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  • Letter
  • Open Access

Second-harmonic generation in the topological multifold semimetal RhSi

Baozhu Lu1, Sharareh Sayyad2,3, Miguel Ángel Sánchez-Martínez2, Kaustuv Manna4,5, Claudia Felser4, Adolfo G. Grushin2,*, and Darius H. Torchinsky1,†

  • 1Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
  • 2Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
  • 3Max Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
  • 4Max Planck Institute for Chemical Physics of Solids, Dresden D-01187, Germany
  • 5Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India

  • *adolfo.grushin@neel.cnrs.fr.
  • †dtorchin@temple.edu.
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Phys. Rev. Research 4, L022022 – Published 26 April, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L022022

Abstract

Recent experiments in the topological Weyl semimetal TaAs have observed record-breaking second-harmonic generation (SHG), a nonlinear optical response at 2ω generated by an incoming light source at ω. However, whether SHG is enhanced in topological semimetals in general is a challenging open question because their band structure entangles the contributions arising from trivial bands and topological band crossings. In this work, we circumvent this problem by studying RhSi, a chiral topological semimetal with a simple band structure with topological multifold fermions close to the Fermi energy. We measure SHG in a wide frequency window, ω∈[0.27,1.5]eV and, using first-principles calculations, we establish that, due to their linear dispersion, the contribution of multifold fermions to SHG is subdominant as compared with other regions in the Brillouin zone. Our calculations suggest that parts of the bands where the dispersion is relatively flat contribute significantly to SHG. As a whole, our results suggest avenues to enhance SHG responses.

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References (58)

  1. Y. R. Shen, Surface second harmonic generation: A new technique for surface studies, Annu. Rev. Mater. Sci. 16, 69 (1986).
  2. Y. R. Shen, Surface properties probed by second-harmonic and sum-frequency generation, Nature (London) 337, 519 (1989).
  3. A. Dähn, W. Hübner, and K. H. Bennemann, Symmetry Analysis of the Nonlinear Optical Response: Second Harmonic Generation at Surfaces of Antiferromagnets, Phys. Rev. Lett. 77, 3929 (1996).
  4. J. C. Petersen, M. D. Caswell, J. S. Dodge, I. A. Sergienko, J. He, R. Jin, and D. Mandrus, Nonlinear optical signatures of the tensor order in Cd2Re2O7, Nat. Phys. 2, 605 (2006).
  5. J. W. Harter, Z. Y. Zhao, J.-Q. Yan, D. G. Mandrus, and D. Hsieh, A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2 Re2 O7, Science 356, 295 (2017).
  6. N. Sirica, P. P. Orth, M. S. Scheurer, Y. M. Dai, M. C. Lee, P. Padmanabhan, L. T. Mix, S. W. Teitelbaum, M. Trigo, L. X. Zhao, G. F. Chen, B. Xu, R. Yang, B. Shen, C. C. Lee, H. Lin, T. A. Cochran, S. A. Trugman, J. X. Zhu, M. Z. Hasan et al., Photocurrent-driven transient symmetry breaking in the Weyl semimetal TaAs, Nat. Mater. 21, 62 (2022).
  7. V. Mizrahi and J. E. Sipe, Phenomenological treatment of surface second-harmonic generation, J. Opt. Soc. Am. B 5, 660 (1988).
  8. R.-P. Pan, H. D. Wei, and Y. R. Shen, Optical second-harmonic generation from magnetized surfaces, Phys. Rev. B 39, 1229 (1989).
  9. Y. M. Chang, L. Xu, and H. W. K. Tom, Observation of Coherent Surface Optical Phonon Oscillations by Time-Resolved Surface Second-Harmonic Generation, Phys. Rev. Lett. 78, 4649 (1997).
  10. A. Kirilyuk and T. Rasing, Magnetization-induced-second-harmonic generation from surfaces and interfaces, J. Opt. Soc. Am. B 22, 148 (2005).
  11. D. Hsieh, J. W. McIver, D. H. Torchinsky, D. R. Gardner, Y. S. Lee, and N. Gedik, Nonlinear Optical Probe of Tunable Surface Electrons on a Topological Insulator, Phys. Rev. Lett. 106, 057401 (2011).
  12. C. Lee, F. Katmis, P. Jarillo-Herrero, J. S. Moodera, and N. Gedik, Direct measurement of proximity-induced magnetism at the interface between a topological insulator and a ferromagnet, Nat. Commun. 7, 1 (2016).
  13. 2. far-infrared wave generation, in Physical Principles of Far-Infrared Radiation, Methods in Experimental Physics, edited by L.C. Robinson (Academic Press, 1973), Vol. 10, pp. 10–81.
  14. J. Zhao, J. Fan, W. Liu, H. Shi, N. Xiao, and M. Hu, Ultra-broadband second-harmonic generation in ZnO nano-tetrapod with over-one-octave bandwidth, IEEE Photonics Technol. Lett. 31, 250 (2019).
  15. L. Wu, S. Patankar, T. Morimoto, N. L. Nair, E. Thewalt, A. Little, J. G. Analytis, J. E. Moore, and J. Orenstein, Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals, Nat. Phys. 13, 350 (2017).
  16. S. Patankar, L. Wu, B. Lu, M. Rai, J. D. Tran, T. Morimoto, D. E. Parker, A. G. Grushin, N. L. Nair, J. G. Analytis, J. E. Moore, J. Orenstein, and D. H. Torchinsky, Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs, Phys. Rev. B 98, 165113 (2018).
  17. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
  18. H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides, Phys. Rev. X 5, 011029 (2015).
  19. B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Experimental Discovery of Weyl Semimetal TaAs, Phys. Rev. X 5, 031013 (2015).
  20. S.-Ming Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Hasan, A Weyl fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class, Nat. Commun. 6, 7373 (2015).
  21. L. X. Yang, Z. K. Liu, Y. Sun, H. Peng, H. F. Yang, T. Zhang, B. Zhou, Y. Zhang, Y. F. Guo, M. Rahn, D. Prabhakaran, Z. Hussain, S. K. Mo, C. Felser, B. Yan, and Y. L. Chen, Weyl semimetal phase in the non-centrosymmetric compound TaAs, Nat. Phys. 11, 728 (2015).
  22. S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee et al., Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349, 613 (2015).
  23. B. Q. Lv, N. Xu, H. M. Weng, J. Z. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, C. E. Matt, F. Bisti et al., Observation of weyl nodes in taas, Nat. Phys. 11, 724 (2015).
  24. Z. Li, Y.-Q. Jin, T. Tohyama, T. Iitaka, J.-X. Zhang, and H. Su, Second harmonic generation in the Weyl semimetal TaAs from a quantum kinetic equation, Phys. Rev. B 97, 085201 (2018).
  25. G. Chang, S.-Y. Xu, B. J. Wieder, D. S. Sanchez, S.-M. Huang, I. Belopolski, T.-R. Chang, S. Zhang, A. Bansil, H. Lin, and M. Z. Hasan, Unconventional Chiral Fermions and Large Topological Fermi Arcs in RhSi, Phys. Rev. Lett. 119, 206401 (2017).
  26. P. Tang, Q. Zhou, and S.-C. Zhang, Multiple Types of Topological Fermions in Transition Metal Silicides, Phys. Rev. Lett. 119, 206402 (2017).
  27. D. S. Sanchez, I. Belopolski, T. A. Cochran, X. Xu, J. X. Yin, G. Chang, W. Xie, K. Manna, V. Süß, C. Y. Huang, N. Alidoust, D. Multer, S. S. Zhang, N. Shumiya, X. Wang, G. Q. Wang, T. R. Chang, C. Felser, S. Y. Xu, S. Jia et al., Topological chiral crystals with helicoid-arc quantum states, Nature (London) 567, 500 (2019).
  28. T. A. Cochran, G. Chang, I. Belopolski, K. Manna, D. S. Sanchez, Z. Chéng, J.-X. Yin, H. Borrmann, J. Denlinger, C. Felser, H. Lin, and M. Zahid Hasan, A Fermi Arc Quantum Ladder, arXiv:2004.11365 (2020).
  29. J. Buckeridge, D. Jevdokimovs, C. R. A. Catlow, and A. A. Sokol, Bulk electronic, elastic, structural, and dielectric properties of the Weyl semimetal TaAs, Phys. Rev. B 93, 125205 (2016).
  30. J. L. Mañes, Existence of bulk chiral fermions and crystal symmetry, Phys. Rev. B 85, 155118 (2012).
  31. B. J. Wieder, Y. Kim, A. M. Rappe, and C. L. Kane, Double Dirac Semimetals in Three Dimensions, Phys. Rev. Lett. 116, 186402 (2016).
  32. B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals, Science 353, aaf5037 (2016).
  33. G. Chang, B. J. Wieder, F. Schindler, D. S. Sanchez, I. Belopolski, S.-M. Huang, B. Singh, D. Wu, T.-R. Chang, T. Neupert et al., Topological quantum properties of chiral crystals, Nat. Mater. 17, 978 (2018).
  34. D. Rees, K. Manna, B. Lu, T. Morimoto, H. Borrmann, C. Felser, J. E. Moore, D. H. Torchinsky, and J. Orenstein, Helicity-dependent photocurrents in the chiral Weyl semimetal RhSi, Sci. Adv. 6, eaba0509 (2020).
  35. Z. Ni, B. Xu, M.-Á. Sánchez-Martínez, Y. Zhang, K. Manna, C. Bernhard, J. W. F. Venderbos, F. de Juan, C. Felser, A. G. Grushin, and L. Wu, Linear and nonlinear optical responses in the chiral multifold semimetal RhSi, npj Quantum Mater. 5, 96(2020).
  36. Z. Ni, K. Wang, Y. Zhang, O. Pozo, B. Xu, X. Han, K. Manna, J. Paglione, C. Felser, A. G. Grushin et al., Giant topological longitudinal circular photo-galvanic effect in the chiral multifold semimetal CoSi, Nat. Commun. 12 (2021).
  37. Z. H. Levine and D. C. Allan, Linear Optical Response in Silicon and Germanium Including Self-Energy Effects, Phys. Rev. Lett. 63, 1719 (1989).
  38. J. L. P. Hughes and J. E. Sipe, Calculation of second-order optical response in semiconductors, Phys. Rev. B 53, 10751 (1996).
  39. F. Nastos, B. Olejnik, K. Schwarz, and J. E. Sipe, Scissors implementation within length-gauge formulations of the frequency-dependent nonlinear optical response of semiconductors, Phys. Rev. B 72, 045223 (2005).
  40. B. Sadhukhan, Y. Zhang, R. Ray, and J. van den Brink, First-principles calculation of shift current in chalcopyrite semiconductor ZnSnP2, Phys. Rev. Mater. 4, 064602 (2020).
  41. W. Song, G.-Y. Guo, S. Huang, L. Yang, and L. Yang, First-principles studies of second-order nonlinear optical properties of organic-inorganic hybrid halide perovskites, Phys. Rev. Appl. 13, 014052 (2020).
  42. X. Yang, K. Burch, and Y. Ran, Divergent bulk photovoltaic effect in Weyl semimetals, arXiv:1712.09363.
  43. O. Pozo and F. de Juan, Computing observables without eigenstates: Applications to bloch hamiltonians, Phys. Rev. B 102, 115138 (2020).
  44. Z. Rao, H. Li, T. Zhang, S. Tian, C. Li, B. Fu, C. Tang, L. Wang, Z. Li, W. Fan et al., Observation of unconventional chiral fermions with long Fermi arcs in CoSi, Nature (London) 567, 496 (2019).
  45. D. Takane, Z. Wang, S. Souma, K. Nakayama, T. Nakamura, H. Oinuma, Y. Nakata, H. Iwasawa, C. Cacho, T. Kim, K. Horiba, H. Kumigashira, T. Takahashi, Y. Ando, and T. Sato, Observation of Chiral Fermions with a Large Topological Charge and Associated Fermi-Arc Surface States in CoSi, Phys. Rev. Lett. 122, 076402 (2019).
  46. N. B. M. Schröter, D. Pei, M. G. Vergniory, Y. Sun, K. Manna, F. de Juan, J. A. Krieger, V. Süss, M. Schmidt, P. Dudin et al., Chiral topological semimetal with multifold band crossings and long Fermi arcs, Nat. Phys.1 (2019).
  47. N. B. M. Schröter, S. Stolz, K. Manna, F. de Juan, M. G. Vergniory, J. A. Krieger, D. Pei, T. Schmitt, P. Dudin, T. K. Kim, C. Cacho, B. Bradlyn, H. Borrmann, M. Schmidt, R. Widmer, V. N. Strocov, and C. Felser, Observation and control of maximal chern numbers in a chiral topological semimetal, Science 369, 179 (2020).
  48. M. Yao, K. Manna, Q. Yang, A. Fedorov, V. Voroshnin, B. V. Schwarze, J. Hornung, S. Chattopadhyay, Z. Sun, S. N. Guin, J. Wosnitza, H. Borrmann, C. Shekhar, N. Kumar, J. Fink, Y. Sun, and C. Felser, Observation of giant spin-split Fermi-arc with maximal Chern number in the chiral topological semimetal PtGa, Nat. Commun. 11, 2033 (2020).
  49. P. Sessi, F.-R. Fan, F. Küster, K. Manna, N. B. M. Schröter, J.-R. Ji, S. Stolz, J. A. Krieger, D. Pei, T. K. Kim, P. Dudin, C. Cacho, R. Widmer, H. Borrmann, W. Shi, K. Chang, Y. Sun, C. Felser, and S. S. P. Parkin, Handedness-dependent quasiparticle interference in the two enantiomers of the topological chiral semimetal PdGa, Nat. Commun. 11, 3507 (2020).
  50. F. de Juan, A. G. Grushin, T. Morimoto, and J. E. Moore, Quantized circular photogalvanic effect in Weyl semimetals, Nat. Commun. 8, 15995 (2017).
  51. E. J. König, H.-Y. Xie, D. A. Pesin, and A. Levchenko, Photogalvanic effect in Weyl semimetals, Phys. Rev. B 96, 075123 (2017).
  52. F. Flicker, F. de Juan, B. Bradlyn, T. Morimoto, M. G. Vergniory, and A. G. Grushin, Chiral optical response of multifold fermions, Phys. Rev. B 98, 155145 (2018).
  53. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L022022 for details on the experimental measurements, details on calculating the second-harmonic generation response function within the scissor approximation, the SHG in family of transition metal silicides, and further details on the low-energy model discussed in the main text.
  54. A. Gulans, S. Kontur, C. Meisenbichler, D. Nabok, P. Pavone, S. Rigamonti, S. Sagmeister, U. Werner, and C. Draxl, exciting: a full-potential all-electron package implementing density-functional theory and many-body perturbation theory, J. Phys.: Condens. Matter 26, 363202 (2014).
  55. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996).
  56. I. Engström and T. Johnsson, Least-squares refinement of the structure of RhSi (FeSi-type), Acta Chem. Scand. 19, 1508 (1965).
  57. S. Bergfeld and W. Daum, Second-Harmonic Generation in GaAs: Experiment Versus Theoretical Predictions of χxyz(2), Phys. Rev. Lett. 90, 036801 (2003).
  58. L. Z. Tan and A. M. Rappe, Upper limit on shift current generation in extended systems, Phys. Rev. B 100, 085102 (2019).

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Phys. Rev. Research 4, L022022– Published 26 April, 2022
  • Received 18 February 2021
  • Revised 14 May 2021
  • Accepted 8 April 2022
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