- Open Access
Anisotropy-driven circular high-harmonic generation in semi-Dirac semimetals
Phys. Rev. B 114, 105114 – Published 12 August, 2026
DOI: https://doi.org/10.1103/mxwy-m8zd
Abstract
Generating elliptically polarized higher-order harmonics is essential for probing a wide range of chiral-sensitive light-matter interactions in nature. We demonstrate that semi-Dirac semimetals produce efficient odd-order harmonics under circularly polarized driving fields, remarkably contrasting with known two-dimensional semimetals, where circular polarization typically suppresses high-harmonic generation. The underlying mechanism is attributed to anisotropy-induced dipole coupling, which manifests distinctly in the ellipticity dependence of the harmonic yield. Specifically, the total yield is minimal for linear polarization and rises sharply as the polarization approaches circular, exhibiting nonmonotonic, harmonic-specific behavior. We find that the polarization dependence exhibits a pronounced twofold anisotropy, with each harmonic order showing a distinct angular distribution of maximum intensity. This characteristic anisotropy arises directly from the unique band dispersion of semi-Dirac semimetals. Our results not only uncover a link between anisotropic dispersion and strong-field nonlinear optics, but also position semi-Dirac semimetals as promising platforms for symmetry-engineered and polarization-tailored ultrafast light-matter control.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (72)
- D. N. Basov, R. D. Averitt, and D. Hsieh, Towards properties on demand in quantum materials, Nat. Mater. 16, 1077 (2017).
- N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
- C. Bao, P. Tang, D. Sun, and S. Zhou, Light-induced emergent phenomena in 2D materials and topological materials, Nat. Rev. Phys. 4, 33 (2022).
- A. Bharti, M. Ivanov, and G. Dixit, How massless are Weyl fermions in Weyl semimetals, Phys. Rev. B 108, L020305 (2023).
- J. W. McIver, D. Hsieh, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, Control over topological insulator photocurrents with light polarization, Nat. Nanotechnol. 7, 96 (2012).
- B. Yan and C. Felser, Topological materials: Weyl semimetals, Annu. Rev. Condens. Matter Phys. 8, 337 (2017).
- A. Bharti and G. Dixit, Photocurrent generation in solids via linearly polarized laser, Phys. Rev. B 109, 104309 (2024).
- M. U. Farooq, A. Hashmi, M. Tani, K. Yabana, K. L. Ishikawa, L. Huang, and T. Otobe, Nonlinear Hall effect in bilayer induced by strong laser fields, Phys. Rev. B 112, 035143 (2025).
- N. S. Sirica and R. P. Prasankumar, Shaking up topology with light, Nat. Mater. 20, 283 (2021).
- F. Qin, R. Chen, and C. H. Lee, Light-enhanced nonlinear Hall effect, Commun. Phys. 7, 368 (2024).
- F. Krausz and M. Ivanov, Attosecond physics, Rev. Mod. Phys. 81, 163 (2009).
- 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).
- 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. Photon. 16, 620 (2022).
- M. S. Mrudul, 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).
- N. Saito, P. Xia, F. Lu, T. Kanai, J. Itatani, and N. Ishii, Observation of selection rules for circularly polarized fields in high-harmonic generation from a crystalline solid, Optica 4, 1333 (2017).
- K. Kaneshima, Y. Shinohara, K. Takeuchi, N. Ishii, K. Imasaka, T. Kaji, S. Ashihara, K. L. Ishikawa, and J. Itatani, Polarization-resolved study of high harmonics from bulk semiconductors, Phys. Rev. Lett. 120, 243903 (2018).
- 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).
- 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).
- 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).
- 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).
- 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).
- H. Lakhotia, H. Y. Kim, M. Zhan, S. Hu, S. Meng, and E. Goulielmakis, Laser picoscopy of valence electrons in solids, Nature (London) 583, 55 (2020).
- A. Pattanayak, M. S. Mrudul, and G. Dixit, Influence of vacancy defects in solid high-order harmonic generation, Phys. Rev. A 101, 013404 (2020).
- S. Ghimire and D. A. Reis, High-harmonic generation from solids, Nat. Phys. 15, 10 (2019).
- J. Alcalà, U. Bhattacharya, J. Biegert, M. Ciappina, U. Elu, T. Graß, P. T. Grochowski, M. Lewenstein, A. Palau, T. P. H. Sidiropoulos, et al., High-harmonic spectroscopy of quantum phase transitions in a high-Tc superconductor, Proc. Natl. Acad. Sci. USA 119, e2207766119 (2022).
- L. Li, P. Lan, X. Zhu, and P. Lu, High harmonic generation in solids: Particle and wave perspectives, Rep. Prog. Phys. 86, 116401 (2023).
- C. Heide, Y. Kobayashi, S. R. Ul Haque, and S. Ghimire, Ultrafast high-harmonic spectroscopy of solids, Nat. Phys. 20, 1546 (2024).
- N. Yoshikawa, T. Tamaya, and K. Tanaka, High-harmonic generation in graphene enhanced by elliptically polarized light excitation, Science 356, 736 (2017).
- 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).
- 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).
- Y. Murakami and M. Schüler, Doping and gap size dependence of high-harmonic generation in graphene: Importance of consistent formulation of light-matter coupling, Phys. Rev. B 106, 035204 (2022).
- F. Dong, Q. Xia, and J. Liu, Ellipticity of the harmonic emission from graphene irradiated by a linearly polarized laser, Phys. Rev. A 104, 033119 (2021).
- Y. Zhang, L. Li, J. Li, T. Huang, P. Lan, and P. Lu, Orientation dependence of high-order harmonic generation in graphene, Phys. Rev. A 104, 033110 (2021).
- R. Boyero-García, A. García-Cabrera, O. Zurrón-Cifuentes, C. Hernández-García, and L. Plaja, Non-classical high harmonic generation in graphene driven by linearly-polarized laser pulses, Opt. Express 30, 15546 (2022).
- Z. Guan, Z. Yin, J. You, B. Wang, X. Li, G.-L. Wang, X.-X. Zhou, and C. Jin, Optimal generation and systematic analysis of tunable terahertz emissions from single-layer graphene using two-color laser pulses with different durations, Phys. Rev. A 108, 023515 (2023).
- N. Rana, M. S. Mrudul, D. Kartashov, M. Ivanov, and G. Dixit, High-harmonic spectroscopy of coherent lattice dynamics in graphene, Phys. Rev. B 106, 064303 (2022).
- F. Dong and J. Liu, Knee structure in the laser-intensity dependence of harmonic generation for graphene, Phys. Rev. A 106, 043103 (2022).
- Ó. Zurrón-Cifuentes, R. Boyero-García, C. Hernández-García, A. Picón, and L. Plaja, Optical anisotropy of non-perturbative high-order harmonic generation in gapless graphene, Opt. Express 27, 7776 (2019).
- M. S. Mrudul, Dependence of high-harmonic generation in twisted bilayer graphene on laser pulse ellipticity, Phys. Rev. B 110, 115415 (2024).
- Ó. Zurrón, A. Picón, and L. Plaja, Theory of high-order harmonic generation for gapless graphene, New J. Phys. 20, 053033 (2018).
- C. Liu, Y. Zheng, Z. Zeng, and R. Li, Driving-laser ellipticity dependence of high-order harmonic generation in graphene, Phys. Rev. A 97, 063412 (2018).
- S. A. Sørngård, S. I. Simonsen, and J. P. Hansen, High-order harmonic generation from graphene: Strong attosecond pulses with arbitrary polarization, Phys. Rev. A 87, 053803 (2013).
- L. A. Chizhova, F. Libisch, and J. Burgdörfer, Nonlinear response of graphene to a few-cycle terahertz laser pulse: Role of doping and disorder, Phys. Rev. B 94, 075412 (2016).
- H. K. Avetissian, A. K. Avetissian, G. F. Mkrtchian, and K. V. Sedrakian, Creation of particle-hole superposition states in graphene at multiphoton resonant excitation by laser radiation, Phys. Rev. B 85, 115443 (2012).
- H. K. Avetissian and G. F. Mkrtchian, Impact of electron-electron Coulomb interaction on the high harmonic generation process in graphene, Phys. Rev. B 97, 115454 (2018).
- 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, Non-perturbative nonlinear optical responses in Weyl semimetals, Appl. Phys. Lett. 125, 051104 (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).
- 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).
- L. Wang, M. F. Ciappina, T. Brabec, and X. J. Liu, Tabletop tunable chiral photonic emitter, Phys. Rev. Lett. 133, 113804 (2024).
- S. Kovalev, R. M. A. Dantas, S. Germanskiy, J.-C. Deinert, B. Green, I. Ilyakov, N. Awari, M. Chen, M. Bawatna, J. Ling, et al., Non-perturbative terahertz high-harmonic generation in the three-dimensional Dirac semimetal , Nat. Commun. 11, 2451 (2020).
- B. Cheng, N. Kanda, T. N. Ikeda, T. Matsuda, P. Xia, T. Schumann, S. Stemmer, J. Itatani, N. P. Armitage, and R. Matsunaga, Efficient terahertz harmonic generation with coherent acceleration of electrons in the Dirac semimetal , Phys. Rev. Lett. 124, 117402 (2020).
- J. Lim, Y. S. Ang, F. J. García de Abajo, I. Kaminer, L. K. Ang, and L. J. Wong, Efficient generation of extreme terahertz harmonics in three-dimensional Dirac semimetals, Phys. Rev. Res. 2, 043252 (2020).
- Y. Shao, S. Moon, A. N. Rudenko, J. Wang, J. Herzog-Arbeitman, M. Ozerov, D. Graf, Z. Sun, R. Queiroz, S. H. Lee, et al., Semi-Dirac fermions in a topological metal, Phys. Rev. X 14, 041057 (2024).
- J. Kim, S. S. Baik, S. H. Ryu, Y. Sohn, S. Park, B.-G. Park, J. Denlinger, Y. Yi, H. J. Choi, and K. S. Kim, Observation of tunable band gap and anisotropic Dirac semimetal state in black phosphorus, Science 349, 723 (2015).
- X. Yuan, C. Zhang, Y. Liu, A. Narayan, C. Song, S. Shen, X. Sui, J. Xu, H. Yu, Z. An, et al., Observation of quasi-two-dimensional Dirac fermions in , NPG Asia Mater. 8, e325 (2016).
- M. G. Olmos, Y. Baba, M. Amado, and R. A. Molina, Zero momentum topological insulator in 2D semi-Dirac materials, J. Phys.: Mater. 7, 045008 (2024).
- N. Mohanta, J. M. Ok, J. Zhang, H. Miao, E. Dagotto, H. N. Lee, and S. Okamoto, Semi-Dirac and Weyl fermions in transition metal oxides, Phys. Rev. B 104, 235121 (2021).
- S. Banerjee, R. R. P. Singh, V. Pardo, and W. E. Pickett, Tight-binding modeling and low-energy behavior of the semi-Dirac point, Phys. Rev. Lett. 103, 016402 (2009).
- V. Pardo and W. E. Pickett, Half-metallic semi-Dirac-point generated by quantum confinement in nanostructures, Phys. Rev. Lett. 102, 166803 (2009).
- 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).
- A. Bharti and G. Dixit, Role of topological charges in the nonlinear optical response from Weyl semimetals, Phys. Rev. B 107, 224308 (2023).
- N. Rana, M. S. Mrudul, and G. Dixit, High-harmonic generation from strain-engineered graphene for polarization tailoring, Phys. Rev. B 110, 054103 (2024).
- N. Rana, M. S. Mrudul, A. Bharti, S. Giri, and G. Dixit, Nonlinear optical spectroscopy of nodal line semimetals, Phys. Rev. Appl. 24, L021001 (2025).
- M. S. Mrudul and G. Dixit, High-harmonic generation from monolayer and bilayer graphene, Phys. Rev. B 103, 094308 (2021).
- D. Baykusheva, D. Zindel, V. Svoboda, E. Bommeli, M. Ochsner, A. Tehlar, and H. J. Wörner, Real-time probing of chirality during a chemical reaction, Proc. Natl. Acad. Sci. USA 116, 23923 (2019).
- S. Giri, A. M. Dudzinski, J. C. Tremblay, and G. Dixit, Time-dependent electronic current densities in chiral molecules, Phys. Rev. A 102, 063103 (2020).
- N. Rana and G. Dixit, Probing phonon-driven symmetry alterations in graphene via high-order-harmonic spectroscopy, Phys. Rev. A 106, 053116 (2022).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/mxwy-m8zd for integrated harmonic yield as a function of the driving laser ellipticity and polarization sensitivity of the normalized harmonic yield for a driving wavelength of 2000 nm.
- S. Kandel, G. Gumbs, and O. L. Berman, Anisotropic optical conductivities of model topological nodal-line semimetals, J. Phys.: Condens. Matter 36, 025301 (2024).
- G. Dixit, M. S. Mrudul and K. Prabhu, Data for high-harmonic generation from semi-Dirac materials [Dataset], Zenodo, 2026, https://doi.org/10.5281/zenodo.20079579.