Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Visible and terahertz nonlinear responses in the topological noble metal dichalcogenide PdTe2

George J. de Coster1,2,*,†, Lucas Lafeta3,*,‡, Stefan Heiserer1, Cormac Ó Coileáin1, Zdenek Sofer4, Achim Hartschuh3, Georg S. Duesberg1, and Paul Seifert1,§

  • *These authors contributed equally to this work.
  • †Contact author: george.j.decoster.civ@army.mil
  • ‡Contact author: lucas.lafeta@cup.lmu.de
  • §Contact author: paul.seifert@unibw.de

Phys. Rev. B 113, 165419 – Published 20 April, 2026

DOI: https://doi.org/10.1103/x5kl-blc5

Abstract

Nonlinear processes can offer pathways to next-generation sensors and frequency mixing devices to overcome modern imaging, detection, and communication challenges. In this article, we report on strong second- and third-order nonlinear optical responses in visible and terahertz light in single crystals of the noble metal dichalcogenide PdTe2. We find that buried conduction and valence topological surface states of PdTe2 lead to resonant optical second-harmonic generation. On the other hand, although the nonlinear responses obtained with terahertz excitation are not close to this resonance, they can be clearly observed in reflection geometry, even in the presence of broadband excitation, where optical filters are not necessary to observe the enhanced odd-order higher harmonic output. By carefully considering the radiative photocurrent framework of stimulated terahertz emission, we are able to extract fingerprints of both second- and third-order processes in the terahertz regime, and show that PdTe2 is a promising material candidate for radio-frequency rectification, frequency mixing, and beam focusing.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (74)

  1. J. Orenstein, J. E. Moore, T. Morimoto, D. H. Torchinsky, J. W. Harter, and D. Hsieh, Topology and symmetry of quantum materials via nonlinear optical responses, Annu. Rev. Condens. Matter Phys. 12, 247 (2021).
  2. J. Shi et al., Giant room-temperature nonlinearities in a monolayer Janus topological semiconductor, Nat. Commun. 14, 4953 (2023).
  3. I. Sodemann and L. Fu, Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials, Phys. Rev. Lett. 115, 216806 (2015).
  4. Y. Onishi and L. Fu, High-efficiency energy harvesting based on a nonlinear Hall rectifier, Phys. Rev. B 110, 075122 (2024).
  5. H. Wu, Y. Wang, Y. Xu, P. K. Sivakumar, C. Pasco, U. Filippozzi, S. S. P. Parkin, Y.-J. Zeng, T. McQueen, and M. N. Ali, The field-free Josephson diode in a van der Waals heterostructure, Nature (London) 604, 653 (2022).
  6. P. K. Sivakumar, M. T. Ahari, J.-K. Kim, Y. Wu, A. Dixit, G. J. de Coster, A. K. Pandeya, M. J. Gilbert, and S. S. P. Parkin, Long-range phase coherence and tunable second order φ0-Josephson effect in a Dirac semimetal 1T−PtTe2, Commun. Phys. 7, 354 (2024).
  7. Y. Liu and Q. Shao, Two-dimensional materials for energy-efficient spin-orbit torque devices, ACS Nano 14, 9389 (2020).
  8. J. Hidding, K. Mërtiri, F. Mujid, C. Liang, J. Park, and M. H. D. Guimarães, Role of self-torques in transition metal dichalcogenide/ferromagnet bilayers, Phys. Rev. B 108, 064419 (2023).
  9. B. C. Connelly, P. J. Taylor, and G. J. de Coster, Emergence of threefold symmetric helical photocurrents in epitaxial low twinned Bi2Se3, Proc. Natl. Acad. Sci. USA 121, e2307425121 (2024).
  10. H. Plank et al., Infrared/terahertz spectra of the photogalvanic effect in (Bi, Sb)Te based three-dimensional topological insulators, Phys. Rev. Mater. 2, 024202 (2018).
  11. Y.-M. Xie and N. Nagaosa, Photon-drag photovoltaic effects and quantum geometric nature, Proc. Natl. Acad. Sci. USA 122, e2424294122 (2025).
  12. M. Hemmat et al., Layer-controlled nonlinear terahertz valleytronics in two-dimensional semimetal and semiconductor PtSe2, InfoMat 5, e12468 (2023).
  13. Y. Pan et al., Helicity dependent photocurrent in electrically gated (Bi1−xSbx)2Te3 thin films, Nat. Commun. 8, 1037 (2017).
  14. F. Hu, P. Zhao, L. Yang, S. Zhao, J. Lei, W. Li, J. Lai, Z. Yu, H. Park, C. Wong, R. Sharma, G. Eda, S. A. Yang, X. Xu, F. Wang, and H. Yang, Ultrabroadband nonlinear Hall rectifier using SnTe, Nat. Nanotechnol. 20, 1588 (2025).
  15. Y. Zhang and L. Fu, Terahertz detection based on nonlinear Hall effect without magnetic field, Proc. Natl. Acad. Sci. USA 118, e2100736118 (2021).
  16. C. Yim, K. Lee, N. McEvoy, M. O'Brien, S. Riazimehr, N. C. Berner, C. P. Cullen, J. Kotakoski, J. C. Meyer, M. C. Lemme, and G. S. Duesberg, High-performance hybrid electronic devices from layered PtSe2 films grown at low temperature, ACS Nano 10, 9550 (2016).
  17. J. B. McManus, D. V. Horvath, M. P. Browne, C. P. Cullen, G. Cunningham, T. Hallam, K. Zhussupbekov, D. Mullarkey, C. Ó Coileáin, I. V. Shvets, M. Pumera, G. S. Duesberg, and N. McEvoy, Low-temperature synthesis and electrocatalytic application of large-area PtTe2 thin films, Nanotechnology 31, 375601 (2020).
  18. W. Zheng et al., Detailed study of the Fermi surfaces of the type-II Dirac semimetallic candidates XTe2 (X = Pd, Pt), Phys. Rev. B 97, 235154 (2018).
  19. O. J. Clark et al., Fermiology and superconductivity of topological surface states in PdTe2, Phys. Rev. Lett. 120, 156401 (2018).
  20. M. N. Ali et al., Galvanomagnetic properties of the putative type-II Dirac semimetal PtTe2, Sci. Rep. 8, 15383 (2018).
  21. Y. Wang et al., De Hass-van Alphen and magnetoresistance reveal predominantly single-band transport behavior in PdTe2, Sci. Rep. 6, 31554 (2016).
  22. K. Zhussupbekov, L. Ansari, J. B. McManus, A. Zhussupbekova, I. V. Shvets, G. S. Duesberg, P. K. Hurley, F. Gity, C. Coileáin, and N. McEvoy, Imaging and identification of point defects in PtTe2, npj 2D Mater. Appl. 5, 14 (2021).
  23. M. K. Lin, R. A. B. Villaos, J. A. Hlevyak, P. Chen, R.-Y. Liu, C.-H. Hsu, J. Avila, S.-K. Mo, F.-C. Chuang, and T.-C. Chiang, Dimensionality-mediated semimetal-semiconductor transition in ultrathin PtSe2 films, Phys. Rev. Lett. 124, 036402 (2020).
  24. Q. Gao et al., Layer-dependent band gaps of platinum dichalcogenides, ACS Nano 15, 13249 (2021).
  25. Z. Huang et al., Crossover from 2D metal to 3D Dirac semimetal in metallic PtTe2 films, Mater. Today Phys. 11, 100161 (2019).
  26. S. M. Faizanuddin, C.-H. Chien, Y.-J. Chan, S.-T. Liu, C.-N. Kuo, C. S. Lue, and Y.-C. Wen, Surface second harmonic generation from topological Dirac semimetal PdTe2, arXiv:2308.09053.
  27. G. Wang, K. Wang, N. McEvoy, Z. Bai, C. P. Cullen, C. N. Murphy, J. B. McManus, J. J. Magan, C. M. Smith, G. S. Duesberg, I. Kaminer, J. Wang, and W. J. Blau, Ultrafast carrier dynamics and bandgap renormalization in layered PtSe2, Small 15, 1902728 (2019).
  28. H. Wang, C. Zhang, and F. Rana, Surface recombination limited lifetimes of photoexcited carriers in few-layer transition metal dichalcogenide MoS2, Nano Lett. 15, 8204 (2015).
  29. L. Chu, Z. Li, H. Zhu, H. Lv, and F. Chen, Intense second-harmonic generation in two-dimensional PtSe2, Nanophotonics 13, 3457 (2024).
  30. C. Guo et al., Anisotropic ultrasensitive PdTe2-based phototransistor for room-temperature long-wavelength detection, Sci. Adv. 6, eabb6500 (2020).
  31. C. Yim, V. Passi, M. C. Lemme, G. S. Duesberg, C. Ó Coileáin, E. Pallecchi, D. Fadil, and N. McEvoy, Electrical devices from top-down structured platinum diselenide films, npj 2D Mater. Appl. 2, 5 (2018).
  32. Z. Peng, X. Chen, Y. Fan, D. J. Srolovitz, and D. Lei, Strain engineering of 2D semiconductors and graphene: From strain fields to band-structure tuning and photonic applications, Light: Sci. Appl. 9, 190 (2020).
  33. X. Ge, X. Zhou, D. Sun, and X. Chen, First-principles study of structural and electronic properties of monolayer PtX2 and Janus PtXY (X,Y=S,Se, and Te) via strain engineering, ACS Omega 8, 5715 (2023).
  34. M. Cai et al., Giant room-temperature terahertz photothermoelectric response mediated by hot carriers at the metal-semimetal interfaces, Sci. Adv. 11, eadv0768 (2025).
  35. S. Heiserer et al., Impact of strain in free-standing PtSe2 in scalable 2D MEMS, Adv. Mater. 37, e12564 (2025).
  36. L. M. Malard, T. V. Alencar, A. P. M. Barboza, K. F. Mak, and A. M. de Paula, Observation of intense second harmonic generation from MoS2 atomic crystals, Phys. Rev. B 87, 201401(R) (2013).
  37. Y. Li, Y. Rao, K. F. Mak, Y. You, S. Wang, C. R. Dean, and T. F. Heinz, Probing symmetry properties of few-layer MoS2 and h-BN by optical second-harmonic generation, Nano Lett. 13, 3329 (2013).
  38. L. Lafeta, S. Hartmann, B. Rosa, S. Reitzenstein, L. M. Malard, and A. Hartschuh, Probing noncentrosymmetric 2D materials by Fourier space second harmonic imaging, ACS Photonics 12, 357 (2025).
  39. L. Lafeta et al., Second- and third-order optical susceptibilities across excitons states in 2D monolayer transition metal dichalcogenides, 2D Mater. 8, 035010 (2021).
  40. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, Burlington, 2008).
  41. 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).
  42. J. W. McIver, D. Hsieh, S. G. Drapcho, D. H. Torchinsky, D. R. Gardner, Y. S. Lee, and N. Gedik, Theoretical and experimental study of second harmonic generation from the surface of the topological insulator Bi2Se3, Phys. Rev. B 86, 035327 (2012).
  43. Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, New York, 1984).
  44. J. Yu et al., Giant nonlinear optical activity in two-dimensional palladium diselenide, Nat. Commun. 12, 1080 (2021).
  45. A. Virga et al., Coherent anti-Stokes Raman spectroscopy of single and multi-layer graphene, Nat. Commun. 10, 3658 (2019).
  46. G. Gordeev, L. Lafeta, B. S. Flavel, A. Jorio, and L. M. Malard, Excitonic resonances in coherent anti-Stokes Raman scattering from single-walled carbon nanotubes, J. Phys. Chem. C 127, 20438 (2023).
  47. L. Lafeta et al., Anomalous nonlinear optical response of graphene near phonon resonances, Nano Lett. 17, 3447 (2017).
  48. L. Lange et al., Ultrafast phase-control of the nonlinear optical response of 2D semiconductors, ACS Photonics 11, 3112 (2024).
  49. X. Wen, Z. Gong, and D. Li, Nonlinear optics of two-dimensional transition metal dichalcogenides, InfoMat 1, 317 (2019).
  50. A. Autere, H. Jussila, Y. Dai, Y. Wang, H. Lipsanen, and Z. Sun, Nonlinear optics with 2D layered materials, Adv. Mater. 30, 1705963 (2018).
  51. M. S. Mrudul and G. Dixit, High-harmonic generation from monolayer and bilayer graphene, Phys. Rev. B 103, 094308 (2021).
  52. W. Mao, A. Rubio, and S. A. Sato, Enhancement of high-order harmonic generation in graphene by mid-infrared and terahertz fields, Phys. Rev. B 109, 045421 (2024).
  53. S. A. Mikhailov, Quantum theory of third-harmonic generation in graphene, Phys. Rev. B 90, 241301(R) (2014).
  54. H. A. Hafez et al., Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions, Nature (London) 561, 507 (2018).
  55. K.-J. Tielrooij et al., Milliwatt terahertz harmonic generation from topological insulator metamaterials, Light: Sci. Appl. 11, 315 (2022).
  56. G. Soavi et al., Broadband, electrically tunable third-harmonic generation in graphene, Nat. Nanotechnol. 13, 583 (2018).
  57. L. Wu, M. Brahlek, R. Valdés Aguilar, A. V. Stier, C. M. Morris, Y. Lubashevsky, L. S. Bilbro, N. Bansal, S. Oh, and N. P. Armitage, A sudden collapse in the transport lifetime across the topological phase transition in (Bi1−xInx)2Se3, Nat. Phys. 9, 410 (2013).
  58. L. Braun et al., Ultrafast photocurrents at the surface of the three-dimensional topological insulator Bi2Se3, Nat. Commun. 7, 13259 (2016).
  59. J. Stensberg, X. Han, Z. Ni, X. Yao, X. Yuan, D. Mallick, A. Gandhi, S. Oh, and L. Wu, Observation of terahertz second harmonic generation from Dirac surface states in the topological insulator Bi2Se3, Phys. Rev. B 109, 245112 (2024).
  60. L. Cheng, Y. Xiong, L. Kang, Y. Gao, Q. Chang, M. Chen, J. Qi, H. Yang, Z. Liu, J. C. W. Song, and E. E. M. Chia, Giant photon momentum locked THz emission in a centrosymmetric Dirac semimetal, Sci. Adv. 9, eadd7856 (2023).
  61. H. Plank, L. E. Golub, S. Bauer, V. V. Bel'kov, T. Herrmann, P. Olbrich, M. Eschbach, L. Plucinski, C. M. Schneider, J. Kampmeier, M. Lanius, G. Mussler, D. Grützmacher, and S. D. Ganichev, Photon drag effect in (Bi1−xSbx)2Te3 three-dimensional topological insulators, Phys. Rev. B 93, 125434 (2016).
  62. D. E. Parker, T. Morimoto, J. Orenstein, and J. E. Moore, Diagrammatic approach to nonlinear optical response with application to Weyl semimetals, Phys. Rev. B 99, 045121 (2019).
  63. H. Chen, C. Xie, X. Zhong, Y. Liang, W. Yang, C. Wu, and L. Luo, A quasi-2D perovskite antireflection coating to boost the performance of multilayered PdTe2/Ge heterostructure-based near-infrared photodetectors, J. Mater. Chem. C 10, 6025 (2022).
  64. C. Janisch, Y. Wang, D. Ma, N. Mehta, A. L. Elías, N. Perea-López, M. Terrones, V. Crespi, and Z. Liu, Extraordinary second harmonic generation in tungsten disulfide monolayers, Sci. Rep. 4, 5530 (2014).
  65. N. Kumar, S. Najmaei, Q. Cui, F. Ceballos, P. M. Ajayan, J. Lou, and H. Zhao, Second harmonic microscopy of monolayer MoS2, Phys. Rev. B 87, 161403(R) (2013).
  66. S. Puri, S. Patel, J. L. Cabellos, L. E. Rosas-Hernandez, K. Reynolds, H. O. H. Churchill, S. Barraza-Lopez, B. S. Mendoza, and H. Nakamura, Substrate interference and strain in the second-harmonic generation from MoSe2 monolayers, Nano Lett. 24, 13061 (2024).
  67. Z. Zhu, T. Yoo, K. Shaikh, A. C. Johnson, Q. Li, F. Liu, H. Deng, and Y. Kobayashi, Determining the complex second-order optical susceptibility in macroscale van der Waals heterobilayers, J. Chem. Phys. 163, 174707 (2025).
  68. H. G. Rosa, H. Y. Wei, I. Verzhbitskiy, M. J. F. L. Rodrigues, T. Taniguchi, K. Watanabe, G. Eda, V. M. Pereira, and J. C. V. Gomes, Characterization of the second- and third-harmonic optical susceptibilities of atomically thin tungsten diselenide, Sci. Rep. 8, 10035 (2018).
  69. M. Lobet, M. Sarrazin, F. Cecchet, N. Reckinger, A. Vlad, J.-F. Colomer, and D. Lis, Probing graphene χ(2) using a gold photon sieve, Nano Lett. 16, 48 (2016).
  70. S. Ha, H. Kim, H. Nam, J. Choi, K. Chae, J.-U. Lee, J.-Y. Park, Y. Yoo, and D.-I. Yeom, Enhanced optical third-harmonic generation in phase-engineered MoTe2 thin films, ACS Photonics 9, 2600 (2022).
  71. A. Autere, H. Jussila, A. Marini, J. R. M. Saavedra, Y. Dai, A. Säynätjoki, L. Karvonen, H. Yang, B. Amirsolaimani, R. A. Norwood, N. Peyghambarian, H. Lipsanen, K. Kieu, F. J. G. de Abajo, and Z. Sun, Optical harmonic generation in monolayer group-VI transition metal dichalcogenides, Phys. Rev. B 98, 115426 (2018).
  72. J. Pettine, P. Padmanabhan, N. Sirica, R. P. Prasankumar, A. J. Taylor, and H.-T. Chen, Ultrafast terahertz emission from emerging symmetry-broken materials, Light: Sci. Appl. 12, 133 (2023).
  73. A. Avdoshkin, V. Kozii, and J. E. Moore, Interactions remove the quantization of the chiral photocurrent at Weyl points, Phys. Rev. Lett. 124, 196603 (2020).
  74. J. Orenstein and J. S. Dodge, Terahertz time-domain spectroscopy of transient metallic and superconducting states, Phys. Rev. B 92, 134507 (2015).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation