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  • Letter
  • Open Access

Kohn-Sham-Proca equations for ultrafast exciton dynamics

J. K. Dewhurst

D. Gill and S. Shallcross

S. Sharma*

  • *Contact author: sharma@mbi-berlin.de
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Phys. Rev. B 111, L060302 – Published 6 February, 2025

DOI: https://doi.org/10.1103/PhysRevB.111.L060302

Abstract

A longstanding problem in time-dependent density functional theory has been the absence of a functional able to capture excitonic physics under laser pump conditions. Here we introduce a scheme of coupled Kohn-Sham and Proca equations in a pump-probe setup that we show (i) produces linear-response excitonic effects in the weak pump regime in excellent agreement with experiment, but also (ii) captures excitonic physics in the highly nonlinear regime of ultrafast strong laser pumping. In particular ”bleaching” (i.e., reduction) of the excitonic weight and the appearance of excitonic side bands is demonstrated. The approach is a procedural functional—the Kohn-Sham and Proca equations are simultaneously time propagated—allowing the straightforward inclusion of, for example, lattice and spin degrees of freedom into excitonic physics. The functional is shown to have universal applicability to a wide range of materials, and we also establish a relation between the parameters used in the functional and the exciton Bohr radii of the materials.

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References (55)

  1. I. Zutić, J. Fabian, and S. D. Sarma, Spintronics: Fundamentals and applications, Rev. Mod. Phys. 76, 323 (2004).
  2. J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, Valleytronics in 2D materials, Nat. Rev. Mater. 1, 16055 (2016).
  3. A. Melnikov, I. Razdolski, T. O. Wehling, E. T. Papaioannou, V. Roddatis, P. Fumagalli, O. Aktsipetrov, A. I. Lichtenstein, and U. Bovensiepen, Ultrafast transport of laser-excited spin-polarized carriers in Au/Fe/MgO (001), Phys. Rev. Lett. 107, 076601 (2011).
  4. S.-Y. Chen, T. Goldstein, J. Tong, T. Taniguchi, K. Watanabe, and J. Yan, Superior valley polarization and coherence of 2s excitons in monolayer WSe2, Phys. Rev. Lett. 120, 046402 (2018).
  5. E. J. Sie, A. Steinhoff, C. Gies, C. H. Lui, Q. Ma, M. Rosner, G. Schönhoff, F. Jahnke, T. O. Wehling, Y.-H. Lee et al., Observation of exciton redshift-blueshift crossover in monolayer WS2, Nano Lett. 17, 4210 (2017).
  6. H. Ouyang, H. Chen, Y. Tang, J. Zhang, C. Zhang, B. Zhang, X. Cheng, and T. Jiang, All-optical dynamic tuning of local excitonic emission of monolayer MoS2 by integration with Ge2Sb2Te5, Nanophotonics 9, 2351 (2020).
  7. Y. Kobayashi, C. Heide, A. C. Johnson, V. Tiwari, F. Liu, D. A. Reis, T. F. Heinz, and S. Ghimire, Floquet engineering of strongly driven excitons in monolayer tungsten disulfide, Nat. Phys. 19, 171 (2023).
  8. E. Runge and E. K. U. Gross, Density-functional theory for time-dependent systems, Phys. Rev. Lett. 52, 997 (1984).
  9. K. Krieger, J. K. Dewhurst, P. Elliott, S. Sharma, and E. K. U. Gross, Laser-induced demagnetization at ultrashort time scales: Predictions of TDDFT, J. Chem. Theory Comput. 11, 4870 (2015).
  10. J. K. Dewhurst, P. Elliott, S. Shallcross, E. K. Gross, and S. Sharma, Laser-induced intersite spin transfer, Nano Lett. 18, 1842 (2018).
  11. F. Siegrist, J. A. Gessner, M. Ossiander, C. Denker, Y. P. Chang, M. C. Schroder, A. Guggenmos, Y. Cui, J. Walowski, U. Martens, J. K. Dewhurst, U. Kleineberg, M. Münzenberg, S. Sharma, and M. Schultze, Light-wave dynamic control of magnetism, Nature (London) 571, 240 (2019).
  12. S. Sharma, P. Elliott, and S. Shallcross, THz induced giant spin and valley currents, Sci. Adv. 9, eadf3673 (2023).
  13. S. Sharma, P. Elliott, and S. Shallcross, Valley control by linearly polarized laser pulses: Example of WSe2, Optica 9, 947 (2022).
  14. M. Hofherr, S. Häuser, J. Dewhurst, P. Tengdin, S. Sakshath, H. Nembach, S. Weber, J. Shaw, T. J. Silva, H. Kapteyn et al., Ultrafast optically induced spin transfer in ferromagnetic alloys, Sci. Adv. 6, eaay8717 (2020).
  15. M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. Borja, D. Prendergast, K. Yabana et al., Attosecond band-gap dynamics in silicon, Science 346, 1348 (2014).
  16. 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 WSe2, Phys. Rev. Lett. 117, 277201 (2016).
  17. F. Sottile, V. Olevano, and L. Reining, Parameter-free calculation of response functions in time-dependent density-functional theory, Phys. Rev. Lett. 91, 056402 (2003).
  18. L. Reining, V. Olevano, A. Rubio, and G. Onida, Excitonic effects in solids described by time-dependent density-functional theory, Phys. Rev. Lett. 88, 066404 (2002).
  19. S. Botti, F. Sottile, N. Vast, V. Olevano, L. Reining, H.-C. Weissker, A. Rubio, G. Onida, R. Del Sole, and R. W. Godby, Long-range contribution to the exchange-correlation kernel of time-dependent density functional theory, Phys. Rev. B 69, 155112 (2004).
  20. S. Sharma, J. K. Dewhurst, A. Sanna, and E. K. U. Gross, Bootstrap approximation for the exchange-correlation kernel of time-dependent density-functional theory, Phys. Rev. Lett. 107, 186401 (2011).
  21. G. Onida, L. Reining, and A. Rubio, Electronic excitations: Density-functional versus many-body Green's-function approaches, Rev. Mod. Phys. 74, 601 (2002).
  22. P. Ghosez, X. Gonze, and R. W. Godby, Long-wavelength behavior of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems, Phys. Rev. B 56, 12811 (1997).
  23. S. Sharma, J. K. Dewhurst, and E. K. U. Gross, Optical response of extended systems using time-dependent density functional theory, First principles approaches to spectroscopic properties of complex materials, edited by C. Di Valentin, S. Botti, and M. Cococcioni (Springer, Berlin, Heidelberg, 2014), pp. 235–257.
  24. G. Vignale and M. Rasolt, Current-and spin-density-functional theory for inhomogeneous electronic systems in strong magnetic fields, Phys. Rev. B 37, 10685 (1988).
  25. P. Romaniello and P. L. de Boeij, Time-dependent current-density-functional theory for the metallic response of solids, Phys. Rev. B 71, 155108 (2005).
  26. 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).
  27. K. Yabana, T. Sugiyama, Y. Shinohara, T. Otobe, and G. F. Bertsch, Time-dependent density functional theory for strong electromagnetic fields in crystalline solids, Phys. Rev. B 85, 045134 (2012).
  28. K. Yabana, T. Nakatsukasa, J.-I. Iwata, and G. Bertsch, Real-time, real-space implementation of the linear response time-dependent density-functional theory, Physica Status Solidi (B) 243, 1121 (2006).
  29. K. Yabana and G. F. Bertsch, Time-dependent local-density approximation in real time, Phys. Rev. B 54, 4484 (1996).
  30. D. J. Singh, Planewaves Pseudopotentials and the LAPW Method (Kluwer Academic, Boston, 1994).
  31. J. K. Dewhurst, S. Sharma et al., elk.sourceforge.net.
  32. J. K. Dewhurst, K. Krieger, S. Sharma, and E. K. U. Gross, An efficient algorithm for time propagation as applied to linearized augmented plane wave method, Comput. Phys. Commun. 209, 92 (2016).
  33. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.111.L060302 for the table of the values of a0 and a2 for all studied materials. Results for Si and LiF obtained using the GGA functional and the effect of local fields are also presented. LiCl data are shown in a larger energy window.
  34. D. Roessler and W. Walker, Optical constants of magnesium oxide and lithium fluoride in the far ultraviolet, JOSA 57, 835 (1967).
  35. V. Saile, M. Skibowski, W. Steinmann, P. Gürtler, E. Koch, and A. Kozevnikov, Observation of surface excitons in rare-gas solids, Phys. Rev. Lett. 37, 305 (1976).
  36. G. Baldini, Ultraviolet absorption of solid argon, krypton, and xenon, Phys. Rev. 128, 1562 (1962).
  37. R. Knox and N. Inchauspé, Exciton states in ionic crystals, Phys. Rev. 116, 1093 (1959).
  38. P. Lautenschlager, M. Garriga, L. Vina, and M. Cardona, Temperature dependence of the dielectric function and interband critical points in silicon, Phys. Rev. B 36, 4821 (1987).
  39. P. Lautenschlager, M. Garriga, S. Logothetidis, and M. Cardona, Interband critical points of GaAs and their temperature dependence, Phys. Rev. B 35, 9174 (1987).
  40. M. Garriga, M. Kelly, and K. Ploog, Temperature dependence of the dielectric function and interband critical points of AlAs obtained on an MBe grown layer, Thin Solid Films 233, 122 (1993).
  41. H. Phillip and E. Taft, Kramers-Kronig analysis of reflectance data for diamond, Phys. Rev. 136, A1445 (1964).
  42. V. Cimalla, V. Lebedev, U. Kaiser, R. Goldhahn, C. Foerster, J. Pezoldt, and O. Ambacher, Polytype control and properties of ALn on silicon, Phys. Status Solidi (C) 2, 2199 (2005).
  43. J. Sanmartín-Matalobos, P. Bermejo-Barrera, M. Aboal-Somoza, M. Fondo, A. M. García-Deibe, J. Corredoira-Vázquez, and Y. Alves-Iglesias, Semiconductor quantum dots as target analytes: Properties, surface chemistry and detection, Nanomaterials 12, 2501 (2022).
  44. P. Puschnig and C. Ambrosch-Draxl, Optical absorption spectra of semiconductors and insulators including electron-hole correlations: An ab initio study within the LAPW method, Phys. Rev. B 66, 165105 (2002).
  45. M. Shahrokhi and B. Mortazavi, Lithium halide monolayer sheets: First-principles many-body calculations, Comput. Mater. Sci. 143, 103 (2018).
  46. H. Okushi, H. Watanabe, and S. Kanno, Characteristics of excitonic emission in diamond, Phys. Status Solidi (A) 202, 2051 (2005).
  47. F. Bechstedt, K. Seino, P. H. Hahn, and W. G. Schmidt, Quasiparticle bands and optical spectra of highly ionic crystals: AIN and NaCl, Phys. Rev. B 72, 245114 (2005).
  48. F. Sottile, M. Marsili, V. Olevano, and L. Reining, Efficient ab initio calculations of bound and continuum excitons in the absorption spectra of semiconductors and insulators, Phys. Rev. B 76, 161103(R) (2007).
  49. A. Marini, R. Del Sole, and A. Rubio, Bound excitons in time-dependent density-functional theory: Optical and energy-loss spectra, Phys. Rev. Lett. 91, 256402 (2003).
  50. D. Sangalli, S. Dal Conte, C. Manzoni, G. Cerullo, and A. Marini, Nonequilibrium optical properties in semiconductors from first principles: A combined theoretical and experimental study of bulk silicon, Phys. Rev. B 93, 195205 (2016).
  51. 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 MoS2, ACS Nano 8, 10931 (2014).
  52. C. Mai, A. Barrette, Y. Yu, Y. G. Semenov, K. W. Kim, L. Cao, and K. Gundogdu, Many-body effects in valleytronics: Direct measurement of valley lifetimes in single-layer MoS2, Nano Lett. 14, 202 (2014).
  53. V. Smejkal, F. Libisch, A. Molina-Sanchez, C. Trovatello, L. Wirtz, and A. Marini, Time-dependent screening explains the ultrafast excitonic signal rise in 2D semiconductors, ACS Nano 15, 1179 (2021).
  54. M. Lucchini, S. A. Sato, G. D. Lucarelli, B. Moio, G. Inzani, R. Borrego-Varillas, F. Frassetto, L. Poletto, H. Hübener, U. De Giovannini et al., Unravelling the intertwined atomic and bulk nature of localised excitons by attosecond spectroscopy, Nat. Commun. 12, 1021 (2021).
  55. S. Sim, J. Park, J.-G. Song, C. In, Y.-S. Lee, H. Kim, and H. Choi, Exciton dynamics in atomically thin MoS2: Interexcitonic interaction and broadening kinetics, Phys. Rev. B 88, 075434 (2013).

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Phys. Rev. B 111, L060302– Published 6 February, 2025
  • Received 30 January 2024
  • Accepted 17 January 2025
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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.

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