- Open Access
Ab initio Maxwell-Bloch approach for x-ray excitations in two-dimensional materials
Phys. Rev. B 112, 085307 – Published 26 August, 2025
DOI: https://doi.org/10.1103/m8gf-z5fm
Abstract
The combination of Maxwell and Bloch equations is an ideal framework to describe ultrafast time-resolved x-ray experiments on an attosecond timescale in crystals. However, broadband experiments such as x-ray absorption near-edge spectroscopy or resonant inelastic x-ray scattering require detailed knowledge of the electronic structure and transition matrix elements. Here, we show how to fill this gap by combining the Maxwell-Bloch formalism with first-principles calculations treating explicitly the core states. The resulting x-ray absorption spectrum recovers key spectral signatures which were missing in previous work relying on a semiempirical tight-binding approach.
Physics Subject Headings (PhySH)
Article Text
References (42)
- M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, X-ray pulses approaching the attosecond frontier, Science 291, 1923 (2001).
- S. L. Cousin, N. Di Palo, B. Buades, S. M. Teichmann, M. Reduzzi, M. Devetta, A. Kheifets, G. Sansone, and J. Biegert, Attosecond streaking in the water window: A new regime of attosecond pulse characterization, Phys. Rev. X 7, 041030 (2017).
- J. Duris, S. Li, T. Driver, E. G. Champenois, J. P. MacArthur, A. A. Lutman, Z. Zhang, P. Rosenberger, J. W. Aldrich, R. Coffee et al., Tunable isolated attosecond X-ray pulses with gigawatt peak power from a free-electron laser, Nat. Photonics 14, 30 (2020).
- X. Xu, Y. Zhang, H. Zhang, H. Lu, W. Zhou, C. Zhou, B. Dromey, S. Zhu, M. Zepf, X. He et al., Production of 100-TW single attosecond X-ray pulse, Optica 7, 355 (2020).
- E. Goulielmakis, Z.-H. Loh, A. Wirth, R. Santra, N. Rohringer, V. S. Yakovlev, S. Zherebtsov, T. Pfeifer, A. M. Azzeer, M. F. Kling et al., Real-time observation of valence electron motion, Nature (London) 466, 739 (2010).
- F. Calegari, D. Ayuso, A. Trabattoni, L. Belshaw, S. De Camillis, S. Anumula, F. Frassetto, L. Poletto, A. Palacios, P. Decleva et al., Ultrafast electron dynamics in phenylalanine initiated by attosecond pulses, Science 346, 336 (2014).
- M. Nisoli, P. Decleva, F. Calegari, A. Palacios, and F. Martín, Attosecond electron dynamics in molecules, Chem. Rev. 117, 10760 (2017).
- P. Peng, C. Marceau, and D. M. Villeneuve, Attosecond imaging of molecules using high harmonic spectroscopy, Nat. Rev. Phys. 1, 144 (2019).
- A. Palacios and F. Martín, The quantum chemistry of attosecond molecular science, WIREs Comput. Mol. Sci. 10, e1430 (2020).
- I. D. Young, M. Ibrahim, R. Chatterjee, S. Gul, F. D. Fuller, S. Koroidov, A. S. Brewster, R. Tran, R. Alonso-Mori, T. Kroll et al., Structure of photosystem II and substrate binding at room temperature, Nature (London) 540, 453 (2016).
- J. Kern, R. Chatterjee, I. D. Young, F. D. Fuller, L. Lassalle, M. Ibrahim, S. Gul, T. Fransson, A. S. Brewster, R. Alonso-Mori et al., Structures of the intermediates of Kok's photosynthetic water oxidation clock, Nature (London) 563, 421 (2018).
- H. Kasai, K. Tolborg, M. Sist, J. Zhang, V. R. Hathwar, M. Ø. Filsø, S. Cenedese, K. Sugimoto, J. Overgaard, E. Nishibori et al., X-ray electron density investigation of chemical bonding in van der Waals materials, Nat. Mater. 17, 249 (2018).
- S. Bag, S. Chandra, J. Ghosh, A. Bera, E. R. Bernstein, and A. Bhattacharya, The attochemistry of chemical bonding, Int. Rev. Phys. Chem. 40, 405 (2021).
- L. Greten, R. Salzwedel, M. Katzer, H. Mittenzwey, D. Christiansen, A. Knorr, and M. Selig, Dipolar coupling at interfaces of ultrathin semiconductors, semimetals, plasmonic nanoparticles and molecules, Phys. Status Solidi A 221, 2300102 (2024).
- J. J. Rehr and R. C. Albers, Theoretical approaches to X-ray absorption fine structure, Rev. Mod. Phys. 72, 621 (2000).
- O. Bunău and Y. Joly, Time-dependent density functional theory applied to X-ray absorption spectroscopy, Phys. Rev. B 85, 155121 (2012).
- D. Christiansen, M. Selig, J. Biegert, and A. Knorr, Theory of X-ray absorption spectroscopy: A microscopic Bloch equation approach for two-dimensional solid states, Phys. Rev. Res. 5, 023002 (2023).
- P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo et al., Quantum Espresso: a modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
- 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).
- F. Karsai, M. Humer, E. Flage-Larsen, P. Blaha, and G. Kresse, Effects of electron-phonon coupling on absorption spectrum: edge of hexagonal boron nitride, Phys. Rev. B 98, 235205 (2018).
- B. Hetényi, F. De Angelis, P. Giannozzi, and R. Car, Calculation of near-edge X-ray-absorption fine structure at finite temperatures: Spectral signatures of hydrogen bond breaking in liquid water, J. Chem. Phys. 120, 8632 (2004).
- P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. B 136, B864 (1964).
- W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. A 140, A1133 (1965).
- R. M. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, Cambridge, UK, 2020).
- W. E. Pickett, Pseudopotential methods in condensed matter applications, Comput. Phys. Rep. 9, 115 (1989).
- P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
- P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni et al., Advanced capabilities for materials modelling with quantum espresso, J. Phys.: Condens. Matter 29, 465901 (2017).
- T. Susi, D. J. Mowbray, M. P. Ljungberg, and P. Ayala, Calculation of the graphene C core level binding energy, Phys. Rev. B 91, 081401(R) (2015).
- J. Xu, P. Krüger, C. R. Natoli, K. Hayakawa, Z. Wu, and K. Hatada, X-ray absorption spectra of graphene and graphene oxide by full-potential multiple scattering calculations with self-consistent charge density, Phys. Rev. B 92, 125408 (2015).
- G. Onida, L. Reining, and A. Rubio, Electronic excitations: Density-functional versus many-body Green's-function approaches, Rev. Mod. Phys. 74, 601 (2002).
- R. Del Sole and R. Girlanda, Optical properties of semiconductors within the independent-quasiparticle approximation, Phys. Rev. B 48, 11789 (1993).
- G. D. Mahan, Many-Particle Physics (Springer, New York, 2013).
- L. Inhester, G. Groenhof, and H. Grubmüller, Core hole screening and decay rates of double core ionized first row hydrides, J. Chem. Phys. 138, 164304 (2013).
- M. Ohno, Dynamics of core-hole decay in adsorbates, Phys. Rev. B 45, 3865 (1992).
- H.-Y. Chen, V. A. Jhalani, M. Palummo, and M. Bernardi, Ab initio calculations of exciton radiative lifetimes in bulk crystals, nanostructures, and molecules, Phys. Rev. B 100, 075135 (2019).
- H.-Y. Chen, D. Sangalli, and M. Bernardi, Exciton-phonon interaction and relaxation times from first principles, Phys. Rev. Lett. 125, 107401 (2020).
- R. Géneaux, C. J. Kaplan, L. Yue, A. D. Ross, J. E. Bækhøj, P. M. Kraus, H.-T. Chang, A. Guggenmos, M.-Y. Huang, M. Zürch et al., Attosecond time-domain measurement of core-level-exciton decay in magnesium oxide, Phys. Rev. Lett. 124, 207401 (2020).
- J. D. Gaynor, A. P. Fidler, Y.-C. Lin, H.-T. Chang, M. Zuerch, D. M. Neumark, and S. R. Leone, Solid state core-exciton dynamics in NaCl observed by tabletop attosecond four-wave mixing spectroscopy, Phys. Rev. B 103, 245140 (2021).
- H.-T. Chang, A. Guggenmos, C. T. Chen, J. Oh, R. Géneaux, Y.-D. Chuang, A. M. Schwartzberg, S. Aloni, D. M. Neumark, and S. R. Leone, Coupled valence carrier and core-exciton dynamics in probed by few-femtosecond extreme ultraviolet transient absorption spectroscopy, Phys. Rev. B 104, 064309 (2021).
- M. Papagno, A. F. Rodríguez, Ç. Girit, J. Meyer, A. Zettl, and D. Pacilé, Polarization-dependent C near-edge X-ray absorption fine-structure of graphene, Chem. Phys. Lett. 475, 269 (2009).
- J. Vinson, J. J. Rehr, J. J. Kas, and E. L. Shirley, Bethe-Salpeter equation calculations of core excitation spectra, Phys. Rev. B 83, 115106 (2011).
- K. Gilmore, J. Vinson, E. L. Shirley, D. Prendergast, C. D. Pemmaraju, J. J. Kas, F. D. Vila, and J. J. Rehr, Efficient implementation of core-excitation Bethe–Salpeter equation calculations, Comput. Phys. Commun. 197, 109 (2015).