- Open Access
Attosecond pulse generation from Weyl semimetals
Phys. Rev. B 113, 125144 – Published 25 March, 2026
DOI: https://doi.org/10.1103/6nxz-kgxd
Abstract
The generation of attosecond pulses from higher-order harmonics is an essential milestone toward enabling time-resolved spectroscopy of electronic processes in matter on the attosecond timescale. The avenue for high-harmonic generation from solids has proliferated since its discovery a decade ago. However, isolated attosecond pulse generation from solids remains scarce. We report a theoretical proposal that leverages Weyl semimetals for highly efficient attosecond pulse generation in the far-ultraviolet region. The generation of isolated attosecond pulses from Weyl semimetals is achieved using two-color laser pulses, which generate a broad higher-harmonic plateau ranging from 3 to 11 eV. Attosecond pulses with comparable durations – spanning approximately 500 to 900 as – are generated in both collinear and orthogonal configurations of the two-color fields. The strength and duration of the attosecond pulses can be optimized by tailoring the polarization direction and relative strength of the two-color field.
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References (93)
- A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. McIntyre, K. Boyer, and C. K. Rhodes, Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases, J. Opt. Soc. Am. B 4, 595 (1987).
- M. Ferray, A. L'Huillier, X. Li, L. Lompre, G. Mainfray, and C. Manus, Multiple-harmonic conversion of 1064 nm radiation in rare gases, J. Phys. B 21, L31 (1988).
- 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).
- G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, et al., Isolated single-cycle attosecond pulses, Science 314, 443 (2006).
- E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. Gullikson, D. T. Attwood, R. Kienberger, et al., Single-cycle nonlinear optics, Science 320, 1614 (2008).
- F. Krausz and M. Ivanov, Attosecond physics, Rev. Mod. Phys. 81, 163 (2009).
- P. B. Corkum, Plasma perspective on strong field multiphoton ionization, Phys. Rev. Lett. 71, 1994 (1993).
- M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L'Huillier, and P. B. Corkum, Theory of high-harmonic generation by low-frequency laser fields, Phys. Rev. A 49, 2117 (1994).
- M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, Time-resolved atomic inner-shell spectroscopy, Nature (London) 419, 803 (2002).
- S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirilă, M. Lein, J. W. G. Tisch, and J. P. Marangos, Probing proton dynamics in molecules on an attosecond time scale, Science 312, 424 (2006).
- W. Li, X. Zhou, R. Lock, S. Patchkovskii, A. Stolow, H. C. Kapteyn, and M. M. Murnane, Time-resolved dynamics in N2O4 probed using high harmonic generation, Science 322, 1207 (2008).
- G. Sansone, F. Kelkensberg, J. F. Pérez-Torres, F. Morales, M. F. Kling, W. Siu, O. Ghafur, P. Johnsson, M. Swoboda, E. Benedetti, F. Ferrari, F. Lépine, J. L. Sanz-Vicario, S. Zherebtsov, I. Znakovskaya, A. L'Huillier, M. Y. Ivanov, M. Nisoli, F. Martin, and M. J. J. Vrakking, Electron localization following attosecond molecular photoionization, Nature (London) 465, 763 (2010).
- S. Haessler, J. Caillat, W. Boutu, C. Giovanetti-Teixeira, T. Ruchon, T. Auguste, Z. Diveki, P. Breger, A. Maquet, B. Carré, R. Taieb, and P. Saliéres, Attosecond imaging of molecular electronic wavepackets, Nat. Phys. 6, 200 (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).
- F. Krausz and M. I. Stockman, Attosecond metrology: From electron capture to future signal processing, Nat. Photonics 8, 205 (2014).
- E. Frumker, C. T. Hebeisen, N. Kajumba, J. B. Bertrand, H. J. Wörner, M. Spanner, D. M. Villeneuve, A. Naumov, and P. B. Corkum, Oriented rotational wave-packet dynamics studies via high harmonic generation, Phys. Rev. Lett. 109, 113901 (2012).
- G. Dixit, O. Vendrell, and R. Santra, Imaging electronic quantum motion with light, Proc. Natl. Acad. Sci. USA 109, 11636 (2012).
- V. Gruson, L. Barreau, Á. Jiménez-Galan, F. Risoud, J. Caillat, A. Maquet, B. Carré, F. Lepetit, J. F. Hergott, T. Ruchon, L. Argenti, R. Taieb, F. Martín, and P. Saliéres, Attosecond dynamics through a Fano resonance: Monitoring the birth of a photoelectron, Science 354, 734 (2016).
- P.-M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H. G. Muller, and P. Agostini, Observation of a train of attosecond pulses from high harmonic generation, Science 292, 1689 (2001).
- M. Hentschel, R. Kienberger, C. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, Attosecond metrology, Nature (London) 414, 509 (2001).
- M. Chini, K. Zhao, and Z. Chang, The generation, characterization and applications of broadband isolated attosecond pulses, Nat. Photonics 8, 178 (2014).
- K. Midorikawa, Progress on table-top isolated attosecond light sources, Nat. Photonics 16, 267 (2022).
- T. Gaumnitz, A. Jain, Y. Pertot, M. Huppert, I. Jordan, F. Ardana-Lamas, and H. J. Wörner, Streaking of 43-attosecond soft-x-ray pulses generated by a passively CEP-stable mid-infrared driver, Opt. Express 25, 27506 (2017).
- F. Krausz, Nobel lecture: Sub-atomic motions, Rev. Mod. Phys. 96, 030502 (2024).
- P. Agostini, Nobel lecture: Genesis and applications of attosecond pulse trains, Rev. Mod. Phys. 96, 030501 (2024).
- A. L'Huillier, Nobel lecture: The route to attosecond pulses, Rev. Mod. Phys. 96, 030503 (2024).
- S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, Observation of high-order harmonic generation in a bulk crystal, Nat. Phys. 7, 138 (2011).
- S. Ghimire and D. A. Reis, High-harmonic generation from solids, Nat. Phys. 15, 10 (2019).
- E. Goulielmakis and T. Brabec, High harmonic generation in condensed matter, Nat. Photonics 16, 411 (2022).
- T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. Th. Hassan, and E. Goulielmakis, Extreme ultraviolet high-harmonic spectroscopy of solids, Nature (London) 521, 498 (2015).
- G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, D. D. Klug, and P. B. Corkum, All-optical reconstruction of crystal band structure, Phys. Rev. Lett. 115, 193603 (2015).
- M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, Real-time observation of interfering crystal electrons in high-harmonic generation, Nature (London) 523, 572 (2015).
- N. Tancogne-Dejean, O. D. Mücke, F. X. Kärtner, and A. Rubio, Ellipticity dependence of high-harmonic generation in solids originating from coupled intraband and interband dynamics, Nat. Commun. 8, 745 (2017).
- H. Liu, C. Guo, G. Vampa, J. L. Zhang, T. Sarmiento, M. Xiao, P. H. Bucksbaum, J. Vučković, S. Fan, and D. A. Reis, Enhanced high-harmonic generation from an all-dielectric metasurface, Nat. Phys. 14, 1006 (2018).
- M. M. S., A. Pattanayak, M. Ivanov, and G. Dixit, Direct numerical observation of real-space recollision in high-order harmonic generation from solids, Phys. Rev. A 100, 043420 (2019).
- D. Gauthier, S. Kaassamani, D. Franz, R. Nicolas, J.-T. Gomes, L. Lavoute, D. Gaponov, S. Février, G. Jargot, M. Hanna, et al., Orbital angular momentum from semiconductor high-order harmonics, Opt. Lett. 44, 546 (2019).
- S. Imai, A. Ono, and S. Ishihara, High harmonic generation in a correlated electron system, Phys. Rev. Lett. 124, 157404 (2020).
- L. Yue and M. B. Gaarde, Imperfect recollisions in high-harmonic generation in solids, Phys. Rev. Lett. 124, 153204 (2020).
- M. S. Mrudul, N. Tancogne-Dejean, A. Rubio, and G. Dixit, High-harmonic generation from spin-polarised defects in solids, npj Comput. Mater. 6, 10 (2020).
- M. Borsch, C. P. Schmid, L. Weigl, S. Schlauderer, N. Hofmann, C. Lange, J. T. Steiner, S. W. Koch, R. Huber, and M. Kira, Super-resolution lightwave tomography of electronic bands in quantum materials, Science 370, 1204 (2020).
- V. Nefedova, S. Fröhlich, F. Navarrete, N. Tancogne-Dejean, D. Franz, A. Hamdou, S. Kaassamani, D. Gauthier, R. Nicolas, G. Jargot, et al., Enhanced extreme ultraviolet high-harmonic generation from chromium-doped magnesium oxide, Appl. Phys. Lett. 118, 201103 (2021).
- C. P. Schmid, L. Weigl, P. Grössing, V. Junk, C. Gorini, S. Schlauderer, S. Ito, M. Meierhofer, N. Hofmann, D. Afanasiev, et al., Tunable non-integer high-harmonic generation in a topological insulator, Nature (London) 593, 385 (2021).
- M. R. Shcherbakov, H. Zhang, M. Tripepi, G. Sartorello, N. Talisa, A. AlShafey, Z. Fan, J. Twardowski, L. A. Krivitsky, A. I. Kuznetsov, et al., Generation of even and odd high harmonics in resonant metasurfaces using single and multiple ultra-intense laser pulses, Nat. Commun. 12, 4185 (2021).
- C. Heide, Y. Kobayashi, D. R. Baykusheva, D. Jain, J. A. Sobota, M. Hashimoto, P. S. Kirchmann, S. Oh, T. F. Heinz, D. A. Reis, et al., Probing topological phase transitions using high-harmonic generation, Nat. Photonics 16, 620 (2022).
- S. Kaassamani, T. Auguste, N. Tancogne-Dejean, X. Liu, W. Boutu, H. Merdji, and D. Gauthier, Polarization spectroscopy of high-order harmonic generation in gallium arsenide, Opt. Express 30, 40531 (2022).
- A. Pattanayak, S. Pujari, and G. Dixit, Role of Majorana fermions in high-harmonic generation from Kitaev chain, Sci. Rep. 12, 6722 (2022).
- C. Qian, C. Yu, S. Jiang, T. Zhang, J. Gao, S. Shi, H. Pi, H. Weng, and R. Lu, Role of shift vector in high-harmonic generation from noncentrosymmetric topological insulators under strong laser fields, Phys. Rev. X 12, 021030 (2022).
- N. Rana, M. S. Mrudul, and G. Dixit, Generation of circularly polarized high harmonics with identical helicity in two-dimensional materials, Phys. Rev. Appl. 18, 064049 (2022).
- S. Cha, M. Kim, Y. Kim, S. Choi, S. Kang, H. Kim, S. Yoon, G. Moon, T. Kim, Y. W. Lee, et al., Gate-tunable quantum pathways of high harmonic generation in graphene, Nat. Commun. 13, 6630 (2022).
- J. Shi, H. Xu, C. Heide, C. HuangFu, C. Xia, F. de Quesada, H. Shen, T. Zhang, L. Yu, A. Johnson, et al., Giant room-temperature nonlinearities in a monolayer Janus topological semiconductor, Nat. Commun. 14, 4953 (2023).
- L. Li, P. Lan, X. Zhu, and P. Lu, High harmonic generation in solids: Particle and wave perspectives, Rep. Prog. Phys. 86, 116401 (2023).
- H. K. Avetissian, H. H. Matevosyan, and G. F. Mkrtchian, Berry curvature and shift vector effects at high-order wave mixing in biased bilayer graphene, Phys. Rev. B 111, 045415 (2025).
- N. Rana, M. S. Mrudul, and G. Dixit, High-harmonic generation from strain-engineered graphene for polarization tailoring, Phys. Rev. B 110, 054103 (2024).
- Y. Kim, M. J. Kim, S. Cha, S. Choi, C.-J. Kim, B. Kim, M.-H. Jo, J. Kim, and J. Lee, Dephasing dynamics accessed by high harmonic generation: Determination of electron–hole decoherence of Dirac fermions, Nano Lett. 24, 1277 (2024).
- C. Heide, Y. Kobayashi, S. R. U. Haque, and S. Ghimire, Ultrafast high-harmonic spectroscopy of solids, Nat. Phys. 20, 1546 (2024).
- G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, Solid-state harmonics beyond the atomic limit, Nature (London) 534, 520 (2016).
- N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
- Y.-Y. Lv, J. Xu, S. Han, C. Zhang, Y. Han, J. Zhou, S.-H. Yao, X.-P. Liu, M.-H. Lu, H. Weng, et al., High-harmonic generation in Weyl semimetal crystals, Nat. Commun. 12, 6437 (2021).
- G. Vampa, T. Hammond, N. Thiré, B. Schmidt, F. Légaré, C. McDonald, T. Brabec, and P. Corkum, Linking high harmonics from gases and solids, Nature (London) 522, 462 (2015).
- T. T. Luu and H. J. Wörner, Observing broken inversion symmetry in solids using two-color high-order harmonic spectroscopy, Phys. Rev. A 98, 041802(R) (2018).
- H. K. Avetissian, G. F. Mkrtchian, and A. Knorr, Efficient high-harmonic generation in graphene with two-color laser field at orthogonal polarization, Phys. Rev. B 105, 195405 (2022).
- F. Navarrete and U. Thumm, Two-color-driven enhanced high-order harmonic generation in solids, Phys. Rev. A 102, 063123 (2020).
- J.-B. Li, X. Zhang, S.-J. Yue, H.-M. Wu, B.-T. Hu, and H.-C. Du, Enhancement of the second plateau in solid high-order harmonic spectra by the two-color fields, Opt. Express 25, 18603 (2017).
- G. Vampa, J. Lu, Y. S. You, D. R. Baykusheva, M. Wu, H. Liu, K. J. Schafer, M. B. Gaarde, D. A. Reis, and S. Ghimire, Attosecond synchronization of extreme ultraviolet high harmonics from crystals, J. Phys. B 53, 144003 (2020).
- A. Bharti and G. Dixit, Photocurrent generation in solids via linearly polarized laser, Phys. Rev. B 109, 104309 (2024).
- B. Yan and C. Felser, Topological materials: Weyl semimetals, Annu. Rev. Condens. Matter Phys. 8, 337 (2017).
- B. Q. Lv, T. Qian, and H. Ding, Experimental perspective on three-dimensional topological semimetals, Rev. Mod. Phys. 93, 025002 (2021).
- A. Seyen, R. Kohn, U. Bovensiepen, D. von der Linde, and A. Tarasevitch, Toward attosecond pulse synthesis from solids: Spectral shaping, field autocorrelation, and two-color harmonic generation, Phys. Rev. A 99, 033836 (2019).
- Z. Nourbakhsh, N. Tancogne-Dejean, H. Merdji, and A. Rubio, High harmonics and isolated attosecond pulses from MgO, Phys. Rev. Appl. 15, 014013 (2021).
- S. Imai and A. Ono, Theory for Fourier-limited attosecond pulse generation in solids, Phys. Rev. B 109, L041303 (2024).
- A. Sadeghifaraz and E. Irani, Generation of isolated attosecond pulses in CdS semiconductor using polarization gating technique and tailored two-color pulse system, Sci. Rep. 15, 7586 (2025).
- X. Song, X. Bu, X. Zhao, R. Zhang, S. Wang, and F. Dong, Isolated elliptically-polarized attosecond pulse generation in gapped graphene driven by linearly polarized laser fields, Phys. Rev. A 112, 043107 (2025).
- A. Nayak, D. Rajak, B. Farkas, C. Granados, P. Stammer, J. Rivera-Dean, T. Lamprou, K. Varju, Y. Mairesse, M. F. Ciappina, et al., Attosecond metrology of vacuum-ultraviolet high-order harmonics generated in semiconductors via laser-dressed photoionization of alkali metals, Nat. Commun. 16, 1428 (2025).
- Z. Chen, M. Levit, Y. Kern, B. Roy, A. Goldner, and M. Krüger, Attosecond pulses from a solid driven by a synthesized two-color field at megahertz repetition rate, ACS Photonics 12, 2819 (2025).
- M. S. Mrudul and G. Dixit, High-harmonic generation from monolayer and bilayer graphene, Phys. Rev. B 103, 094308 (2021).
- A. Bharti and G. Dixit, Tailoring photocurrent in Weyl semimetals via intense laser irradiation, Phys. Rev. B 108, L161113 (2023).
- A. Bharti, M. S. Mrudul, and G. Dixit, High-harmonic spectroscopy of light-driven nonlinear anisotropic anomalous Hall effect in a Weyl semimetal, Phys. Rev. B 105, 155140 (2022).
- A. Bharti and G. Dixit, Non-perturbative nonlinear optical responses in Weyl semimetals, Appl. Phys. Lett. 125, 051104 (2024).
- L. Wang, M. F. Ciappina, T. Brabec, and X. J. Liu, Tabletop tunable chiral photonic emitter, Phys. Rev. Lett. 133, 113804 (2024).
- H. K. Avetissian, V. N. Avetisyan, B. R. Avchyan, and G. F. Mkrtchian, High-order harmonic generation in three-dimensional Weyl semimetals with broken time-reversal symmetry, Phys. Rev. A 106, 033107 (2022).
- L. Medic, J. Mravlje, A. Ramšak, and T. Rejec, High-harmonic generation in semi-Dirac and Weyl semimetals with broken time-reversal symmetry: Exploration of the merging of Weyl nodes, Phys. Rev. B 109, 205130 (2024).
- Z.-Y. Li, Q. Li, and Z. Li, High-order harmonic generations in tilted Weyl semimetals, Chin. Phys. B 31, 124204 (2022).
- A. Bharti and G. Dixit, Role of topological charges in the nonlinear optical response from Weyl semimetals, Phys. Rev. B 107, 224308 (2023).
- S. Roscam Abbing, F. Campi, F. S. Sajjadian, N. Lin, P. Smorenburg, and P. M. Kraus, Divergence control of high-harmonic generation, Phys. Rev. Appl. 13, 054029 (2020).
- Q. Ma, S.-Y. Xu, C.-K. Chan, C.-L. Zhang, G. Chang, Y. Lin, W. Xie, T. Palacios, H. Lin, S. Jia, et al., Direct optical detection of Weyl fermion chirality in a topological semimetal, Nat. Phys. 13, 842 (2017).
- M. Kretschmar, E. Svirplys, M. Volkov, T. Witting, T. Nagy, M. J. Vrakking, and B. Schütte, Compact realization of all-attosecond pump-probe spectroscopy, Sci. Adv. 10, eadk9605 (2024).
- Z. Guo, T. Driver, S. Beauvarlet, D. Cesar, J. Duris, P. L. Franz, O. Alexander, D. Bohler, C. Bostedt, V. Averbukh, et al., Experimental demonstration of attosecond pump–probe spectroscopy with an x-ray free-electron laser, Nat. Photonics 18, 691 (2024).
- S. Li, L. Lu, S. Bhattacharyya, C. Pearce, K. Li, E. T. Nienhuis, G. Doumy, R. D. Schaller, S. Moeller, M.-F. Lin, et al., Attosecond-pump attosecond-probe x-ray spectroscopy of liquid water, Science 383, 1118 (2024).
- C.-X. Yun, H. Teng, W. Zhang, M.-J. Zhan, H.-N. Han, X. Zhong, Z.-Y. Wei, B.-B. Wang, and X. Hou, High-order harmonics generation by few-cycle and multi-cycle femtosecond laser pulses, Chin. Phys. B 19, 124210 (2010).
- Q. Guo, M. Dendzik, A. Grubišić-Čabo, M. H. Berntsen, C. Li, W. Chen, B. Matta, U. Starke, B. Hessmo, J. Weissenrieder, et al., A narrow bandwidth extreme ultra-violet light source for time-and angle-resolved photoemission spectroscopy, Struct. Dyn. 9, 024304 (2022).
- D. Alam, N. Ud Din, M. Chini, and V. Turkowski, Electron-electron interactions and high-order harmonics in solids, Phys. Rev. B 106, 235124 (2022).
- S. Eich, A. Stange, A. Carr, J. Urbancic, T. Popmintchev, M. Wiesenmayer, K. Jansen, A. Ruffing, S. Jakobs, T. Rohwer, et al., Time-and angle-resolved photoemission spectroscopy with optimized high-harmonic pulses using frequency-doubled Ti: Sapphire lasers, J. Electron Spectrosc. Relat. Phenom. 195, 231 (2014).
- A. Mondal, B. Waser, T. Balciunas, O. Neufeld, Z. Yin, N. Tancogne-Dejean, A. Rubio, and H. J. Wörner, High-harmonic generation in liquids with few-cycle pulses: Effect of laser-pulse duration on the cut-off energy, Opt. Express 31, 34348 (2023).