Abstract
In quantum materials, emergent functional properties resulting from strong correlations or electronic topology offer opportunities for new applications. Over the past decade, ultrafast techniques such as photoemission, scattering and optical spectroscopies have complemented traditional control knobs such as temperature, pressure, chemical substitution and external fields, adding the time coordinate as a new dimension for understanding and engineering the properties of quantum materials out of equilibrium. Despite remarkable progress, there remains a host of open questions that will require detailed understanding of the non-equilibrium response of quantum materials to enable applications in areas such as clean energy production, energy storage and quantum computation and communication. In this Review, we survey three categories of emerging ultrafast spectroscopies for investigating condensed matter systems — attosecond transient absorption spectroscopy, solid-state high-harmonic generation spectroscopy and extreme ultraviolet second-harmonic generation spectroscopy — and we discuss their potential applications to the study of quantum materials. We analyse these ultrafast tools from the standpoint of open questions in quantum materials, highlighting the unique observables and capabilities these methods can offer to address them.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 per month
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$119.00 per year
only $9.92 per issue
Rent or buy this article
Get just this article for as long as you need it
$39.95
Prices may be subject to local taxes which are calculated during checkout







References
Bovensiepen, U. & Kirchmann, P. Elementary relaxation processes investigated by femtosecond photoelectron spectroscopy of two-dimensional materials. Laser Photon. Rev. 6, 589–606 (2012).
Smallwood, C. L., Kaindl, R. A. & Lanzara, A. Ultrafast angle-resolved photoemission spectroscopy of quantum materials. Europhys. Lett. 115, 27001 (2016).
Zhou, X. et al. New developments in laser-based photoemission spectroscopy and its scientific applications: a key issues review. Rep. Prog. Phys. 81, 062101 (2018).
Sobota, J. A., He, Y. & Shen, Z.-X. Angle-resolved photoemission studies of quantum materials. Rev. Mod. Phys. 93, 025006 (2021).
Giannetti, C. et al. Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach. Adv. Phys. 65, 58–238 (2016).
Orenstein, J. Ultrafast spectroscopy of quantum materials. Phys. Today 65, 44–50 (2012).
Prasankumar, R. P. & Taylor, A. J. Optical Techniques for Solid-State Materials Characterization (CRC Press, 2011).
Cao, Y. et al. Ultrafast dynamics of spin and orbital correlations in quantum materials: an energy- and momentum-resolved perspective. Philos. Trans. R. Soc. A 377, 20170480 (2019).
Buzzi, M., Först, M., Mankowsky, R. & Cavalleri, A. Probing dynamics in quantum materials with femtosecond X-rays. Nat. Rev. Mater. 3, 299–311 (2018).
Mitrano, M. & Wang, Y. Probing light-driven quantum materials with ultrafast resonant inelastic X-ray scattering. Commun. Phys. 3, 184 (2020).
Zong, A., Kogar, A. & Gedik, N. Unconventional light-induced states visualized by ultrafast electron diffraction and microscopy. MRS Bull. 46, 720–730 (2021).
Filippetto, D. et al. Ultrafast electron diffraction: visualizing dynamic states of matter. Rev. Mod. Phys. 94, 045004 (2022).
Wen, H., Cherukara, M. J. & Holt, M. V. Time-resolved X-ray microscopy for materials science. Annu. Rev. Mater. Res. 49, 389–415 (2019).
de la Torre, A. et al. Colloquium: nonthermal pathways to ultrafast control in quantum materials. Rev. Mod. Phys. 93, 041002 (2021). This review contains a detailed account of established ultrafast techniques and the science they have enabled for studying quantum materials.
Bao, C., Tang, P., Sun, D. & Zhou, S. Light-induced emergent phenomena in 2D materials and topological materials. Nat. Rev. Phys. 4, 33–48 (2022).
Lloyd-Hughes, J. et al. The 2021 ultrafast spectroscopic probes of condensed matter roadmap. J. Phys. Condens. Matter 33, 353001 (2021).
Disa, A. S., Nova, T. F. & Cavalleri, A. Engineering crystal structures with light. Nat. Phys. 17, 1087–1092 (2021).
Zong, A. in Emergent States in Photoinduced Charge-Density-Wave Transitions 1–36 (Springer, 2021).
Rudner, M. S. & Lindner, N. H. Band structure engineering and non-equilibrium dynamics in Floquet topological insulators. Nat. Rev. Phys. 2, 229–244 (2020).
Oka, T. & Kitamura, S. Floquet engineering of quantum materials. Annu. Rev. Condens. Matter Phys. 10, 387–408 (2019).
Jin, C. et al. Ultrafast dynamics in van der Waals heterostructures. Nat. Nanotechnol. 13, 994–1003 (2018).
Basov, D. N., Averitt, R. D. & Hsieh, D. Towards properties on demand in quantum materials. Nat. Mater. 16, 1077–1088 (2017).
Zhang, J. & Averitt, R. Dynamics and control in complex transition metal oxides. Annu. Rev. Mater. Res. 44, 19–43 (2014).
Kirilyuk, A., Kimel, A. V. & Rasing, T. Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 82, 2731–2784 (2010).
Baykusheva, D. R. et al. Ultrafast renormalization of the on-site Coulomb repulsion in a cuprate superconductor. Phys. Rev. X 12, 011013 (2022).
Alexandradinata, A. et al. The future of the correlated electron problem. Preprint at https://doi.org/10.48550/arXiv.2010.00584 (2020).
Chowdhury, D., Georges, A., Parcollet, O. & Sachdev, S. Sachdev-Ye-Kitaev models and beyond: window into non-Fermi liquids. Rev. Mod. Phys. 94, 035004 (2022).
Phillips, P. W., Hussey, N. E. & Abbamonte, P. Stranger than metals. Science 377, eabh4273 (2022).
Kaplan, C. J. et al. Retrieval of the complex-valued refractive index of germanium near the M4,5 absorption edge. J. Opt. Soc. Am. B 36, 1716 (2019).
Goulielmakis, E. et al. Real-time observation of valence electron motion. Nature 466, 739–743 (2010).
Leone, S. R. et al. What will it take to observe processes in real time? Nat. Photon. 8, 162–166 (2014).
Kraus, P. M., Zürch, M., Cushing, S. K., Neumark, D. M. & Leone, S. R. The ultrafast X-ray spectroscopic revolution in chemical dynamics. Nat. Rev. Chem. 2, 82–94 (2018).
Vinko, S. M. et al. Time-resolved XUV opacity measurements of warm dense aluminum. Phys. Rev. Lett. 124, 225002 (2020).
Niedermayr, A. et al. Few-femtosecond dynamics of free-free opacity in optically heated metals. Phys. Rev. X 12, 021045 (2022).
Volkov, M. et al. Attosecond screening dynamics mediated by electron localization in transition metals. Nat. Phys. 15, 1145–1149 (2019). This work applies attosecond transient absorption spectroscopy to study photoinduced electron dynamics in elemental Ti, demonstrating the importance of a many-body theoretical treatment to correlated metallic systems.
Petek, H. & Ogawa, S. Femtosecond time-resolved two-photon photoemission studies of electron dynamics in metals. Prog. Surf. Sci. 56, 239–310 (1997).
Zürch, M. et al. Direct and simultaneous observation of ultrafast electron and hole dynamics in germanium. Nat. Commun. 8, 15734 (2017).
Cushing, S. K. et al. Differentiating photoexcited carrier and phonon dynamics in the δ, L, and σ valleys of Si(100) with transient extreme ultraviolet spectroscopy. J. Phys. Chem. C 123, 3343–3352 (2019).
Liu, H., Michelsen, J. M., Klein, I. M. & Cushing, S. K. Measuring photoexcited electron and hole dynamics in ZnTe and modeling excited state core-valence effects in transient XUV reflection spectroscopy. Preprint at https://doi.org/10.48550/arXiv.2108.02262 (2021).
Schultze, M. et al. Controlling dielectrics with the electric field of light. Nature 493, 75–78 (2013). This work is the first attosecond transient absorption spectroscopy study of strong-field driven, sub-femtosecond coherent dynamics in solids, demonstrated in dielectric SiO2.
Geneaux, R., Marroux, H. J. B., Guggenmos, A., Neumark, D. M. & Leone, S. R. Transient absorption spectroscopy using high harmonic generation: a review of ultrafast X-ray dynamics in molecules and solids. Philos. Trans. R. Soc. A 377, 20170463 (2019).
Moulet, A. et al. Soft X-ray excitonics. Science 357, 1134–1138 (2017). This work presents the capability of attosecond transient absorption spectroscopy to directly probe core excitons and characterize their transient properties.
Jager, M. F. et al. Tracking the insulator-to-metal phase transition in VO2 with few-femtosecond extreme UV transient absorption spectroscopy. Proc. Natl Acad. Sci. USA 114, 9558–9563 (2017). This work uncovers a record speed for the photoinduced metal-to-insulator transition in a correlated transition metal oxide, VO2.
Rohde, G. et al. Ultrafast formation of a Fermi–Dirac distributed electron gas. Phys. Rev. Lett. 121, 256401 (2018).
Schumacher, Z. et al. Ultrafast electron localization and screening in a transition metal dichalcogenide. Preprint at https://doi.org/10.48550/arXiv.2210.05465 (2022).
Beaurepaire, E., Merle, J.-C., Daunois, A. & Bigot, J.-Y. Ultrafast spin dynamics in ferromagnetic nickel. Phys. Rev. Lett. 76, 4250–4253 (1996).
Roth, T. et al. Temperature dependence of laser-induced demagnetization in Ni: a key for identifying the underlying mechanism. Phys. Rev. X 2, 021006 (2012).
Schlauderer, S. et al. Temporal and spectral fingerprints of ultrafast all-coherent spin switching. Nature 569, 383–387 (2019).
Disa, A. S. et al. Polarizing an antiferromagnet by optical engineering of the crystal field. Nat. Phys. 16, 937–941 (2020).
Siegrist, F. et al. Light-wave dynamic control of magnetism. Nature 571, 240–244 (2019). This work demonstrates the sub-femtosecond to few-femtosecond control of spin in an Ni-Pt multilayer sample through the optically induced spin and orbital momentum transfer (OISTR) mechanism.
Tengdin, P. et al. Direct light-induced spin transfer between different elements in a spintronic Heusler material via femtosecond laser excitation. Sci. Adv. 6, eaaz1100 (2020).
Hofherr, M. et al. Ultrafast optically induced spin transfer in ferromagnetic alloys. Sci. Adv. 6, eaay8717 (2020).
Géneaux, R. et al. Attosecond time-domain measurement of core-level-exciton decay in magnesium oxide. Phys. Rev. Lett. 124, 207401 (2020).
Porter, I. J. et al. Characterization of carrier cooling bottleneck in silicon nanoparticles by extreme ultraviolet (XUV) transient absorption spectroscopy. J. Phys. Chem. C 125, 9319–9329 (2021).
Verkamp, M. et al. Carrier-specific hot phonon bottleneck in CH3NH3PbI3 revealed by femtosecond XUV absorption. J. Am. Chem. Soc. 143, 20176–20182 (2021).
Carneiro, L. M. et al. Excitation-wavelength-dependent small polaron trapping of photoexcited carriers in α-Fe2O3. Nat. Mater. 16, 819–825 (2017). This work displays the capability of attosecond transient absorption spectroscopy to capture photoinduced polarons and related electron–phonon dynamics.
Géneaux, R. et al. Coherent energy exchange between carriers and phonons in Peierls-distorted bismuth unveiled by broadband XUV pulses. Phys. Rev. Res. 3, 033210 (2021).
Attar, A. R. et al. Simultaneous observation of carrier-specific redistribution and coherent lattice dynamics in 2H-MoTe2 with femtosecond core-level spectroscopy. ACS Nano 14, 15829–15840 (2020).
Sidiropoulos, T. P. H. et al. Probing the energy conversion pathways between light, carriers, and lattice in real time with attosecond core-level spectroscopy. Phys. Rev. X 11, 041060 (2021). This work displays a table-top high-energy attosecond transient absorption spectroscopy instrument reaching the carbon K-edge, and it identifies a previously unreported high-frequency phonon oscillation (≳75 THz) in graphite.
Heinrich, T. et al. Electronic and structural fingerprints of charge density wave excitations in extreme ultraviolet transient absorption spectroscopy. Preprint at https://doi.org/10.48550/arXiv.2211.03562 (2022).
Zeiger, H. J. et al. Theory for displacive excitation of coherent phonons. Phys. Rev. B 45, 768–778 (1992).
Giret, Y., Gellé, A. & Arnaud, B. Entropy driven atomic motion in laser-excited bismuth. Phys. Rev. Lett. 106, 155503 (2011).
Gerber, S. et al. Femtosecond electron–phonon lock-in by photoemission and X-ray free-electron laser. Science 357, 71–75 (2017).
Ghimire, S. et al. Observation of high-order harmonic generation in a bulk crystal. Nat. Phys. 7, 138–141 (2011). This work is the first to experimentally observe solid-state high-harmonic generation from a solid ZnO crystal.
You, Y. S., Lu, J., Cunningham, E. F., Roedel, C. & Ghimire, S. Crystal orientation-dependent polarization state of high-order harmonics. Opt. Lett. 44, 530 (2019).
Bionta, M. R. et al. Tracking ultrafast solid-state dynamics using high harmonic spectroscopy. Phys. Rev. Res. 3, 023250 (2021). This work develops the ultrafast capabilities of solid-state high-harmonic generation by observing coherent phonons and measuring phase fractions in the VO2 insulator-to-metal transition.
Bowlan, P., Martinez-Moreno, E., Reimann, K., Elsaesser, T. & Woerner, M. Ultrafast terahertz response of multilayer graphene in the nonperturbative regime. Phys. Rev. B 89, 041408(R) (2014).
Taucer, M. et al. Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light. Phys. Rev. B 96, 195420 (2017).
Yoshikawa, N., Tamaya, T. & Tanaka, K. High-harmonic generation in graphene enhanced by elliptically polarized light excitation. Science 356, 736–738 (2017).
Feng, Y. et al. Semiclassical analysis of ellipticity dependence of harmonic yield in graphene. Phys. Rev. A 104, 43525 (2021).
Mrudul, M. S. & Dixit, G. High-harmonic generation from monolayer and bilayer graphene. Phys. Rev. B 103, 94308 (2021).
Zhang, Y. et al. Orientation dependence of high-order harmonic generation in graphene. Phys. Rev. A 104, 033110 (2021).
Baudisch, M. et al. Ultrafast nonlinear optical response of Dirac fermions in graphene. Nat. Commun. 9, 1018 (2018).
Rana, N., Mrudul, M. S., Kartashov, D., Ivanov, M. & Dixit, G. High-harmonic spectroscopy of coherent lattice dynamics in graphene. Phys. Rev. B 106, 064303 (2022).
Liu, H. et al. High-harmonic generation from an atomically thin semiconductor. Nat. Phys. 13, 262–265 (2017).
Yoshikawa, N. et al. Interband resonant high-harmonic generation by valley polarized electron–hole pairs. Nat. Commun. 10, 3709 (2019).
Heide, C. et al. Probing electron–hole coherence in strongly driven 2D materials using high-harmonic generation. Optica 9, 512–516 (2022). This is a critical work in the advancement of solid-state high-harmonic generation spectroscopy that built on previous results from the model 2D system MoS2 by utilizing ultrafast pump–probe spectroscopy to study carrier dynamics.
Yue, L. et al. Signatures of multiband effects in high-harmonic generation in monolayer MoS2. Phys. Rev. Lett. 129, 147401 (2022). This work is a key amalgamation of theory and experiment in solid-state high-harmonic generation (sHHG), demonstrating unique details in sHHG measurements that show the inherently multiband nature of sHHG.
Lou, Z. et al. Ellipticity dependence of nonperturbative harmonic generation in few-layer MoS2. Opt. Commun. 469, 125769 (2020).
Lv, Y. Y. et al. High-harmonic generation in Weyl semimetal β-WP2 crystals. Nat. Commun. 12, 6437 (2021).
Baykusheva, D. et al. All-optical probe of three-dimensional topological insulators based on high-harmonic generation by circularly polarized laser fields. Nano Lett. 21, 8970–8978 (2021).
Schmid, C. P. et al. Tunable non-integer high-harmonic generation in a topological insulator. Nature 593, 385–390 (2021).
Heide, C. et al. Probing topological phase transitions using high-harmonic generation. Nat. Photonics 16, 620–624 (2022). This is a critical work applying solid-state high-harmonic generation spectroscopy and associated theory to study a topological phase transition in In-doped Bi2Se3.
Ndabashimiye, G. et al. Solid-state harmonics beyond the atomic limit. Nature 534, 520–523 (2016).
You, Y. S. et al. Laser waveform control of extreme ultraviolet high harmonics from solids. Opt. Lett. 42, 1816 (2017).
Vampa, G. et al. Observation of backward high-harmonic emission from solids. Opt. Express 26, 12210–12218 (2018).
Ghimire, S. Locking the waveform with a quartz crystal. Nat. Photonics 12, 256–257 (2018).
Garg, M., Kim, H. Y. & Goulielmakis, E. Ultimate waveform reproducibility of extreme-ultraviolet pulses by high-harmonic generation in quartz. Nat. Photonics 12, 291–296 (2018).
Orenstein, G. et al. Shaping electron–hole trajectories for solid-state high harmonic generation control. Opt. Express 27, 37835 (2019).
Vampa, G. et al. Attosecond synchronization of extreme ultraviolet high harmonics from crystals. J. Phys. B 53, 144003 (2020).
Lesko, D. M. B., Chang, K. F. & Diddams, S. A. High-sensitivity frequency comb carrier–envelope-phase metrology in solid state high harmonic generation. Optica 9, 1156–1162 (2022).
Hollinger, R. et al. Polarization dependent excitation and high harmonic generation from intense mid-IR laser pulses in ZnO. Nanomaterials 11, 11 (2021).
Sing You, Y., Reis, D. A. & Ghimire, S. Anisotropic high-harmonic generation in bulk crystals. Nat. Phys. 13, 345–349 (2017).
Ghimire, S. & Reis, D. A. High-harmonic generation from solids. Nat. Phys. 15, 10–16 (2019).
Goulielmakis, E. & Brabec, T. High harmonic generation in condensed matter. Nat. Photonics 16, 411–421 (2022).
Park, J., Subramani, A., Kim, S. & Ciappina, M. F. Recent trends in high-order harmonic generation in solids. Adv. Phys. X 7, 2003244 (2022). This recent review provides a good introduction to solid-state high-harmonic generation for the unfamiliar reader along with highlighting several key results in the field.
Yue, L. & Gaarde, M. B. Introduction to theory of high-harmonic generation in solids: tutorial. J. Opt. Soc. Am. B 39, 535–555 (2022). This work provides a detailed resource for the current state of the art in theory for modelling solid-state high-harmonic generation (sHHG), allowing the retrieval of critical material properties from sHHG spectra.
Li, J. et al. Attosecond science based on high harmonic generation from gases and solids. Nat. Commun. 11, 2748 (2020). This review of attosecond science provides further reading on how solid-state high-harmonic generation along with attosecond transient absorption spectroscopy can push the limits of time resolution in ultrafast spectroscopy.
Nakagawa, K. et al. Size-controlled quantum dots reveal the impact of intraband transitions on high-order harmonic generation in solids. Nat. Phys. 18, 874–878 (2022).
Vampa, G. et al. All-optical reconstruction of crystal band structure. Phys. Rev. Lett. 115, 193603 (2015).
Huttner, U., Huber, R., Kira, M. & Koch, S. W. Strong-field terahertz excitations in semiconductors. in Encyclopedia of Modern Optics 2nd edn (eds Guenther, B. D. & Steel, D. G.) 33–39 (Elsevier, 2018).
Valovcin, D. C. et al. Optical frequency combs from high-order sideband generation. Opt. Express 26, 29807–29816 (2018).
Langer, F. et al. Lightwave-driven quasiparticle collisions on a subcycle timescale. Nature 533, 225–229 (2016).
Langer, F. et al. Lightwave valleytronics in a monolayer of tungsten diselenide. Nature 557, 76–80 (2018).
Borsch, M. et al. Super-resolution lightwave tomography of electronic bands in quantum materials. Science 370, 1204–1207 (2020).
Nishidome, H. et al. Control of high-harmonic generation by tuning the electronic structure and carrier injection. Nano Lett. 20, 6215–6221 (2020).
Kobayashi, Y. et al. Polarization flipping of even-order harmonics in monolayer transition-metal dichalcogenides. Ultrafast Sci. 2021, 9820716 (2021).
Guan, M.-X. et al. Cooperative evolution of intraband and interband excitations for high-harmonic generation in strained MoS2. Phys. Rev. B 99, 184306 (2019).
He, Y. L., Guo, J., Gao, F. Y. & Liu, X. S. Dynamical symmetry and valley-selective circularly polarized high-harmonic generation in monolayer molybdenum disulfide. Phys. Rev. B 105, 024305 (2022).
Wang, Z. et al. The roles of photo-carrier doping and driving wavelength in high harmonic generation from a semiconductor. Nat. Commun. 8, 1686 (2017).
Neufeld, O., Zhang, J., De Giovannini, U., Hübener, H. & Rubio, A. Probing phonon dynamics with multidimensional high harmonic carrier–envelope-phase spectroscopy. Proc. Natl Acad. Sci. USA 119, e2204219119 (2022).
Giustino F. Electron-phonon interactions from first principles. Rev. Mod. Phys. 89, 015003 (2017).
Fujimoto, M. The Physics of Structural Phase Transitions (Springer, 2005).
Uchida, K. et al. High-order harmonic generation and its unconventional scaling law in the Mott-insulating Ca2RuO4. Phys. Rev. Lett. 128, 127401 (2022).
Alcalà, J. et al. High-harmonic spectroscopy of quantum phase transitions in a high-Tc superconductor. Proc. Natl Acad. Sci. USA 119, e2207766119 (2022).
Luu, T. T. & Wörner, H. J. Measurement of the Berry curvature of solids using high-harmonic spectroscopy. Nat. Commun. 9, 916 (2018).
Xiao, D., Chang, M. C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010).
Bharti, A., Mrudul, M. S. & Dixit, G. High-harmonic spectroscopy of light-driven nonlinear anisotropic anomalous Hall effect in a Weyl semimetal. Phys. Rev. B 105, 155140 (2022).
Yue, L. & Gaarde, M. B. Characterizing anomalous high-harmonic generation in solids. Preprint at https://doi.org/10.48550/arXiv.2206.11935 (2022).
Baykusheva, D. et al. Strong-field physics in three-dimensional topological insulators. Phys. Rev. A 103, 23101 (2021).
Silva, R. E., Blinov, I. V., Rubtsov, A. N., Smirnova, O. & Ivanov, M. High-harmonic spectroscopy of ultrafast many-body dynamics in strongly correlated systems. Nat. Photonics 12, 266–270 (2018).
Murakami, Y., Eckstein, M. & Werner, P. High-harmonic generation in Mott insulators. Phys. Rev. Lett. 121, 57405 (2018).
Tancogne-dejean, N., Sentef, M. A. & Rubio, A. Ultrafast modification of Hubbard U in a strongly correlated material: Ab initio high-harmonic generation in NiO. Phys. Rev. Lett. 121, 97402 (2018).
Imai, S., Ono, A. & Ishihara, S. High harmonic generation in a correlated electron system. Phys. Rev. Lett. 124, 157404 (2020).
Orthodoxou, C., Zaïr, A. & Booth, G. H. High harmonic generation in two-dimensional Mott insulators. npj Quantum Mater. 6, 76 (2021).
Udono, M., Sugimoto, K., Kaneko, T. & Ohta, Y. Excitonic effects on high-harmonic generation in Mott insulators. Phys. Rev. B 105, L241108 (2022).
Murakami, Y., Uchida, K., Koga, A., Tanaka, K. & Werner, P. Anomalous temperature dependence of high-harmonic generation in Mott insulators. Phys. Rev. Lett. 129, 157401 (2022).
Shao, C. et al. High-harmonic generation approaching the quantum critical point of strongly correlated systems. Phys. Rev. Lett. 128, 47401 (2022).
Takayoshi, S., Murakami, Y. & Werner, P. High-harmonic generation in quantum spin systems. Phys. Rev. B 99, 184303 (2019).
Dieny, B. et al. Opportunities and challenges for spintronics in the microelectronics industry. Nat. Electron. 3, 446–459 (2020).
Pirro, P., Vasyuchka, V. I., Serga, A. A. & Hillebrands, B. Advances in coherent magnonics. Nat. Rev. Mater. 6, 1114–1135 (2021).
Zhang, G. P., Si, M. S., Murakami, M., Bai, Y. H. & George, T. F. Generating high-order optical and spin harmonics from ferromagnetic monolayers. Nat. Commun. 9, 916 (2018).
Lysne, M., Murakami, Y., Schüler, M. & Werner, P. High-harmonic generation in spin–orbit coupled systems. Phys. Rev. B 102, 081121(R) (2020).
Torchinsky, D. H. & Hsieh, D. Rotational Anisotropy Nonlinear Harmonic Generation (Springer, 2017).
Denev, S. et al. Magnetic color symmetry of lattice rotations in a diamagnetic material. Phys. Rev. Lett. 100, 257601 (2008).
Padmanabhan, H. et al. Linear and nonlinear optical probe of the ferroelectric-like phase transition in a polar metal, LiOsO3. Appl. Phys. Lett. 113, 122906 (2018).
Jin, W. et al. Observation of a ferro-rotational order coupled with second-order nonlinear optical fields. Nat. Phys. 16, 42–46 (2020).
Fiebig, M., Pavlov, V. V. & Pisarev, R. V. Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals: review. J. Opt. Soc. Am. B 22, 96 (2005).
Fichera, B. T. et al. Second harmonic generation as a probe of broken mirror symmetry. Phys. Rev. B 101, 241106 (2020).
Harter, J. W., Zhao, Z. Y., Yan, J.-Q., Mandrus, D. G. & Hsieh, D. A parity-breaking electronic nematic phase transition in the spin–orbit coupled metal Cd2Re2O7. Science 356, 295–299 (2017).
Zhao, L. et al. A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy. Nat. Phys. 13, 250–254 (2017).
Laurita, N. J. et al. Evidence for a parity broken monoclinic ground state in the S = 1/2 Kagomé antiferromagnet herbertsmithite. Preprint at https://doi.org/10.48550/arXiv.1910.13606 (2019).
Minerbi, E. & Shwartz, S. Difference frequency generation of ultraviolet from X-ray pulses in opaque materials. J. Opt. Soc. Am. B 36, 624 (2019).
Glover, T. E. et al. X-ray and optical wave mixing. Nature 488, 603–608 (2012).
Szlachetko, J. et al. Establishing nonlinearity thresholds with ultraintense X-ray pulses. Sci. Rep. 6, 33292 (2016).
Beye, M. et al. Non-linear soft X-ray methods on solids with MUSIX — the multi-dimensional spectroscopy and inelastic X-ray scattering endstation. J. Condens. Matter Phys. 31, 014003 (2019).
Bohinc, R. et al. Nonlinear XUV-optical transient grating spectroscopy at the Si L2,3-edge. Appl. Phys. Lett. 114, 181101 (2019).
Shwartz, S. et al. X-ray second harmonic generation. Phys. Rev. Lett. 112, 163901 (2014). This work is the first to use X-rays to generate second-harmonic generation signals.
Guetg, M. W. et al. Generation of high-power high-intensity short X-ray free-electron-laser pulses. Phys. Rev. Lett. 120, 014801 (2018).
Huang, Z. & Kim, K.-J. Review of X-ray free-electron laser theory. Phys. Rev. ST Accel. Beams 10, 034801 (2007).
Uzundal, C. B. et al. Polarization-resolved extreme-ultraviolet second-harmonic generation from LiNbO3. Phys. Rev. Lett. 127, 237402 (2021).
Freund, I. & Levine, B. F. Parametric conversion of X-rays. Phys. Rev. Lett. 23, 854–857 (1969).
Eisenberger, P. & McCall, S. L. X-ray parametric conversion. Phys. Rev. Lett. 26, 684–688 (1971).
Fuchs, M. et al. Anomalous nonlinear X-ray Compton scattering. Nat. Phys. 11, 964–970 (2015).
Lam, R. K. et al. Soft X-ray second harmonic generation as an interfacial probe. Phys. Rev. Lett. 120, 023901 (2018). This work first proved the applicability of extreme ultraviolet second-harmonic generation as a surface-sensitive probe.
Yamamoto, S. et al. Element selectivity in second-harmonic generation of GaFeO3 by a soft-X-ray free-electron laser. Phys. Rev. Lett. 120, 223902 (2018).
Schwartz, C. P. et al. Angstrom-resolved interfacial structure in buried organic–inorganic junctions. Phys. Rev. Lett. 127, 096801 (2021). This work further demonstrates the interface sensitivity of extreme ultraviolet second-harmonic generation by applying the technique to buried interfaces in a boron–parylene heterojunction.
Berger, E. et al. Extreme ultraviolet second harmonic generation spectroscopy in a polar metal. Nano Lett. 21, 6095–6101 (2021). This work uses the element-specific symmetry sensitivity of extreme ultraviolet second-harmonic generation to observe Li displacement in the polar metal LiOsO3.
Anderson, P. W. & Blount, E. I. Symmetry considerations on martensitic transformations: ‘ferroelectric’ metals? Phys. Rev. Lett. 14, 532–532 (1965).
Shi, Y. et al. A ferroelectric-like structural transition in a metal. Nat. Mater. 12, 1024–1027 (2013).
Sumi, T. et al. Separating non-linear optical signals of a sample from high harmonic radiation in a soft X-ray free electron laser. e-J. Surf. Sci. Nanotechnol. 20, 31–35 (2022).
Helk, T., Zürch, M. & Spielmann, C. Perspective: towards single shot time-resolved microscopy using short wavelength table-top light sources. Struct. Dyn. 6, 010902 (2019).
Helk, T. et al. Table-top extreme ultraviolet second harmonic generation. Sci. Adv. 7, eabe2265 (2021).
Shi, X. et al. Attosecond light science and its application for probing quantum materials. J. Phys. B 53, 184008 (2020).
Buades, B. et al. Attosecond state-resolved carrier motion in quantum materials probed by soft X-ray XANES. Appl. Phys. Rev. 8, 011408 (2021).
Liu, H., Klein, I. M., Michelsen, J. M. & Cushing, S. K. Element-specific electronic and structural dynamics using transient XUV and soft X-ray spectroscopy. Chem 7, 2569–2584 (2021).
Ramasesha, K., Leone, S. R. & Neumark, D. M. Real-time probing of electron dynamics using attosecond time-resolved spectroscopy. Annu. Rev. Phys. Chem. 67, 41–63 (2016).
Duncan, C. J. R. et al. Multi-scale time-resolved electron diffraction enabled by high repetition rate, high dynamic range direct electron detection. Preprint at https://doi.org/10.48550/arXiv.2206.08404 (2022).
Yu, Y. et al. High-temperature superconductivity in monolayer Bi2Sr2CaCu2O8+δ. Nature 575, 156–163 (2019).
Bie, Y.-Q., Zong, A., Wang, X., Jarillo-Herrero, P. & Gedik, N. A versatile sample fabrication method for ultrafast electron diffraction. Ultramicroscopy 230, 113389 (2021).
Lu, D. et al. Synthesis of freestanding single-crystal perovskite films and heterostructures by etching of sacrificial water-soluble layers. Nat. Mater. 15, 1255–1260 (2016).
Hong, S. S. et al. Two-dimensional limit of crystalline order in perovskite membrane films. Sci. Adv. 3, eaao5173 (2017).
Ji, D. et al. Freestanding crystalline oxide perovskites down to the monolayer limit. Nature 570, 87–90 (2019).
Paskiewicz, D. M., Sichel-Tissot, R., Karapetrova, E., Stan, L. & Fong, D. D. Single-crystalline SrRuO3 nanomembranes: a platform for flexible oxide electronics. Nano Lett. 16, 534–542 (2016).
Kum, H. S. et al. Heterogeneous integration of single-crystalline complex-oxide membranes. Nature 578, 75–81 (2020).
Bakaul, S. R. et al. Single crystal functional oxides on silicon. Nat. Commun. 7, 10547 (2016).
Legros, A. et al. Universal T-linear resistivity and Planckian dissipation in overdoped cuprates. Nat. Phys. 15, 142–147 (2019).
Bruin, J. A. N., Sakai, H., Perry, R. S. & Mackenzie, A. P. Similarity of scattering rates in metals showing T-linear resistivity. Science 339, 804–807 (2013).
Cao, Y. et al. Strange metal in magic-angle graphene with near Planckian dissipation. Phys. Rev. Lett. 124, 076801 (2020).
Lin, Z. et al. Dramatic plasmon response to the charge-density-wave gap development in 1T-TiSe2. Phys. Rev. Lett. 129, 187601 (2022).
Fujimori, A. The chicken and egg question in excitonic insulators. Journal Club for Condensed Matter Physics https://doi.org/10.36471/JCCM_August_2020_01 (2020).
Kong, X.-S., Liang, H., Wu, X.-Y. & Peng, L.-Y. Symmetry analyses of high-order harmonic generation in monolayer hexagonal boron nitride. J. Phys. B 54, 124004 (2021).
Kong, X.-S. et al. Manipulation of the high-order harmonic generation in monolayer hexagonal boron nitride by two-color laser field. J. Chem. Phys. 156, 074701 (2022).
Spies, J. A. et al. Collaboration between experiment and theory in solar fuels research. Chem. Soc. Rev. 48, 1865–1873 (2019).
Husremović, S. et al. Hard ferromagnetism down to the thinnest limit of iron-intercalated tantalum disulfide. J. Am. Chem. Soc. 144, 12167–12176 (2022).
Ahn, Y. et al. Photoinduced domain pattern transformation in ferroelectric–dielectric superlattices. Phys. Rev. Lett. 119, 057601 (2017).
Stoica, V. A. et al. Optical creation of a supercrystal with three-dimensional nanoscale periodicity. Nat. Mater. 18, 377–383 (2019).
Lee, H. J. et al. Structural evidence for ultrafast polarization rotation in ferroelectric/dielectric superlattice nanodomains. Phys. Rev. X 11, 031031 (2021).
Li, Q. et al. Subterahertz collective dynamics of polar vortices. Nature 592, 376–380 (2021).
Yu, Y. et al. Tunable angle-dependent electrochemistry at twisted bilayer graphene with moiré flat bands. Nat. Chem. 14, 267–273 (2022).
Acknowledgements
The authors are grateful for input by Graham Fleming, Craig Schwartz, Anshul Kogar, Hanzhe Liu and Matteo Mitrano. A.Z. acknowledges support from the Miller Institute for Basic Research in Science. B.R.N. acknowledges funding by the National Science Foundation Graduate Research Fellowship Programme. S.-C.L. acknowledges support by the Berkeley–Taiwan Fellowship. J.A.S. acknowledges support by the Arnold O. Beckman Postdoctoral Fellowship Programme. M.Z. acknowledges funding by the W. M. Keck Foundation, funding from the Hellman Fellows Fund, funding from the UC Office of the President within the Multicampus Research Programmes and Initiatives (M21PL3263) and funding from Laboratory Directed Research and Development Programme at Berkeley Lab (107573 and 108232).
Author information
Authors and Affiliations
Contributions
All authors contributed to literature review, manuscript writing, figure composition and article integration. A.Z. and M.Z. conceived the topical focus of this review. M.Z. supervised the project.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Reviews Materials thanks Shambhu Ghimire, Dragan Mihailović and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zong, A., Nebgen, B.R., Lin, SC. et al. Emerging ultrafast techniques for studying quantum materials. Nat Rev Mater (2023). https://doi.org/10.1038/s41578-022-00530-0
Accepted:
Published:
DOI: https://doi.org/10.1038/s41578-022-00530-0