevlett.124.076601 2020

  46. [48]

    & Stefanucci, G

    Pavlyukh, Y., Perfetto, E. & Stefanucci, G. Photoinduced dynamics of organic molecules using nonequilibrium Green’s functions with second-born, GW, T- matrix, and three-particle correlations.Phys. Rev. B104, 035124 (2021). URL https://link.aps.org/doi/10.1103/PhysRevB.104.035124

    work page doi:10.1103/physrevb.104.035124 2021

  47. [49]

    Time-linear scaling nonequilibrium Green’s function methods for real- time simulations of interacting electrons and bosons. I. Formalism

    Pavlyukh, Y., Perfetto, E., Karlsson, D., van Leeuwen, R. & Stefanucci, G. Time- linear scaling nonequilibrium Green’s function methods for real-time simulations of interacting electrons and bosons. I. Formalism.Phys. Rev. B105, 125134 24 (2022). URL https://link.aps.org/doi/10.1103/PhysRevB.105.125134

    work page doi:10.1103/physrevb.105.125134 2022

  48. [50]

    & Perfetto, E

    Stefanucci, G., van Leeuwen, R. & Perfetto, E. In and out-of-equilibrium ab initio theory of electrons and phonons.Phys. Rev. X13, 031026 (2023). URL https://link.aps.org/doi/10.1103/PhysRevX.13.031026

    work page doi:10.1103/physrevx.13.031026 2023

  49. [51]

    andˇSpiˇ cka, V

    Lipavsk´ y, P. andˇSpiˇ cka, V. and Velick´ y, B. Generalized Kadanoff-Baym ansatz for deriving quantum transport equations.Phys. Rev. B34, 6933–6942 (1986). URL https://link.aps.org/doi/10.1103/PhysRevB.34.6933

    work page doi:10.1103/physrevb.34.6933 1986

  50. [52]

    Fast Green’s Function Method for Ultrafast Electron-Boson Dynamics.Phys

    Karlsson, Daniel and van Leeuwen, Robert and Pavlyukh, Yaroslav and Perfetto, Enrico and Stefanucci, Gianluca. Fast Green’s Function Method for Ultrafast Electron-Boson Dynamics.Phys. Rev. Lett.127, 036402 (2021). URL https: //link.aps.org/doi/10.1103/PhysRevLett.127.036402

    work page doi:10.1103/physrevlett.127.036402 2021

  51. [53]

    & Stefanucci, G

    Perfetto, E. & Stefanucci, G. Cheers: a tool for correlated hole-electron evolution from real-time simulations.J. Phys. Condens. Matter30, 465901 (2018). URL http://stacks.iop.org/0953-8984/30/i=46/a=465901

    work page 2018

  52. [54]

    & Stefanucci, G

    Perfetto, E., Sangalli, D., Marini, A. & Stefanucci, G. Nonequilibrium Bethe- Salpeter equation for transient photoabsorption spectroscopy.Phys. Rev. B92, 205304 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.205304

    work page doi:10.1103/physrevb.92.205304 2015

  53. [55]

    & Xiao, D

    Liu, G.-B., Shan, W.-Y., Yao, Y., Yao, W. & Xiao, D. Three-band tight-binding model for monolayers of group-vib transition metal dichalcogenides.Phys. Rev. B 88, 085433 (2013). URL https://link.aps.org/doi/10.1103/PhysRevB.88.085433

    work page doi:10.1103/physrevb.88.085433 2013

  54. [56]

    & MacDonald, A

    Wu, F., Qu, F. & MacDonald, A. H. Exciton band structure of monolayer MoS2.Phys. Rev. B91, 075310 (2015). URL https://link.aps.org/doi/10.1103/ PhysRevB.91.075310. 25

    work page 2015

  55. [57]

    Keldysh, L. V. Coulomb interaction in thin semiconductor and semimetal films. Soviet Journal of Experimental and Theoretical Physics Letters29, 658 (1979)

    work page 1979

  56. [58]

    Cudazzo, P., Tokatly, I. V. & Rubio, A. Dielectric screening in two-dimensional insulators: Implications for excitonic and impurity states in graphane.Phys. Rev. B84, 085406 (2011). URL https://link.aps.org/doi/10.1103/PhysRevB.84. 085406

    work page doi:10.1103/physrevb.84 2011

  57. [59]

    Stier, A. V. and Wilson, N. P. and Velizhanin, K. A. and Kono, J. and Xu, X. and Crooker, S. A. Magnetooptics of Exciton Rydberg States in a Monolayer Semiconductor.Phys. Rev. Lett.120, 057405 (2018). URL https://link.aps.org/ doi/10.1103/PhysRevLett.120.057405

    work page doi:10.1103/physrevlett.120.057405 2018

  58. [60]

    How dielectric screening in two-dimensional crystals affects the convergence of excited-state calculations: Monolayer MoS 2.Phys

    H¨ user, Falco and Olsen, Thomas and Thygesen, Kristian S. How dielectric screening in two-dimensional crystals affects the convergence of excited-state calculations: Monolayer MoS 2.Phys. Rev. B88, 245309 (2013). URL https: //link.aps.org/doi/10.1103/PhysRevB.88.245309

    work page doi:10.1103/physrevb.88.245309 2013

  59. [61]

    Ridolfi, E., Lewenkopf, C. H. & Pereira, V. M. Excitonic structure of the optical conductivity in MoS 2 monolayers.Phys. Rev. B97, 205409 (2018). URL https: //link.aps.org/doi/10.1103/PhysRevB.97.205409

    work page doi:10.1103/physrevb.97.205409 2018

  60. [62]

    Li, X.et al.Intrinsic electrical transport properties of monolayer silicene and MoS2 from first principles.Phys. Rev. B87, 115418 (2013). URL https://link. aps.org/doi/10.1103/PhysRevB.87.115418. 26

    work page doi:10.1103/physrevb.87.115418 2013