- Open Access
Unified First-Principles Formula for Time-Resolved ARPES Spectra of Coherent and Incoherent Excitons beyond the Dilute Limit
Phys. Rev. Lett. 137, 026402 – Published 8 July, 2026
DOI: https://doi.org/10.1103/zhs1-rv1k
Abstract
Despite major experimental progresses in time-resolved and angle-resolved photoemission spectroscopy, a quantitative, microscopic framework for interpreting exciton-induced modifications of electronic band structures—applicable even beyond the low-density limit—is still lacking. Here, we close this gap by introducing a unified approach that links the dynamics of coherent and incoherent excitons to distinct and experimentally observable excitonic sidebands. Our central result is a general, first-principles formula for time-resolved photoemission spectra, applicable across a broad range of temperatures, excitation densities, and pump-probe delays. This advance provides a predictive tool for quantitatively tracking excitonic dynamics in complex materials.
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References (64)
- G. Onida, L. Reining, and A. Rubio, Electronic excitations: Density-functional versus many-body Green’s-function approaches, Rev. Mod. Phys. 74, 601 (2002).
- H. Zhang, T. Pincelli, C. Jozwiak, T. Kondo, R. Ernstorfer, T. Sato, and S. Zhou, Angle-resolved photoemission spectroscopy, Nat. Rev. Methods Primers 2, 54 (2022).
- F. Boschini, M. Zonno, and A. Damascelli, Time-resolved ARPES studies of quantum materials, Rev. Mod. Phys. 96, 015003 (2024).
- C. Xu and A. Zong, Time-domain study of coupled collective excitations in quantum materials, npj Quantum Mater. 10, 21 (2025).
- J. Madéo, M. K. L. Man, C. Sahoo, M. Campbell, V. Pareek, E. L. Wong, A. Al-Mahboob, N. S. Chan, A. Karmakar, B. M. K. Mariserla, X. Li, T. F. Heinz, T. Cao, and K. M. Dani, Directly visualizing the momentum-forbidden dark excitons and their dynamics in atomically thin semiconductors, Science 370, 1199 (2020).
- M. Dendzik et al., Observation of an excitonic Mott transition through ultrafast core-cum-conduction photoemission spectroscopy, Phys. Rev. Lett. 125, 096401 (2020).
- H. Tanimura and K. Tanimura, Time- and angle-resolved photoemission spectroscopy for the saddle-point excitons in GaAs, Phys. Rev. B 102, 045204 (2020).
- R. Wallauer, R. Perea-Causin, L. Münster, S. Zajusch, S. Brem, J. Güdde, K. Tanimura, K.-Q. Lin, R. Huber, E. Malic, and U. Höfer, Momentum-resolved observation of exciton formation dynamics in monolayer , Nano Lett. 21, 5867 (2021).
- K. Fukutani, R. Stania, C. Il Kwon, J. S. Kim, K. J. Kong, J. Kim, and H. W. Yeom, Detecting photoelectrons from spontaneously formed excitons, Nat. Phys. 17, 1024 (2021).
- A. Kunin, S. Chernov, J. Bakalis, Z. Li, S. Cheng, Z. H. Withers, M. G. White, G. Schönhense, X. Du, R. K. Kawakami, and T. K. Allison, Momentum-resolved exciton coupling and valley polarization dynamics in monolayer , Phys. Rev. Lett. 130, 046202 (2023).
- J. P. Bange, D. Schmitt, W. Bennecke, G. Meneghini, A. AlMutairi, K. Watanabe, T. Taniguchi, D. Steil, S. Steil, R. T. Weitz, G. S. M. Jansen, S. Hofmann, S. Brem, E. Malic, M. Reutzel, and S. Mathias, Probing electron-hole Coulomb correlations in the exciton landscape of a twisted semiconductor heterostructure, Sci. Adv. 10, eadi1323 (2024).
- V. Gosetti, J. Cervantes-Villanueva, S. Mor, D. Sangalli, A. García-Cristóbal, A. Molina-Sánchez, V. F. Agekyan, M. Tuniz, D. Puntel, W. Bronsch, F. Cilento, and S. Pagliara, Unveiling exciton formation: exploring the early stages in time, energy and momentum domain, arXiv:2412.02507.
- M. K. L. Man, J. Madéo, C. Sahoo, K. Xie, M. Campbell, V. Pareek, A. Karmakar, E. L. Wong, A. Al-Mahboob, N. S. Chan, D. R. Bacon, X. Zhu, M. M. M. Abdelrasoul, X. Li, T. F. Heinz, F. H. da Jornada, T. Cao, and K. M. Dani, Experimental measurement of the intrinsic excitonic wave function, Sci. Adv. 7, eabg0192 (2021).
- S. Dong, M. Puppin, T. Pincelli, S. Beaulieu, D. Christiansen, H. Hübener, C. W. Nicholson, R. P. Xian, M. Dendzik, Y. Deng, Y. W. Windsor, M. Selig, E. Malic, A. Rubio, A. Knorr, M. Wolf, L. Rettig, and R. Ernstorfer, Direct measurement of key exciton properties: Energy, dynamics, and spatial distribution of the wave function, Nat. Sci. 1, e10010 (2021).
- G. Meneghini, M. Reutzel, S. Mathias, S. Brem, and E. Malic, Hybrid exciton signatures in ARPES spectra of van der Waals materials, ACS Photonics 10, 3570 (2023).
- R. Mori, S. Ciocys, K. Takasan, P. Ai, K. Currier, T. Morimoto, J. E. Moore, and A. Lanzara, Spin-polarized spatially indirect excitons in a topological insulator, Nature (London) 614, 249 (2023).
- S. Beaulieu, S. Dong, V. Christiansson, P. Werner, T. Pincelli, J. D. Ziegler, T. Taniguchi, K. Watanabe, A. Chernikov, M. Wolf, L. Rettig, R. Ernstorfer, and M. Schüler, Berry curvature signatures in chiroptical excitonic transitions, Sci. Adv. 10, eadk3897 (2024).
- M. Na, A. K. Mills, and D. J. Jones, Advancing time- and angle-resolved photoemission spectroscopy: The role of ultrafast laser development, Phys. Rep. 1036, 1 (2023).
- H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 2009).
- M. Lindberg and S. W. Koch, Effective Bloch equations for semiconductors, Phys. Rev. B 38, 3342 (1988).
- T. Östreich and K. Schönhammer, Non-stationary excitonic-insulator states in photoexcited semiconductors, Z. Phys. B Condens. Matter 91, 189 (1993).
- K. Hannewald, S. Glutsch, and F. Bechstedt, Excitonic insulator through coherent pulse excitation?, J. Phys. Condens. Matter 13, 275 (2000).
- S. W. Koch, M. Kira, G. Khitrova, and H. M. Gibbs, Semiconductor excitons in new light, Nat. Mater. 5, 523 (2006).
- A. B. Madrid, K. Hyeon-Deuk, B. F. Habenicht, and O. V. Prezhdo, Phonon-induced dephasing of excitons in semiconductor quantum dots: Multiple exciton generation, fission, and luminescence, ACS Nano 3, 2487 (2009).
- Z. Nie, R. Long, L. Sun, C.-C. Huang, J. Zhang, Q. Xiong, D. W. Hewak, Z. Shen, O. V. Prezhdo, and Z.-H. Loh, Ultrafast carrier thermalization and cooling dynamics in few-layer , ACS Nano 8, 10931 (2014).
- P. Dey, J. Paul, Z. Wang, C. E. Stevens, C. Liu, A. H. Romero, J. Shan, D. J. Hilton, and D. Karaiskaj, Optical coherence in atomic-monolayer transition-metal dichalcogenides limited by electron-phonon interactions, Phys. Rev. Lett. 116, 127402 (2016).
- D. Sangalli, E. Perfetto, G. Stefanucci, and A. Marini, An ab-initio approach to describe coherent and non-coherent exciton dynamics, Eur. Phys. J. B 91, 171 (2018).
- G. Stefanucci and E. Perfetto, From carriers and virtual excitons to exciton populations: Insights into time-resolved ARPES spectra from an exactly solvable model, Phys. Rev. B 103, 245103 (2021).
- E. Perfetto and G. Stefanucci, Real-time GW-Ehrenfest-Fan-Migdal method for nonequilibrium 2d materials, Nano Lett. 23, 7029 (2023).
- R. Bertoni, C. W. Nicholson, L. Waldecker, H. Hübener, C. Monney, U. De Giovannini, M. Puppin, M. Hoesch, E. Springate, R. T. Chapman, C. Cacho, M. Wolf, A. Rubio, and R. Ernstorfer, Generation and evolution of spin-, valley-, and layer-polarized excited carriers in inversion-symmetric , Phys. Rev. Lett. 117, 277201 (2016).
- S. Z. Uddin, H. Kim, M. Lorenzon, M. Yeh, D.-H. Lien, E. S. Barnard, H. Htoon, A. Weber-Bargioni, and A. Javey, Neutral exciton diffusion in monolayer , ACS Nano 14, 13433 (2020).
- E. Perfetto and G. Stefanucci, Ultrafast creation and melting of nonequilibrium excitonic condensates in bulk , Phys. Rev. B 103, L241404 (2021).
- G. Stefanucci and E. Perfetto, Excitonic Bloch equations from first principles, SciPost Phys. 18, 009 (2025).
- G. Moody, C. Kavir Dass, K. Hao, C.-H. Chen, L.-J. Li, A. Singh, K. Tran, G. Clark, X. Xu, G. Berghäuser, E. Malic, A. Knorr, and X. Li, Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides, Nat. Commun. 6, 8315 (2015).
- M. Selig, G. Berghäuser, A. Raja, P. Nagler, C. Schüller, T. F. Heinz, T. Korn, A. Chernikov, E. Malic, and A. Knorr, Excitonic linewidth and coherence lifetime in monolayer transition metal dichalcogenides, Nat. Commun. 7, 13279 (2016).
- T. Jakubczyk, K. Nogajewski, M. R. Molas, M. Bartos, W. Langbein, M. Potemski, and J. Kasprzak, Impact of environment on dynamics of exciton complexes in a monolayer, 2D Mater. 5, 031007 (2018).
- E. Perfetto, D. Sangalli, A. Marini, and G. Stefanucci, Pump-driven normal-to-excitonic insulator transition: Josephson oscillations and signatures of BEC-BCS crossover in time-resolved ARPES, Phys. Rev. Mater. 3, 124601 (2019).
- E. Perfetto, S. Bianchi, and G. Stefanucci, Time-resolved ARPES spectra of nonequilibrium excitonic insulators: Revealing macroscopic coherence with ultrashort pulses, Phys. Rev. B 101, 041201(R) (2020).
- E. Perfetto and G. Stefanucci, Floquet topological phase of nondriven -wave nonequilibrium excitonic insulators, Phys. Rev. Lett. 125, 106401 (2020).
- Y.-H. Chan, D. Y. Qiu, F. H. da Jornada, and S. G. Louie, Giant self-driven exciton-Floquet signatures in time-resolved photoemission spectroscopy of from time-dependent GW approach, Proc. Natl. Acad. Sci. U.S.A. 120, e2301957120 (2023).
- V. Pareek, D. R. Bacon, X. Zhu, Y.-H. Chan, F. Bussolotti, M. G. Menezes, N. S. Chan, J. P. Urquizo, K. Watanabe, T. Taniguchi, E. Perfetto, M. K. L. Man, J. Madéo, G. Stefanucci, D. Y. Qiu, K. E. J. Goh, F. H. da Jornada, and K. M. Dani, Driving Floquet physics with excitonic fields, Nat. Phys. 22, 209 (2026).
- E. Perfetto, D. Sangalli, A. Marini, and G. Stefanucci, First-principles approach to excitons in time-resolved and angle-resolved photoemission spectra, Phys. Rev. B 94, 245303 (2016).
- A. Steinhoff, M. Florian, M. Rösner, G. Schönhoff, T. O. Wehling, and F. Jahnke, Exciton fission in monolayer transition metal dichalcogenide semiconductors, Nat. Commun. 8, 1166 (2017).
- A. Rustagi and A. F. Kemper, Photoemission signature of excitons, Phys. Rev. B 97, 235310 (2018).
- D. Christiansen, M. Selig, E. Malic, R. Ernstorfer, and A. Knorr, Theory of exciton dynamics in time-resolved ARPES: Intra- and intervalley scattering in two-dimensional semiconductors, Phys. Rev. B 100, 205401 (2019).
- J. K. Freericks, H. R. Krishnamurthy, and T. Pruschke, Theoretical description of time-resolved photoemission spectroscopy: Application to pump-probe experiments, Phys. Rev. Lett. 102, 136401 (2009).
- N. Stojić, A. Dal Corso, B. Zhou, and S. Baroni, Ab initio simulation of photoemission spectroscopy in solids: Plane-wave pseudopotential approach with applications to normal-emission spectra of cu(001) and cu(111), Phys. Rev. B 77, 195116 (2008).
- S. Moser, An experimentalist’s guide to the matrix element in angle resolved photoemission, J. Electron Spectrosc. Relat. Phenom. 214, 29 (2017).
- M. Schüler, U. De Giovannini, H. Hübener, A. Rubio, M. A. Sentef, T. P. Devereaux, and P. Werner, How circular dichroism in time- and angle-resolved photoemission can be used to spectroscopically detect transient topological states in graphene, Phys. Rev. X 10, 041013 (2020).
- J. H. Ryoo and C.-H. Park, Lippmann-Schwinger approach for accurate photoelectron wave functions and angle-resolved photoemission spectra from first principles, Phys. Rev. Lett. 135, 056403 (2025).
- G. Stefanucci and R. van Leeuwen, Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction, 2nd ed. (Cambridge University Press, Cambridge, England, 2025).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/zhs1-rv1k for finite excitation-density corrections, Lehmann approach, HSEX self-energy, TX self-energy, and numerical details, which includes Ref. [53].
- A. Rustagi and A. F. Kemper, Coherent excitonic quantum beats in time-resolved photoemission measurements, Phys. Rev. B 99, 125303 (2019).
- A. Thränhardt, S. Kuckenburg, A. Knorr, T. Meier, and S. W. Koch, Quantum theory of phonon-assisted exciton formation and luminescence in semiconductor quantum wells, Phys. Rev. B 62, 2706 (2000).
- S. Brem, M. Selig, G. Berghaeuser, and E. Malic, Exciton relaxation cascade in two-dimensional transition metal dichalcogenides, Sci. Rep. 8, 8238 (2018).
- Z. Zhang, W. Hu, E. Perfetto, and G. Stefanucci, Long-lived coherence between incoherent excitons revealed by time-resolved angle-resolved photoemission spectroscopy: An exact solution, Phys. Rev. B 111, 235124 (2025).
- H.-Y. Chen, D. Sangalli, and M. Bernardi, First-principles ultrafast exciton dynamics and time-domain spectroscopies: Dark-exciton mediated valley depolarization in monolayer , Phys. Rev. Res. 4, 043203 (2022).
- D. Kremp, W. Kraeft, and A. Lambert, Equation of state and ionization equilibrium for nonideal plasmas, Physica (Amsterdam) 127A, 72 (1984).
- D. Semkat, F. Richter, D. Kremp, G. Manzke, W.-D. Kraeft, and K. Henneberger, Ionization equilibrium in an excited semiconductor: Mott transition versus Bose-Einstein condensation, Phys. Rev. B 80, 155201 (2009).
- G. Strinati, Application of the Green’s functions method to the study of the optical properties of semiconductors, Riv. Nuovo Cimento 11, 1 (1988).
A tiny difference may arise from the polaronic-like shift of the exciton energy in the incoherent regime, see Ref. [28].
- K.-Q. Lin, C. S. Ong, S. Bange, P. E. Faria Junior, B. Peng, J. D. Ziegler, J. Zipfel, C. Bäuml, N. Paradiso, K. Watanabe, T. Taniguchi, C. Strunk, B. Monserrat, J. Fabian, A. Chernikov, D. Y. Qiu, S. G. Louie, and J. M. Lupton, Narrow-band high-lying excitons with negative-mass electrons in monolayer WSe2, Nat. Commun. 12, 5500 (2021).
- T. Deilmann and K. S. Thygesen, Finite-momentum exciton landscape in mono- and bilayer transition metal dichalcogenides, 2D Mater. 6, 035003 (2019).
- M. S. Foster, V. Gurarie, M. Dzero, and E. A. Yuzbashyan, Quench-induced Floquet topological -wave superfluids, Phys. Rev. Lett. 113, 076403 (2014).