- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Real-time exciton dynamics in two-dimensional materials under ultrashort laser pulses

Dmitry Tumakov1,2,* and Daria Popova-Gorelova2,3,†

  • *Contact author: dm.tumakov@gmail.com
  • †Contact author: daria.gorelova@b-tu.de
PDF

Phys. Rev. B 114, 045127 – Published 27 July, 2026

DOI: https://doi.org/10.1103/ppgw-myxb

Abstract

The optical response of two-dimensional materials is often significantly impacted by excitonic effects due to the reduced screening of attractive Coulomb interactions in low-dimensional systems. Accurate modeling of exciton formation and real-time dynamics is essential to understanding their ultrafast optical properties. In this study, we theoretically investigate the exciton dynamics in a two-dimensional hexagonal boron nitride (h-BN) and a germanium sulfide (GeS) monolayers exposed to an ultrashort laser pulse. We analyze the system's response to the external field in one- and two-photon excitation regimes. For our calculations, we combine a state-of-the-art ab initio approach to study exciton dynamics with a highly precise numerical scheme. We incorporate electron-hole interactions through a nonlocal self-energy operator derived from the many-body perturbation theory (MBPT) within the time-dependent adiabatic GW(TD−aGW) approximation. We implement this approach using the full-electron LAPW+lo method in the all-electron exciting package. Our results elucidate the role of many-body effects in shaping ultrafast excitonic processes in two-dimensional materials, contributing to the fundamental understanding necessary for optoelectronic and photonic applications.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (77)

  1. N. Huang, H. Deng, B. Liu, D. Wang, and Z. Zhao, Features and futures of x-ray free-electron lasers, The Innovation 2, 100097 (2021).
  2. A. Zong, B. R. Nebgen, S.-C. Lin, J. A. Spies, and M. Zuerch, Emerging ultrafast techniques for studying quantum materials, Nat. Rev. Mater. 8, 224 (2023).
  3. M. Chergui, M. Beye, S. Mukamel, C. Svetina, and C. Masciovecchio, Progress and prospects in nonlinear extreme-ultraviolet and x-ray optics and spectroscopy, Nat. Rev. Phys. 5, 578 (2023).
  4. S. M. Cavaletto, K. M. Kowalczyk, F. O. Navarrete, and J. Rivera-Dean, The attoscience of strong-field-driven solids, Nat. Rev. Phys. 738 (2024).
  5. G. Wang, A. Chernikov, M. M. Glazov, T. F. Heinz, X. Marie, T. Amand, and B. Urbaszek, Colloquium: Excitons in atomically thin transition metal dichalcogenides, Rev. Mod. Phys. 90, 021001 (2018).
  6. A. Stolow, A. E. Bragg, and D. M. Neumark, Femtosecond time-resolved photoelectron spectroscopy, Chem. Rev. 104, 1719 (2004).
  7. S. Ghimire and D. A. Reis, High-harmonic generation from solids, Nat. Phys. 15, 10 (2019).
  8. E. B. Molinero, B. Amorim, M. Malakhov, G. Cistaro, Á. Jiménez-Galán, A. Picón, P. San-José, M. Ivanov, and R. E. Silva, Subcycle dynamics of excitons under strong laser fields, Sci. Adv. 10, eadn6985 (2024).
  9. C. Attaccalite, M. Grüning, and A. Marini, Real-time approach to the optical properties of solids and nanostructures: Time-dependent Bethe-Salpeter equation, Phys. Rev. B 84, 245110 (2011).
  10. G. Stefanucci and R. Van Leeuwen, Nonequilibrium many-body theory of quantum systems: A modern introduction (Cambridge University Press, 2013).
  11. E. Perfetto, D. Sangalli, A. Marini, and G. Stefanucci, Nonequilibrium Bethe-Salpeter equation for transient photoabsorption spectroscopy, Phys. Rev. B 92, 205304 (2015).
  12. E. Perfetto, D. Sangalli, M. Palummo, A. Marini, and G. Stefanucci, First-principles nonequilibrium Green's function approach to ultrafast charge migration in glycine, J. Chem. Theory Comput. 15, 4526 (2019).
  13. E. Ridolfi, P. E. Trevisanutto, and V. M. Pereira, Expeditious computation of nonlinear optical properties of arbitrary order with native electronic interactions in the time domain, Phys. Rev. B 102, 245110 (2020).
  14. Y.-H. Chan, D. Y. Qiu, F. H. da Jornada, and S. G. Louie, Giant exciton-enhanced shift currents and direct current conduction with subbandgap photo excitations produced by many-electron interactions, Proc. Natl. Acad. Sci. USA 118, e1906938118 (2021).
  15. D. Sangalli, Excitons and carriers in transient absorption and time-resolved ARPES spectroscopy: An ab initio approach, Phys. Rev. Mater. 5, 083803 (2021).
  16. E. Perfetto, Y. Pavlyukh, and G. Stefanucci, Real-time GW: Toward an ab initio description of the ultrafast carrier and exciton dynamics in two-dimensional materials, Phys. Rev. Lett. 128, 016801 (2022).
  17. B. Hou, J. Wu, V. Chang Lee, J. Guo, L. Y. Liu, and D. Y. Qiu, Data-driven low-rank approximation for the electron-hole kernel and acceleration of time-dependent GW calculations, npj Comput. Mater. 11, 204 (2025).
  18. S. Marek and J. Wilhelm, Linear and nonlinear optical properties of molecules from real-time propagation based on the Bethe–Salpeter equation, J. Chem. Theory Comput. 21, 9814 (2025).
  19. T. Sander and G. Kresse, Macroscopic dielectric function within time-dependent density functional theory—Real time evolution versus the Casida approach, J. Chem. Phys. 146, 064110 (2017).
  20. C. D. Pemmaraju, Simulation of attosecond transient soft x-ray absorption in solids using generalized Kohn–Sham real-time time-dependent density functional theory, New J. Phys. 22, 083063 (2020).
  21. J. Sun, C.-W. Lee, A. Kononov, A. Schleife, and C. A. Ullrich, Real-time exciton dynamics with time-dependent density-functional theory, Phys. Rev. Lett. 127, 077401 (2021).
  22. J. R. Williams, N. Tancogne-Dejean, and C. A. Ullrich, Time-resolved exciton wave functions from time-dependent density-functional theory, J. Chem. Theory Comput. 17, 1795 (2021).
  23. X. Jiang, Q. Zheng, Z. Lan, W. A. Saidi, X. Ren, and J. Zhao, Real-time GW-BSE investigations on spin-valley exciton dynamics in monolayer transition metal dichalcogenide, Sci. Adv. 7, eabf3759 (2021).
  24. G. Cistaro, M. Malakhov, J. J. Esteve-Paredes, A. J. Uría-Álvarez, R. E. Silva, F. Martín, J. J. Palacios, and A. Picón, Theoretical approach for electron dynamics and ultrafast spectroscopy (EDUS), J. Chem. Theory Comput. 19, 333 (2023).
  25. M. Malakhov, G. Cistaro, F. Martín, and A. Picón, Exciton migration in two-dimensional materials, Commun. Phys. 7, 196 (2024).
  26. S. V. B. Jensen, L. B. Madsen, A. Rubio, and N. Tancogne-Dejean, High-harmonic spectroscopy of strongly bound excitons in solids, Phys. Rev. A 109, 063104 (2024).
  27. A. Riefer and W. G. Schmidt, Solving the Bethe-Salpeter equation for the second-harmonic generation in Zn chalcogenides, Phys. Rev. B 96, 235206 (2017).
  28. C. Vorwerk, F. Sottile, and C. Draxl, Excitation pathways in resonant inelastic x-ray scattering of solids, Phys. Rev. Res. 2, 042003 (2020).
  29. D. Sangalli, M. d'Alessandro, and C. Attaccalite, Exciton-exciton transitions involving strongly bound excitons: An ab initio approach, Phys. Rev. B 107, 205203 (2023).
  30. N. Farahani and D. Popova-Gorelova, Revealing fingerprints of valence excitons in x-ray absorption spectra with the Bethe-Salpeter equation, Phys. Rev. B 110, 235126 (2024).
  31. J. Ruan, Y.-H. Chan, and S. G. Louie, Exciton enhanced nonlinear optical responses in monolayer h-BN and MoS2: Insight from first-principles exciton-state coupling formalism and calculations, Nano Lett. 24, 15533 (2024).
  32. C. Attaccalite and M. Grüning, Nonlinear optics from an ab initio approach by means of the dynamical Berry phase: Application to second- and third-harmonic generation in semiconductors, Phys. Rev. B 88, 235113 (2013).
  33. I. Souza, J. Íniguez, and D. Vanderbilt, Dynamics of Berry-phase polarization in time-dependent electric fields, Phys. Rev. B 69, 085106 (2004).
  34. R. King-Smith and D. Vanderbilt, Theory of polarization of crystalline solids, Phys. Rev. B 47, 1651 (1993).
  35. R. Resta, Macroscopic polarization in crystalline dielectrics: The geometric phase approach, Rev. Mod. Phys. 66, 899 (1994).
  36. M. N. Pionteck, M. Grüning, S. Sanna, and C. Attaccalite, A real-time approach to frequency-mixing spectroscopies: Application to sum and difference frequency generation in two-dimensional crystals, SciPost Phys. 19, 129 (2025).
  37. M. Grüning and C. Attaccalite, Second harmonic generation in h-BN and MoS2 monolayers: Role of electron-hole interaction, Phys. Rev. B 89, 081102 (2014).
  38. C. Attaccalite, E. Cannuccia, and M. Grüning, Excitonic effects in third-harmonic generation: The case of carbon nanotubes and nanoribbons, Phys. Rev. B 95, 125403 (2017).
  39. C. Attaccalite, M. Grüning, H. Amara, S. Latil, and F. m. c. Ducastelle, Two-photon absorption in two-dimensional materials: The case of hexagonal boron nitride, Phys. Rev. B 98, 165126 (2018).
  40. A. Marini, C. Hogan, M. Grüning, and D. Varsano, Yambo: An ab initio tool for excited state calculations, Comput. Phys. Commun. 180, 1392 (2009).
  41. D. Sangalli, A. Ferretti, H. Miranda, C. Attaccalite, I. Marri, E. Cannuccia, P. Melo, M. Marsili, F. Paleari, A. Marrazzo, et al., Many-body perturbation theory calculations using the Yambo code, J. Phys.: Condens. Matter 31, 325902 (2019).
  42. A. Gulans, S. Kontur, C. Meisenbichler, D. Nabok, P. Pavone, S. Rigamonti, S. Sagmeister, U. Werner, and C. Draxl, Exciting: A full-potential all-electron package implementing density-functional theory and many-body perturbation theory, J. Phys.: Condens. Matter 26, 363202 (2014).
  43. R. R. Pela and C. Draxl, All-electron full-potential implementation of real-time TDDFT in exciting, Electron. Struct. 3, 037001 (2021).
  44. M. Raya-Moreno, A. Buccheri, N. A. Dasch, N. Farahani, I. G. Oliva, A. Gulans, S. Hong, M. Hossain, H. Kleine, M. Kuban, S. Lubeck, B. Maurer, P. Pavone, F. Peschel, D. Popova-Gorelova, L. Qiao, E. Richter, S. Rigamonti, R. Rodrigues Pela, M. Schebek, K. Sinha, D. T. Speckhard, J. Stutz, S. Tillack, D. Tumakov, J. Uûulis, M. Voiculescu, C. Vona, M. Yang, C. Draxl, et al., An exciting approach to theoretical spectroscopy Adv. Sci. e76167 (2026).
  45. Z. Liu, L. Ma, G. Shi, W. Zhou, Y. Gong, S. Lei, X. Yang, J. Zhang, J. Yu, K. P. Hackenberg, et al., In-plane heterostructures of graphene and hexagonal boron nitride with controlled domain sizes, Nat. Nanotechnol. 8, 119 (2013).
  46. K. Ba, W. Jiang, J. Cheng, J. Bao, N. Xuan, Y. Sun, B. Liu, A. Xie, S. Wu, and Z. Sun, Chemical and bandgap engineering in monolayer hexagonal boron nitride, Sci. Rep. 7, 45584 (2017).
  47. C. Elias, P. Valvin, T. Pelini, A. Summerfield, C. Mellor, T. Cheng, L. Eaves, C. Foxon, P. Beton, S. Novikov, et al., Direct band-gap crossover in epitaxial monolayer boron nitride, Nat. Commun. 10, 2639 (2019).
  48. R. J. P. Román, F. J. C. Costa, A. Zobelli, C. Elias, P. Valvin, G. Cassabois, B. Gil, A. Summerfield, T. S. Cheng, C. J. Mellor, et al., Band gap measurements of monolayer h-BN and insights into carbon-related point defects, 2D Mater. 8, 044001 (2021).
  49. G. Cassabois, P. Valvin, and B. Gil, Hexagonal boron nitride is an indirect bandgap semiconductor, Nat. Photonics 10, 262 (2016).
  50. T. Galvani, F. Paleari, H. P. C. Miranda, A. Molina-Sánchez, L. Wirtz, S. Latil, H. Amara, and F. m. c. Ducastelle, Excitons in boron nitride single layer, Phys. Rev. B 94, 125303 (2016).
  51. R. Roldán, L. Chirolli, E. Prada, J. A. Silva-Guillén, P. San-Jose, and F. Guinea, Theory of 2D crystals: Graphene and beyond, Chem. Soc. Rev. 46, 4387 (2017).
  52. D. Wickramaratne, L. Weston, and C. G. Van de Walle, Monolayer to bulk properties of hexagonal boron nitride, J. Phys. Chem. C 122, 25524 (2018).
  53. F. Ferreira, A. Chaves, N. Peres, and R. Ribeiro, Excitons in hexagonal boron nitride single-layer: A new platform for polaritonics in the ultraviolet, J. Opt. Soc. Am. B 36, 674 (2019).
  54. S. Roy, X. Zhang, A. B. Puthirath, A. Meiyazhagan, S. Bhattacharyya, M. M. Rahman, G. Babu, S. Susarla, S. K. Saju, M. K. Tran, L. M. Sassi, M. A. S. R. Saadi, J. Lai, O. Sahin, S. M. Sajadi, B. Dharmarajan, D. Salpekar, N. Chakingal, A. Baburaj, X. Shuai, et al., Structure, properties and applications of two-dimensional hexagonal boron nitride, Adv. Mater. 33, 2101589 (2021).
  55. A. Rousseau, L. Ren, A. Durand, P. Valvin, B. Gil, K. Watanabe, T. Taniguchi, B. Urbaszek, X. Marie, C. Robert, et al., Monolayer boron nitride: Hyperspectral imaging in the deep ultraviolet, Nano Lett. 21, 10133 (2021).
  56. A. Kirchhoff, T. Deilmann, P. Krüger, and M. Rohlfing, Electronic and optical properties of a hexagonal boron nitride monolayer in its pristine form and with point defects from first principles, Phys. Rev. B 106, 045118 (2022).
  57. F. Zhang, C. S. Ong, J. W. Ruan, M. Wu, X. Q. Shi, Z. K. Tang, and S. G. Louie, Intervalley excitonic hybridization, optical selection rules, and imperfect circular dichroism in monolayer h−BN, Phys. Rev. Lett. 128, 047402 (2022).
  58. F. Li, X. Liu, Y. Wang, and Y. Li, Germanium monosulfide monolayer: A novel two-dimensional semiconductor with a high carrier mobility, J. Mater. Chem. C 4, 2155 (2016).
  59. V. Khuong Dien, P. Thi Bich Thao, N. Thi Han, N. Duy Khanh, L. V. Phuong Thuan, M.-F. Lin, and N. Thanh Tien, Strain-controlled electronic transport and exciton radiative lifetime in monolayer germanium sulfide, Phys. Rev. B 108, 205406 (2023).
  60. J. Esteve-Paredes, M. García-Blázquez, A. Uría-Álvarez, M. Camarasa-Gómez, and J. Palacios, Excitons in nonlinear optical responses: Shift current in MoS2 and GeS monolayers, npj Comput. Mater. 11, 13 (2025).
  61. D. A. Wheeler and J. Z. Zhang, Exciton dynamics in semiconductor nanocrystals, Adv. Mater. 25, 2878 (2013).
  62. S. L. Adler, Quantum theory of the dielectric constant in real solids, Phys. Rev. 126, 413 (1962).
  63. G. A. Baraff and M. Schlüter, Migration of interstitials in silicon, Phys. Rev. B 30, 3460 (1984).
  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).
  65. L. Hedin, New method for calculating the one-particle Green's function with application to the electron-gas problem, Phys. Rev. 139, A796 (1965).
  66. M. S. Hybertsen and S. G. Louie, Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies, Phys. Rev. B 34, 5390 (1986).
  67. G. Strinati, Application of the green's functions method to the study of the optical properties of semiconductors, Riv. Nuovo Cim. 11, 1 (1988).
  68. D. Sangalli, J. A. Berger, C. Attaccalite, M. Grüning, and P. Romaniello, Optical properties of periodic systems within the current-current response framework: Pitfalls and remedies, Phys. Rev. B 95, 155203 (2017).
  69. M. Springborg and B. Kirtman, Analysis of vector potential approach for calculating linear and nonlinear responses of infinite periodic systems to a finite static external electric field, Phys. Rev. B 77, 045102 (2008).
  70. I. Souza, J. Íniguez, and D. Vanderbilt, First-principles approach to insulators in finite electric fields, Phys. Rev. Lett. 89, 117602 (2002).
  71. D. Snoke, Predicting the ionization threshold for carriers in excited semiconductors, Solid State Commun. 146, 73 (2008).
  72. E. Perfetto, A. Marini, and G. Stefanucci, Self-consistent screening enhances the stability of the nonequilibrium excitonic insulator phase, Phys. Rev. B 102, 085203 (2020).
  73. R. W. Nunes and X. Gonze, Berry-phase treatment of the homogeneous electric field perturbation in insulators, Phys. Rev. B 63, 155107 (2001).
  74. C. Vorwerk, B. Aurich, C. Cocchi, and C. Draxl, Bethe–Salpeter equation for absorption and scattering spectroscopy: Implementation in the exciting code, Electron. Struct. 1, 037001 (2019).
  75. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
  76. F. Paleari, T. Galvani, H. Amara, F. Ducastelle, A. Molina-Sánchez, and L. Wirtz, Excitons in few-layer hexagonal boron nitride: Davydov splitting and surface localization, 2D Mater. 5, 045017 (2018).
  77. M. S. Dresselhaus, G. Dresselhaus, and A. Jorio, Group theory: Application to the physics of condensed matter (Springer Science & Business Media, 2007).

Outline

Information

Phys. Rev. B 114, 045127– Published 27 July, 2026
  • Received 9 March 2026
  • Revised 9 June 2026
  • Accepted 8 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation