journal article·2025-07-15Open access

Technical review: Time-dependent density functional theory for attosecond physics ranging from gas-phase to solids

Shunsuke A. Sato, Hannes Hübener, Umberto De Giovannini, Angel Rubio

npj Computational Materials· Volume 11· Issue 1

Abstract

Abstract First-principles electron dynamics calculations can be applied in the investigation of a wide range of ultrafast phenomena in attosecond physics. They offer unique microscopic insight into light-induced ultrafast phenomena in both gas and condensed phases of matter, and thus, they are a powerful tool to develop our understanding of the physics of attosecond phenomena. We specifically review techniques employing time-dependent density functional theory (TDDFT) for investigating attosecond and strong-field phenomena. First, we describe this theoretical framework that enables the modeling of perturbative and non-perturbative electron dynamics in materials, including atoms, molecules, and solids. We then discuss its application to attosecond experiments, focusing on the reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) measurements. We also briefly review first-principles calculations of optical properties of solids with TDDFT in the linear response regime and their extension to calculations of transient optical properties of solids in non-equilibrium phases, by simulating experimental pump-probe setups. We further demonstrate the application of TDDFT simulation to high-order harmonic generation in solids. First-principles calculations have predictive power, and hence they can be utilized to design future experiments to explore non-equilibrium and nonlinear ultrafast phenomena in matter and characterize and control metastable light-induced quantum states.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Laser-Matter Interactions and Applications · Advanced Chemical Physics Studies · Spectroscopy and Quantum Chemical Studies

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (100+)

Show source-provided references
1. Schawlow, A. L. & Townes, C. H. Infrared and optical masers. Phys. Rev. 112, 1940–1949 (1958).10.1103/PhysRev.112.1940 ↗
2. Franken, P. A., Hill, A. E., Peters, C. W. & Weinreich, G. Generation of optical harmonics. Phys. Rev. Lett. 7, 118–119 (1961).10.1103/PhysRevLett.7.118 ↗
3. Mourou, G. et al. Exawatt-zettawatt pulse generation and applications. Opt. Commun. 285, 720–724 (2012).10.1016/j.optcom.2011.10.089 ↗
4. Brabec, T. & Krausz, F. Intense few-cycle laser fields: Frontiers of nonlinear optics. Rev. Mod. Phys. 72, 545–591 (2000).10.1103/RevModPhys.72.545 ↗
5. Strickland, D. & Mourou, G. Compression of amplified chirped optical pulses. Opt. Commun. 56, 219–221 (1985).10.1016/0030-4018(85)90120-8 ↗
6. McPherson, A. et al. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases. J. Opt. Soc. Am. B 4, 595–601 (1987).10.1364/JOSAB.4.000595 ↗
7. Ferray, M. et al. Multiple-harmonic conversion of 1064 nm radiation in rare gases. J. Phys. B: At. Mol. Opt. Phys. 21, L31 (1988).10.1088/0953-4075/21/3/001 ↗
8. Corkum, P. B. Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71, 1994–1997 (1993).10.1103/PhysRevLett.71.1994 ↗
9. Lewenstein, M., Balcou, P., Ivanov, M. Y., L’Huillier, A. & Corkum, P. B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132 (1994).10.1103/PhysRevA.49.2117 ↗
10. Krausz, F. & Ivanov, M. Attosecond physics. Rev. Mod. Phys. 81, 163–234 (2009).10.1103/RevModPhys.81.163 ↗
11. Paul, P. M. et al. Observation of a train of attosecond pulses from high harmonic generation. Science 292, 1689–1692 (2001).10.1126/science.1059413 ↗
12. Hentschel, M. et al. Attosecond metrology. Nature 414, 509–513 (2001).10.1038/35107000 ↗
13. Borrego-Varillas, R., Lucchini, M. & Nisoli, M. Attosecond spectroscopy for the investigation of ultrafast dynamics in atomic, molecular and solid-state physics. Rep. Prog. Phys. 85, 066401 (2022).10.1088/1361-6633/ac5e7f ↗
14. Calegari, F. & Martin, F. Open questions in attochemistry. Commun. Chem. 6, 184 (2023).10.1038/s42004-023-00989-0 ↗
15. Eckle, P. et al. Attosecond ionization and tunneling delay time measurements in helium. Science 322, 1525–1529 (2008).10.1126/science.1163439 ↗
16. Schultze, M. et al. Delay in photoemission. Science 328, 1658–1662 (2010).10.1126/science.1189401 ↗
17. Isinger, M. et al. Photoionization in the time and frequency domain. Science 358, 893–896 (2017).10.1126/science.aao7043 ↗
18. Pazourek, R., Nagele, S. & Burgdörfer, J. Attosecond chronoscopy of photoemission. Rev. Mod. Phys. 87, 765–802 (2015).10.1103/RevModPhys.87.765 ↗
19. Sommer, A. et al. Attosecond nonlinear polarization and light–matter energy transfer in solids. Nature 534, 86–90 (2016).10.1038/nature17650 ↗
20. Lucchini, M. et al. Attosecond dynamical Franz-Keldysh effect in polycrystalline diamond. Science 353, 916–919 (2016).10.1126/science.aag1268 ↗
21. Buades, B. et al. Attosecond state-resolved carrier motion in quantum materials probed by soft x-ray XANES. Appl. Phys. Rev. 8, 011408 (2021).10.1063/5.0020649 ↗
22. Volkov, M. et al. Attosecond screening dynamics mediated by electron localization in transition metals. Nat. Phys. 15, 1145–1149 (2019).10.1038/s41567-019-0602-9 ↗
23. Lucchini, M. et al. Unravelling the intertwined atomic and bulk nature of localised excitons by attosecond spectroscopy. Nat. Commun. 12, 1021 (2021).10.1038/s41467-021-21345-7 ↗
24. Géneaux, R. et al. Attosecond time-domain measurement of core-level-exciton decay in magnesium oxide. Phys. Rev. Lett. 124, 207401 (2020).10.1103/PhysRevLett.124.207401 ↗
25. Zuo, T., Bandrauk, A. & Corkum, P. Laser-induced electron diffraction: a new tool for probing ultrafast molecular dynamics. Chem. Phys. Lett. 259, 313–320 (1996).10.1016/0009-2614(96)00786-5 ↗
26. Lein, M., Marangos, J. P. & Knight, P. L. Electron diffraction in above-threshold ionization of molecules. Phys. Rev. A 66, 051404 (2002).10.1103/PhysRevA.66.051404 ↗
27. Lin, C. D., Le, A.-T., Chen, Z., Morishita, T. & Lucchese, R. Strong-field rescattering physics—self-imaging of a molecule by its own electrons. J. Phys. B: At. Mol. Opt. Phys. 43, 122001 (2010).10.1088/0953-4075/43/12/122001 ↗
28. Pullen, M. G. et al. Imaging an aligned polyatomic molecule with laser-induced electron diffraction. Nat. Commun. 6, 7262 (2015).10.1038/ncomms8262 ↗
29. Lundh, O. et al. Few femtosecond, few kiloampere electron bunch produced by a laser–plasma accelerator. Nat. Phys. 7, 219–222 (2011).10.1038/nphys1872 ↗
30. Priebe, K. E. et al. Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy. Nat. Photonics 11, 793–797 (2017).10.1038/s41566-017-0045-8 ↗
31. Morimoto, Y. & Baum, P. Diffraction and microscopy with attosecond electron pulse trains. Nat. Phys. 14, 252–256 (2018).10.1038/s41567-017-0007-6 ↗
32. Morimoto, Y. & Baum, P. Single-cycle optical control of beam electrons. Phys. Rev. Lett. 125, 193202 (2020).10.1103/PhysRevLett.125.193202 ↗
33. Schiffrin, A. et al. Optical-field-induced current in dielectrics. Nature 493, 70–74 (2013).10.1038/nature11567 ↗
34. Krausz, F. & Stockman, M. I. Attosecond metrology: from electron capture to future signal processing. Nat. Photonics 8, 205–213 (2014).10.1038/nphoton.2014.28 ↗
35. Higuchi, T., Heide, C., Ullmann, K., Weber, H. B. & Hommelhoff, P. Light-field-driven currents in graphene. Nature 550, 224–228 (2017).10.1038/nature23900 ↗
36. Lee, J. D., Yun, W. S. & Park, N. Rectifying the optical-field-induced current in dielectrics: Petahertz diode. Phys. Rev. Lett. 116, 057401 (2016).10.1103/PhysRevLett.116.057401 ↗
37. Schoetz, J. et al. Perspective on petahertz electronics and attosecond nanoscopy. ACS Photonics 6, 3057–3069 (2019).10.1021/acsphotonics.9b01188 ↗
38. Boolakee, T. et al. Light-field control of real and virtual charge carriers. Nature 605, 251–255 (2022).10.1038/s41586-022-04565-9 ↗
39. Runge, E. & Gross, E. K. U. Density-functional theory for time-dependent systems. Phys. Rev. Lett. 52, 997–1000 (1984).10.1103/PhysRevLett.52.997 ↗
40. Yabana, K. & Bertsch, G. F. Time-dependent local-density approximation in real time. Phys. Rev. B 54, 4484–4487 (1996).10.1103/PhysRevB.54.4484 ↗
41. Bertsch, G. F., Iwata, J.-I., Rubio, A. & Yabana, K. Real-space, real-time method for the dielectric function. Phys. Rev. B 62, 7998–8002 (2000).10.1103/PhysRevB.62.7998 ↗
42. Otobe, T. et al. First-principles electron dynamics simulation for optical breakdown of dielectrics under an intense laser field. Phys. Rev. B 77, 165104 (2008).10.1103/PhysRevB.77.165104 ↗
43. Yabana, K., Sugiyama, T., Shinohara, Y., Otobe, T. & Bertsch, G. F. Time-dependent density functional theory for strong electromagnetic fields in crystalline solids. Phys. Rev. B 85, 045134 (2012).10.1103/PhysRevB.85.045134 ↗
44. Sato, S. A. et al. Time-dependent density functional theory of high-intensity short-pulse laser irradiation on insulators. Phys. Rev. B 92, 205413 (2015).10.1103/PhysRevB.92.205413 ↗
45. Andrea Rozzi, C. et al. Quantum coherence controls the charge separation in a prototypical artificial light-harvesting system. Nat. Commun. 4, 1602 (2013).10.1038/ncomms2603 ↗
46. Castro, A., Marques, M. A. L., Alonso, J. A., Bertsch, G. F. & Rubio, A. Excited states dynamics in time-dependent density functional theory. Eur. Phys. J. D. - At. Mol., Opt. Plasma Phys. 28, 211–218 (2004).
47. Sato, S. A., Hübener, H., Rubio, A. & De Giovannini, U. First-principles simulations for attosecond photoelectron spectroscopy based on time-dependent density functional theory. Eur. Phys. J. B 91, 126 (2018).10.1140/epjb/e2018-90108-7 ↗
48. Schultze, M. et al. Attosecond band-gap dynamics in silicon. Science 346, 1348–1352 (2014).10.1126/science.1260311 ↗
49. Zürch, M. et al. Direct and simultaneous observation of ultrafast electron and hole dynamics in germanium. Nat. Commun. 8, 15734 (2017).10.1038/ncomms15734 ↗
50. Siegrist, F. et al. Light-wave dynamic control of magnetism. Nature 571, 240–244 (2019).10.1038/s41586-019-1333-x ↗
51. Schumacher, Z. et al. Ultrafast electron localization and screening in a transition metal dichalcogenide. Proc. Natl Acad. Sci. 120, e2221725120 (2023).10.1073/pnas.2221725120 ↗
52. Sato, S. A. First-principles calculations for attosecond electron dynamics in solids. Comput. Mater. Sci. 194, 110274 (2021).10.1016/j.commatsci.2020.110274 ↗
53. Kleinman, L. & Bylander, D. M. Efficacious form for model pseudopotentials. Phys. Rev. Lett. 48, 1425–1428 (1982).10.1103/PhysRevLett.48.1425 ↗
54. Troullier, N. & Martins, J. L. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 43, 1993–2006 (1991).10.1103/PhysRevB.43.1993 ↗
55. Vignale, G. Mapping from current densities to vector potentials in time-dependent current density functional theory. Phys. Rev. B 70, 201102 (2004).10.1103/PhysRevB.70.201102 ↗
56. Klünder, K. et al. Probing single-photon ionization on the attosecond time scale. Phys. Rev. Lett. 106, 143002 (2011).10.1103/PhysRevLett.106.143002 ↗
57. Guénot, D. et al. Photoemission-time-delay measurements and calculations close to the 3s-ionization-cross-section minimum in Ar. Phys. Rev. A 85, 053424 (2012).10.1103/PhysRevA.85.053424 ↗
58. Tao, L. & Scrinzi, A. Photo-electron momentum spectra from minimal volumes: the time-dependent surface flux method. N. J. Phys. 14, 013021 (2012).10.1088/1367-2630/14/1/013021 ↗
59. Wopperer, P., De Giovannini, U. & Rubio, A. Efficient and accurate modeling of electron photoemission in nanostructures with TDDFT. Eur. Phys. J. B 90, 51 (2017).10.1140/epjb/e2017-70548-3 ↗
60. de Giovannini, U., Hübener, H. & Rubio, A. A first-principles time-dependent density functional theory framework for spin and time-resolved angular-resolved photoelectron spectroscopy in periodic systems. J. Chem. Theory Comput. 13, 265–273 (2017).10.1021/acs.jctc.6b00897 ↗
61. Tancogne-Dejean, N. et al. Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems. J. Chem. Phys. 152, 124119 (2020).10.1063/1.5142502 ↗
62. Perdew, J. P. & Zunger, A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048–5079 (1981).10.1103/PhysRevB.23.5048 ↗
63. Legrand, C., Suraud, E. & Reinhard, P.-G. Comparison of self-interaction-corrections for metal clusters. J. Phys. B: At. Mol. Opt. Phys. 35, 1115 (2002).10.1088/0953-4075/35/4/333 ↗
64. Magrakvelidze, M., Madjet, M. E.-A., Dixit, G., Ivanov, M. & Chakraborty, H. S. Attosecond time delay in valence photoionization and photorecombination of argon: A time-dependent local-density-approximation study. Phys. Rev. A 91, 063415 (2015).10.1103/PhysRevA.91.063415 ↗
65. Möbus, B. et al. Measurements of absolute Ar 3s photoionization cross sections. Phys. Rev. A 47, 3888–3893 (1993).10.1103/PhysRevA.47.3888 ↗
66. Goulielmakis, E. et al. Real-time observation of valence electron motion. Nature 466, 739–743 (2010).10.1038/nature09212 ↗
67. Wang, H. et al. Attosecond time-resolved autoionization of argon. Phys. Rev. Lett. 105, 143002 (2010).10.1103/PhysRevLett.105.143002 ↗
68. Holler, M., Schapper, F., Gallmann, L. & Keller, U. Attosecond electron wave-packet interference observed by transient absorption. Phys. Rev. Lett. 106, 123601 (2011).10.1103/PhysRevLett.106.123601 ↗
69. Reduzzi, M. et al. Observation of autoionization dynamics and sub-cycle quantum beating in electronic molecular wave packets. J. Phys. B: At. Mol. Opt. Phys. 49, 065102 (2016).10.1088/0953-4075/49/6/065102 ↗
70. Mashiko, H., Oguri, K., Yamaguchi, T., Suda, A. & Gotoh, H. Petahertz optical drive with wide-bandgap semiconductor. Nat. Phys. 12, 741–745 (2016).10.1038/nphys3711 ↗
71. Perdew, J. P. & Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 45, 13244–13249 (1992).10.1103/PhysRevB.45.13244 ↗
72. Sato, S. A., Yabana, K., Shinohara, Y., Otobe, T. & Bertsch, G. F. Numerical pump-probe experiments of laser-excited silicon in nonequilibrium phase. Phys. Rev. B 89, 064304 (2014).10.1103/PhysRevB.89.064304 ↗
73. Sato, S. A. First-principles calculations for transient absorption of laser-excited magnetic materials. Electron. Struct. 4, 014007 (2022).10.1088/2516-1075/ac52df ↗
74. Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011).10.1038/nphys1847 ↗
75. Ghimire, S. & Reis, D. A. High-harmonic generation from solids. Nat. Phys. 15, 10–16 (2019).10.1038/s41567-018-0315-5 ↗
76. Otobe, T. First-principle description for the high-harmonic generation in a diamond by intense short laser pulse. J. Appl. Phys. 111, 093112 (2012).10.1063/1.4716192 ↗
77. Tancogne-Dejean, N., Mücke, O. D., Kärtner, F. X. & Rubio, A. Impact of the electronic band structure in high-harmonic generation spectra of solids. Phys. Rev. Lett. 118, 087403 (2017).10.1103/PhysRevLett.118.087403 ↗
78. Floss, I. et al. Ab initio multiscale simulation of high-order harmonic generation in solids. Phys. Rev. A 97, 011401 (2018).10.1103/PhysRevA.97.011401 ↗
79. Guan, M., Hu, S., Zhao, H., Lian, C. & Meng, S. Toward attosecond control of electron dynamics in two-dimensional materials. Appl. Phys. Lett. 116, 043101 (2020).10.1063/1.5135599 ↗
80. Hu, S.-Q., Chen, D.-Q., Du, L.-L. & Meng, S. Solid-state high harmonic spectroscopy for all-optical band structure probing of high-pressure quantum states. Proc. Natl Acad. Sci. 121, e2316775121 (2024).10.1073/pnas.2316775121 ↗
81. Lakhotia, H. et al. Laser picoscopy of valence electrons in solids. Nature 583, 55–59 (2020).10.1038/s41586-020-2429-z ↗
82. Hansen, K. K., Deffge, T. & Bauer, D. High-order harmonic generation in solid slabs beyond the single-active-electron approximation. Phys. Rev. A 96, 053418 (2017).10.1103/PhysRevA.96.053418 ↗
83. Bauer, D. & Hansen, K. K. High-harmonic generation in solids with and without topological edge states. Phys. Rev. Lett. 120, 177401 (2018).10.1103/PhysRevLett.120.177401 ↗
84. Vampa, G. et al. Theoretical analysis of high-harmonic generation in solids. Phys. Rev. Lett. 113, 073901 (2014).10.1103/PhysRevLett.113.073901 ↗
85. Freeman, D., Kheifets, A., Yamada, S., Yamada, A. & Yabana, K. High-order harmonic generation in semiconductors driven at near- and mid-infrared wavelengths. Phys. Rev. B 106, 075202 (2022).10.1103/PhysRevB.106.075202 ↗
86. Liu, H. et al. High-harmonic generation from an atomically thin semiconductor. Nat. Phys. 13, 262–265 (2017).10.1038/nphys3946 ↗
87. Kaneshima, K. et al. Polarization-resolved study of high harmonics from bulk semiconductors. Phys. Rev. Lett. 120, 243903 (2018).10.1103/PhysRevLett.120.243903 ↗
88. Sekiguchi, F. et al. Enhancing high harmonic generation in GaAs by elliptically polarized light excitation. Phys. Rev. B 108, 205201 (2023).10.1103/PhysRevB.108.205201 ↗
89. Goncharov, V. A. Nonlinear optical response in solids from time-dependent density-functional theory simulations. J. Chem. Phys. 139, 084104 (2013).10.1063/1.4818807 ↗
90. Uemoto, M., Kuwabara, Y., Sato, S. A. & Yabana, K. Nonlinear polarization evolution using time-dependent density functional theory. J. Chem. Phys. 150, 094101 (2019).10.1063/1.5068711 ↗
91. Vignale, G. & Kohn, W. Current-dependent exchange-correlation potential for dynamical linear response theory. Phys. Rev. Lett. 77, 2037–2040 (1996).10.1103/PhysRevLett.77.2037 ↗
92. Berger, J. A., Romaniello, P., van Leeuwen, R. & de Boeij, P. L. Performance of the Vignale-Kohn functional in the linear response of metals. Phys. Rev. B 74, 245117 (2006).10.1103/PhysRevB.74.245117 ↗
93. Dinh, P. M., Lacombe, L., Reinhard, P.-G., Suraud, É. & Vincendon, M. On the inclusion of dissipation on top of mean-field approaches. Eur. Phys. J. B 91, 246 (2018).10.1140/epjb/e2018-90147-0 ↗
94. D’Agosta, R. & Vignale, G. Non-v-representability of currents in time-dependent many-particle systems. Phys. Rev. B 71, 245103 (2005).10.1103/PhysRevB.71.245103 ↗
95. Lacombe, L. & Maitra, N. T. Non-adiabatic approximations in time-dependent density functional theory: progress and prospects. npj Comput. Mater. 9, 124 (2023).10.1038/s41524-023-01061-0 ↗
96. Elliott, P., Fuks, J. I., Rubio, A. & Maitra, N. T. Universal dynamical steps in the exact time-dependent exchange-correlation potential. Phys. Rev. Lett. 109, 266404 (2012).10.1103/PhysRevLett.109.266404 ↗
97. Luo, K., Fuks, J. I., Sandoval, E. D., Elliott, P. & Maitra, N. T. Kinetic and interaction components of the exact time-dependent correlation potential. J. Chem. Phys. 140, 18A515 (2014).10.1063/1.4867002 ↗
98. Ramsden, J. D. & Godby, R. W. Exact density-functional potentials for time-dependent quasiparticles. Phys. Rev. Lett. 109, 036402 (2012).10.1103/PhysRevLett.109.036402 ↗
99. Suzuki, Y., Lacombe, L., Watanabe, K. & Maitra, N. T. Exact time-dependent exchange-correlation potential in electron scattering processes. Phys. Rev. Lett. 119, 263401 (2017).10.1103/PhysRevLett.119.263401 ↗
100. Suzuki, Y., Nagai, R. & Haruyama, J. Machine learning exchange-correlation potential in time-dependent density-functional theory. Phys. Rev. A 101, 050501 (2020).10.1103/PhysRevA.101.050501 ↗