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Increase of intensity-dependent excitonic second- and third-harmonic generation induced by static electric fields demonstrated for the exciton of a homobilayer of
Phys. Rev. B 113, 205309 – Published 11 May, 2026
DOI: https://doi.org/10.1103/35yw-mxdh
Abstract
We compute and analyze the dependence of excitonic second- and third-harmonic generation (SHG/THG) as a function of the optical excitation intensity in the presence of static electric fields by solving the semiconductor Bloch equations. Our simulations are performed for excitation of the strongly bound intralayer exciton of an inversion-symmetric homobilayer of with in-plane electric fields. We demonstrate that for resonant excitation at the K-exciton the SHG and the THG show complex dependencies on both the strength of the static field and the peak amplitude of the optical pulse. For sufficiently intense optical excitation, the THG increases and the SHG increases superlinearly with the amplitude of the static field as long as exciton ionization is not yet dominating. Microscopic simulations demonstrate that these dependencies arise from an interplay between several effects including static and transient Stark shifts, exciton ionization, off-resonant Rabi oscillations, and a modified interference between optical nonlinearities induced by the intraband acceleration. Our findings offer several new possibilities for controlling the strong-field dynamics of systems with strongly bound excitons.
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References (117)
- F. Bloch, Über die Quantenmechanik der Elektronen in Kristallgittern, Z. Phys. 52, 555 (1929).
- C. Zener, A theory of the electrical breakdown of solid dielectrics, Proc. R. Soc. A 145, 523 (1934).
- G. H. Wannier, Wave functions and effective Hamiltonian for Bloch electrons in an electric field, Phys. Rev. 117, 432 (1960).
- G. H. Wannier, Dynamics of band electrons in electric and magnetic fields, Rev. Mod. Phys. 34, 645 (1962).
- W. Franz, Einfluß eines elektrischen Feldes auf eine optische Absorptionskante, Z. Naturforsch. 13, 484 (1958).
- L. V. Keldysh, The effect of a strong electric field on the optical properties of insulating crystal, Sov. Phys. JETP 34, 788 (1958).
- K. Tharmalingam, Optical absorption in the presence of a uniform field, Phys. Rev. 130, 2204 (1963).
- K. W. Böer, H. J. Hänsch, and U. Kümmel, Anwendung elektro-optischer Effekte zur Analyse des elektrischen Leitungsvorganges in CdS-Einkristallen, Z. Phys. 155, 170 (1959).
- D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, Band-edge electroabsorption in quantum well structures: The quantum-confined Stark effect, Phys. Rev. Lett. 53, 2173 (1984).
- D. A. B. Miller, D. S. Chemla, and S. Schmitt-Rink, Relation between electroabsorption in bulk semiconductors and in quantum wells: The quantum-confined Franz-Keldysh effect, Phys. Rev. B 33, 6976 (1986).
- F. Cerdeira, C. Vázquez-López, E. Ribeiro, P. A. M. Rodrigues, V. Lemos, M. A. Sacilotti, and A. P. Roth, Franz-Keldysh oscillations in the photomodulated spectra of an strained-layer superlattice, Phys. Rev. B 42, 9480 (1990).
- K. H. Schmidt, N. Linder, G. H. Döhler, H. T. Grahn, K. Ploog, and H. Schneider, Coexistence of Wannier-Stark transitions and miniband Franz-Keldysh oscillations in strongly coupled GaAs-AlAs superlattices, Phys. Rev. Lett. 72, 2769 (1994).
- E. E. Mendez, F. Agulló-Rueda, and J. M. Hong, Stark localization in GaAs-GaAlAs superlattices under an electric field, Phys. Rev. Lett. 60, 2426 (1988).
- P. Voisin, J. Bleuse, C. Bouche, S. Gaillard, C. Alibert, and A. Regreny, Observation of the Wannier-Stark quantization in a semiconductor superlattice, Phys. Rev. Lett. 61, 1639 (1988).
- J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, Optical investigation of Bloch oscillations in a semiconductor superlattice, Phys. Rev. B 46, 7252 (1992).
- C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Köhler, Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice, Phys. Rev. Lett. 70, 3319 (1993).
- P. Leisching, P. Haring Bolivar, W. Beck, Y. Dhaibi, F. Brüggemann, R. Schwedler, and H. Kurz, K. Leo, and K. Köhler, Bloch oscillations of excitonic wave packets in semiconductor superlattices, Phys. Rev. B 50, 14389 (1994).
- G. von Plessen, T. Meier, M. Koch, J. Feldmann, P. Thomas, S. W. Koch, E. O. Göbel, K. W. Goossen, J. M. Kuo, and R. F. Kopf, Exciton ionization induced by an electric field in a strongly coupled superlattice, Phys. Rev. B 53, 13688 (1996).
- 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).
- O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations, Nat. Photon. 8, 119 (2014).
- 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).
- 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).
- 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).
- T. T. Luu and H. J. Wörner, Measurement of the Berry curvature of solids using high-harmonic spectroscopy, Nat. Commun. 9, 916 (2018).
- 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. Photon. 16, 411 (2022).
- 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, and S. Ghimire, Probing topological phase transitions using high-harmonic generation, Nat. Photon. 16, 620 (2022).
- C. Heide, Y. Kobayashi, S. R. U. Haque, and S. Ghimire, Ultrafast high-harmonic spectroscopy of solids, Nat. Phys. 20, 1546 (2024).
- High-Order Harmonic Generation in Solids, edited by M. Ciappina and P. Tzallas (World Scientific, Singapore, 2024).
- J. Zhang, X. Liu, T.-D. Tran, W. Xu, W. Yu, C. Zhang, Z. Wang, L. Geng, J. Zhang, L.-Y. Peng, S. Y. Kruchinin, and T. T. Luu, Noncollinear harmonic spectroscopy reveals crossover of strong-field effects, Nat. Commun. 16, 7660 (2025).
- M. Kira and R. Huber, Unlocking lightwave electronics, Opt. Photon. News 36, 28 (2025).
- C. Schmidt, J. Bühler, A.-C. Heinrich, J. Allerbeck, R. Podzimski, D. Berghoff, T. Meier, W. G. Schmidt, C. Reichl, W. Wegscheider, D. Brida, and A. Leitenstorfer, Signatures of transient Wannier-Stark localization in bulk gallium arsenide, Nat. Commun. 9, 2890 (2018).
- H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 5th ed. (World Scientific, Singapore, 2009).
- H. Kalt and C. F. Klingshirn, Semiconductor Optics 1 (Springer, Cham, 2019).
- C. Gähwiller and G. Harbeke, Excitonic effects in the electroreflectance of lead iodide, Phys. Rev. 185, 1141 (1969).
- H. Lange and E. Gutsche, Electroabsorption of CdS and CdSe single crystals in the exciton region, Phys. Status Solidi B 32, 293 (1969).
- D. F. Blossey, Wannier exciton in an electric field. II. Electroabsorption in direct-band-gap solids, Phys. Rev. B 3, 1382 (1971).
- S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, Linear and nonlinear optical properties of semiconductor quantum wells, Adv. Phys. 38, 89 (1989).
- M. M. Dignam and J. E. Sipe, Exciton Stark ladder in superlattices, Phys. Rev. Lett. 64, 1797 (1990).
- N. Linder, Excitons in superlattices: Absorption asymmetry, dimensionality transition, and exciton localization, Phys. Rev. B 55, 13664 (1997).
- S. T. Cundiff, A. Knorr, J. Feldmann, S. W. Koch, E. O. Göbel, and H. Nickel, Rabi flopping in semiconductors, Phys. Rev. Lett. 73, 1178 (1994).
- A. Schülzgen, R. Binder, M. E. Donovan, M. Lindberg, K. Wundke, H. M. Gibbs, G. Khitrova, and N. Peyghambarian, Direct observation of excitonic Rabi oscillations in semiconductors, Phys. Rev. Lett. 82, 2346 (1999).
- L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Wiley, New York, 1975).
- T. Suzuki, R. Singh, M. Bayer, A. Ludwig, A. D. Wieck, and S. T. Cundiff, Detuning dependence of Rabi oscillations in an InAs self-assembled quantum dot ensemble, Phys. Rev. B 97, 161301(R) (2018).
- D. Fröhlich, A. Nöthe, and K. Reimann, Observation of the resonant optical Stark effect in a semiconductor, Phys. Rev. Lett. 55, 1335 (1985).
- A. Mysyrowicz, D. Hulin, A. Antonetti, A. Migus, W. T. Masselink, and H. Morkoc, Dressed excitons in amultiple-quantum-well structure: Evidence for an optical Stark effect with femtosecond response time, Phys. Rev. Lett. 56, 2748 (1986).
- A. Von Lehmen, D. S. Chemla, J. E. Zucker, and J. P. Heritage, Optical Stark effect on excitons in GaAs quantum wells, Opt. Lett. 11, 609 (1986).
- C. Sieh, T. Meier, F. Jahnke, A. Knorr, S. W. Koch, P. Brick, M. Hübner, C. Ell, J. Prineas, G. Khitrova, and H. M. Gibbs, Coulomb memory signatures in the excitonic optical Stark effect, Phys. Rev. Lett. 82, 3112 (1999).
- K. B. Nordstrom, K. Johnsen, S. J. Allen, A.-P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, Excitonic dynamical Franz-Keldysh effect, Phys. Rev. Lett. 81, 457 (1998).
- Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, Electronics and optoelectronics of two-dimensional transition metal dichalcogenides, Nat. Nanotechnol. 7, 699 (2012).
- D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Coupled spin and valley physics in monolayers of and other Group-VI dichalcogenides, Phys. Rev. Lett. 108, 196802 (2012).
- X. Xu, W. Yao, D. Xiao, and T. F. Heinz, Spin and pseudospins in layered transition metal dichalcogenides, Nat. Phys. 10, 343 (2014).
- A. Manchon, H. C. Koo, J. Nitta, S. M. Frolov, and R. A. Duine, New perspectives for Rashba spin-orbit coupling, Nat. Mater. 14, 871 (2015).
- G. Moody, C. K. Dass, K. Hao, C.-H. Chen, L.-J. Li, A. Singh, K. Tran, G. Clark, X. Xu, G. Berghäuser, E. Malic, A. Knorr, and X. Li, Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides, Nat. Commun. 6, 8315 (2015).
- 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).
- J. Klein, J. Wierzbowski, A. Steinhoff, M. Florian, M. Rösner, F. Heimbach, K. Müller, F. Jahnke, T. O. Wehling, J. J. Finley, and M. Kaniber, Electric-field switchable second-harmonic generation in bilayer by inversion symmetry breaking, Nano Lett. 17, 392 (2017).
- M. Selig, G. Berghäuser, A. Raja, P. Nagler, C. Schüller, T. F. Heinz, T. Korn, A. Chernikov, E. Malic, and A. Knorr, Excitonic linewidth and coherence lifetime in monolayer transition metal dichalcogenides, Nat. Commun. 7, 13279 (2016).
- H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, High-harmonic generation from an atomically thin semiconductor, Nat. Phys. 13, 262 (2017).
- G. Wang, A. Chernikov, M. M. Glazov, T. F. Heinz, X. Marie, T. Amand, and B. Urbaszek, Colloquium: Excitons in atomically thin transition metal dichalcogenides, Rev. Mod. Phys. 90, 021001 (2018).
- K. F. Mak, D. Xiao, and J. Shan, Light-valley interactions in 2D semiconductors, Nat. Photon. 12, 451 (2018).
- R. Ribeiro-Palau, C. Zhang, K. Watanabe, T. Taniguchi, and J. Hone, and C. R. Dean, Twistable electronics with dynamically rotatable heterostructures, Science 361, 690 (2018).
- F. Langer, C. P. Schmid, S. Schlauderer, M. Gmitra, J. Fabian, P. Nagler, C. Schüller, T. Korn, P. G. Hawkins, J. T. Steiner, U. Huttner, S. W. Koch, M. Kira, and R. Huber, Lightwave valleytronics in a monolayer of tungsten diselenide, Nature (London) 557, 76 (2018).
- T. Muelller and E. Malic, Exciton physics and device application of two-dimensional transition metal dichalcogenide semiconductors, npj 2D Mater. Appl. 2, 29 (2018).
- N. Yoshikawa, K. Nagai, K. Uchida, Y. Takaguchi, S. Sasaki, Y. Miyata, and K. Tanaka, Interband resonant high-harmonic generation by valley polarized electron-hole pairs, Nat. Commun. 10, 3709 (2019).
- C. Trovatello, F. Katsch, N. J. Borys, M. Selig, K. Yao, R. Borrego-Varillas, F. Scotognella, I. Kriegel, A. Yan, A. Zettl, P. J. Schuck, A. Knorr, G. Cerullo, and S. D. Conte, The ultrafast onset of exciton formation in 2D semiconductors, Nat. Commun. 11, 5277 (2020).
- S. Shree, D. Lagarde, L. Lombez, C. Robert, A. Balocchi, K. Watanabe, T. Taniguchi, X. Marie, I. C. Gerber, M. M. Glazov, L. E. Golub, B. Urbaszek, and I. Paradisanos, Interlayer exciton mediated second harmonic generation in bilayer , Nat. Commun. 12, 6894 (2021).
- S. Helmrich, K. Sampson, D. Huang, M. Selig, K. Hao, K. Tran, A. Achstein, C. Young, A. Knorr, E. Malic, U. Woggon, N. Owschimikow, and X. Li, Phonon-assisted intervalley scattering determines ultrafast exciton dynamics in bilayers, Phys. Rev. Lett. 127, 157403 (2021).
- A. Ciarrocchi, F. Tagarelli, A. Avsar, and A. Kis, Excitonic devices with van der Waals heterostructures: Valleytronics meets twistronics, Nat. Rev. Mater. 7, 449 (2022).
- 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).
- J. Hader, J. Neuhaus, J. V. Moloney, and S. W. Koch, Coulomb enhancement of high harmonic generation in monolayer transition metal dichalcogenides, Opt. Lett. 48, 2094 (2023).
- V. C. Lee, L. Yue, M. B. Gaarde, Y. Chan, and D. Y. Qiu, Many-body enhancement of high-harmonic generation in monolayer , Nat. Commun. 15, 6228 (2024).
- B. Scharf, T. Frank, M. Gmitra, J. Fabian, I. Žutić, and V. Perebeinos, Excitonic Stark effect in monolayers, Phys. Rev. B 94, 245434 (2016).
- T. G. Pedersen, Exciton Stark shift and electroabsorption in monolayer transition-metal dichalcogenides, Phys. Rev. B 94, 125424 (2016).
- M. Massicotte, F. Vialla, P. Schmidt, M. B. Lundeberg, S. Latini, S. Haastrup, M. Danovich, D. Davydovskaya, K. Watanabe, T. Taniguchi, V. I. Fal'ko, K. S. Thygesen, T. G. Pedersen, and F. H. L. Koppens, Dissociation of two-dimensional excitons in monolayer , Nat. Commun. 9, 1633 (2018).
- B. Zhu, K. Xiao, S. Yang, K. Watanabe, T. Taniguchi, and X. Cui, In-plane electric-field-induced orbital hybridization of excitonic states in monolayer , Phys. Rev. Lett. 131, 036901 (2023).
- S. Klimmer, T. Lettau, L. V. Molina, D. Kartashov, U. Peschel, J. Wilhelm, D. Neshev, and G. Soavi, Probing ultrafast coherent bandgap modulation in monolayer by nonlinear optics, Adv. Opt. Mater. 14, e03236 (2026).
- D. Golde, T. Meier, and S. W. Koch, High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations, Phys. Rev. B 77, 075330 (2008).
- C. Ngo, S. Priyadarshi, H. T. Duc, M. Bieler, and T. Meier, Excitonic anomalous currents in semiconductor quantum wells, Phys. Rev. B 108, 165302 (2023).
- The band structure and wave functions were computed with the Elk code which was obtained from, http://elk.sourceforge.net/.
- N. Bloembergen and P. S. Pershan, Light waves at the boundary of nonlinear media, Phys. Rev. 128, 606 (1962).
- R. W. Boyd, Nonlinear Optics, 4th ed. (Academic Press, New York, 2020).
- H. Fan, A. Proskurin, M. Song, and A. Bogdanov, Electric-field-induced second-harmonic generation, Opto-Electron. Adv. 9, 250193 (2026).
- J. Lee, K. F. Mak, and J. Shan, Electrical control of the valley Hall effect in bilayer transistors, Nat. Nanotechnol. 11, 421 (2016).
- A. Kormányos, V. Zólyomi, V. I. Fal'ko, and G. Burkard, Tunable Berry curvature and valley and spin Hall effect in bilayer , Phys. Rev. B 98, 035408 (2018).
- Z. Gong, G. Liu, H. Yu, D. Xiao, X. Cui, X. Xu, and W. Yao, Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers, Nat. Commun. 4, 2053 (2013).
- S. Wu, J. S. Ross, G.-B. Liu, G. Aivazian, A. Jones, Z. Fei, W. Zhu, D. Xiao, W. Yao, D. Cobden, and X. Xu, Electrical tuning of valley magnetic moment through symmetry control in bilayer , Nat. Phys. 9, 149 (2013).
- D. Vanderbilt, Berry Phase in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators (Cambridge University Press, Cambridge, UK, 2018).
- C. Aversa and J. E. Sipe, Nonlinear optical susceptibilities of semiconductors: Results with a length-gauge analysis, Phys. Rev. B 52, 14636 (1995).
- K. S. Virk and J. E. Sipe, Semiconductor optics in length gauge: A general numerical approach, Phys. Rev. B 76, 035213 (2007).
- L. Meckbach, T. Stroucken, and S. W. Koch, Influence of the effective layer thickness on the ground-state and excitonic properties of transition-metal dichalcogenide systems, Phys. Rev. B 97, 035425 (2018).
- U. Huttner, M. Kira, and S. W. Koch, Ultrahigh off-resonant field effects in semiconductors, Laser Photon. Rev. 11, 1700049 (2017).
- L. Yue and M. B. Gaarde, Structure gauges and laser gauges for the semiconductor Bloch equations in high-order harmonic generation in solids, Phys. Rev. A 101, 053411 (2020).
- L. H. Thong, C. Ngo, H. T. Duc, X. Song, and T. Meier, Microscopic analysis of high harmonic generation in semiconductors with degenerate bands, Phys. Rev. B 103, 085201 (2021).
- G.-B. Liu, D. Xiao, Y. Yao, X. Xu, and W. Yao, Electronic structures and theoretical modelling of two-dimensional group-VIB transition metal dichalcogenides, Chem. Soc. Rev. 44, 2643 (2015).
- C. Louca, A. Genco, S. Chiavazzo, T. P. Lyons, S. Randerson, C. Trovatello, P. Claronino, R. Jayaprakash, X. Hu, J. Howarth, K. Watanabe, T. Taniguchi, S. Dal Conte, R. Gorbachev, D. G. Lidzey, G. Cerullo, O. Kyriienko, and A. I. Tartakovskii, Interspecies exciton interactions lead to enhanced nonlinearity of dipolar excitons and polaritons in homobilayers, Nat. Commun. 14, 3818 (2023).
- D. Erben, A. Steinhoff, C. Gies, G. Schönhoff, and T. O. Wehling, and F. Jahnke, Excitation-induced transition to indirect band gaps in atomically thin transition-metal dichalcogenide semiconductors, Phys. Rev. B 98, 035434 (2018).
- B. Datta, M. Khatoniar, P. Deshmukh, F. Thouin, R. Bushati, S. De Liberato, S. Kena Cohen, and V. M. Menon, Highly nonlinear dipolar exciton-polaritons in bilayer , Nat. Commun. 13, 6341 (2022).
- N. Peimyoo, T. Deilmann, F. Withers, J. Escolar, D. Nutting, T. Taniguchi, K. Watanabe, A. Taghizadeh, M. F. Craciun, K. S. Thygesen, and S. Russo, Electrical tuning of optically active interlayer excitons in bilayer , Nat. Nanotechnol. 16, 888 (2021).
- H. C. Kamban and T. G. Pedersen, Efficient ionization of two-dimensional excitons by intense single-cycle terahertz pulses, Phys. Rev. B 104, 235305 (2021).
- M. Glück, F. Keck, A. R. Kolovsky, and H. J. Korsch, Wannier-Stark states of a quantum particle in 2D lattices, Phys. Rev. Lett. 86, 3116 (2001).
- A. R. Kolovsky and E. N. Bulgakov, Wannier-Stark states and Bloch oscillations in the honeycomb lattice, Phys. Rev. A 87, 033602 (2013).
- T. Meier, G. von Plessen, P. Thomas, and S. W. Koch, Coherent electric-field effects in semiconductors, Phys. Rev. Lett. 73, 902 (1994).
- M. Dignam, J. E. Sipe, and J. Shah, Coherent excitations in the Stark ladder: Excitonic Bloch oscillations, Phys. Rev. B 49, 10502 (1994).
- T. Meier, G. von Plessen, P. Thomas, and S. W. Koch, Coherent effects induced by static and time-dependent electric fields in semiconductors, Phys. Rev. B 51, 14490 (1995).
- F. Schlaepfer, M. Lucchini, S. A. Sato, M. Volkov, L. Kasmi, N. Hartmann, A. Rubio, L. Gallmann, and U. Keller, Attosecond optical-field-enhanced carrier injection into the GaAs conduction band, Nat. Phys. 14, 560 (2018).
- K. Nakagawa, H. Hirori, S. A. Sato, H. Tahara, F. Sekiguchi, G. Yumoto, M. Saruyama, R. Sato, T. Teranishi, and Y. Kanemitsu, Size-controlled quantum dots reveal the impact of intraband transitions on high-order harmonic generation in solids, Nat. Phys. 18, 874 (2022).
- S. Yu Kruchinin, F. Krausz, and V. S. Yakovlev, Colloquium: Strong-field phenomena in periodic systems, Rev. Mod. Phys. 90, 021002 (2018).
- D. H. Dunlap and V. M. Kenkre, Dynamic localization of a charged particle moving under the influence of an electric field, Phys. Rev. B 34, 3625 (1986).
- M. Holthaus, Collapse of minibands in far-infrared irradiated superlattices, Phys. Rev. Lett. 69, 351 (1992).
- T. Meier, F. Rossi, P. Thomas, and S. W. Koch, Dynamic localization in anisotropic Coulomb systems: Field induced crossover of the exciton dimension, Phys. Rev. Lett. 75, 2558 (1995).
- J. H. Shirley, Solution of the Schrödinger equation with a Hamiltonian periodic in time, Phys. Rev. 138, B979 (1965).
- M. Grifoni and P. Hänggi, Driven quantum tunneling, Phys. Rep. 304, 229 (1998).
- W. C. Henneberger, Perturbation method for atoms in intense light beams, Phys. Rev. Lett. 21, 838 (1968).
- F. Grossmann, T. Dittrich, P. Jung, and P. Hänggi, Coherent destruction of tunneling, Phys. Rev. Lett. 67, 516 (1991).
- J. H. Eberly and K. C. Kulander, Atomic stabilization by super-intense lasers, Science 262, 1229 (1993).
- R. Zuo, M. Reichelt, C. Ngo, X. Song, W. Yang, and T. Meier, Unexpected increase of intensity-dependent excitonic second- and third-harmonic generation induced by static electric fields demonstrated for the K exciton of a 2H homobilayer of [Data set], Zenodo (2026), https://doi.org/10.5281/zenodo.19113310.
- W.-R. Hannes and T. Meier, Higher-order contributions and nonperturbative effects in the nondegenerate nonlinear optical absorption of semiconductors using a two-band model, Phys. Rev. B 99, 125301 (2019).