- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Engineering magnetotransport through hierarchical symmetry in Weyl semimetal superlattices

Nathan C. Drucker1,*, Federico Balduini1, Jules Schadt1,2, Lorenzo Rocchino1, Tathagata Paul1, Vicky Hasse3, Claudia Felser3, Heinz Schmid1, Cezar B. Zota1,† et al.

Bernd Gotsmann1,‡

  • *Contact author: nathan.drucker@ibm.com
  • †Contact author: zot@zurich.ibm.com
  • ‡Contact author: bgo@zurich.ibm.com
PDF

Phys. Rev. Research 8, 033023 – Published 6 July, 2026

DOI: https://doi.org/10.1103/l4b4-qzjz

Abstract

Superlattice engineering, the introduction of periodic potentials to a material, can induce selective scattering events that modify the electrical properties of the material in predictable ways. Extending superlattice engineering to three-dimensional (3D) electronic materials can expand the tunability of their transport properties beyond traditional means such as doping. Here, we show that magnetotransport can be modified by superlattices in 3D materials based on the relative symmetry between the Fermi surface and nanostructured superlattice. We demonstrate commensuration oscillations in the ballistic transport regime of a nanostructured 3D material with the Weyl semimetal NbP. The oscillations encode information about the shared properties between the quasiparticles at the Fermi surface—including their momentum, charge, mass, and rotational symmetry—and the structure of the superlattice. These results point toward methods to engineer quantum transport in 3D electronic materials based on the mutual properties of the superlattice and Fermi surface.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (55)

  1. J. Bauer et al., Nanolattices: An emerging class of mechanical metamaterials, Adv. Mater. 29, 1701850 (2017).
  2. P. Jiao, J. Mueller, J. R. Raney, X. (R.) Zheng, and A. H. Alavi, Mechanical metamaterials and beyond, Nat. Commun. 14, 6004 (2023).
  3. S. John, Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett. 58, 2486 (1987).
  4. E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electronics, Phys. Rev. Lett. 58, 2059 (1987).
  5. K. M. Ho, C. T. Chan, and C. M. Soukoulis, Existence of a photonic gap in periodic dielectric structures, Phys. Rev. Lett. 65, 3152 (1990).
  6. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Photonic crystals, Solid State Commun. 102, 165 (1997).
  7. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Photonic crystals: Putting a new twist on light, Nature (London) 386, 143 (1997).
  8. C. R. Dean et al., Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices, Nature (London) 497, 598 (2013).
  9. B. Hunt, J. D. Sanchez-Yamagishi, A. F. Young, M. Yankowitz, B. J. LeRoy, K. Watanabe, T. Taniguchi, P. Moon, M. Koshino, P. Jarillo-Herrero, and R. C. Ashoori, Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure, Science 340, 1427 (2013).
  10. Y. Cao et al., Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature (London) 556, 80 (2018).
  11. Y. Cao et al., Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
  12. J. Cai et al., Signatures of fractional quantum anomalous Hall states in twisted MoTe2, Nature (London) 622, 63 (2023).
  13. Z. Lu et al., Fractional quantum anomalous Hall effect in multilayer graphene, Nature (London) 626, 759 (2024).
  14. F. Balduini et al., Probing the shape of the Weyl Fermi surface of NbP using transverse electron focusing, Phys. Rev. Lett. 133, 096601 (2024).
  15. R. R. Gerhardts, D. Weiss, and K. v. Klitzing, Novel magnetoresistance oscillations in a periodically modulated two-dimensional electron gas, Phys. Rev. Lett. 62, 1173 (1989).
  16. D. Weiss et al., Electron pinball and commensurate orbits in a periodic array of scatterers, Phys. Rev. Lett. 66, 2790 (1991).
  17. D. Weiss et al., Quantized periodic orbits in large antidot arrays, Phys. Rev. Lett. 70, 4118 (1993).
  18. D. R. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B 14, 2239 (1976).
  19. G. H. Wannier, A result not dependent on rationality for Bloch electrons in a magnetic field, Phys. Status Solidi (B) 88, 757 (1978).
  20. R. R. Gerhardts, D. Weiss, and U. Wulf, Magnetoresistance oscillations in a grid potential: Indication of a Hofstadter-type energy spectrum, Phys. Rev. B 43, 5192 (1991).
  21. P. Streda, Quantised Hall effect in a two-dimensional periodic potential, J. Phys. C: Solid State Phys. 15, L1299 (1982).
  22. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49, 405 (1982).
  23. A. H. MacDonald, Landau-level subband structure of electrons on a square lattice, Phys. Rev. B 28, 6713 (1983).
  24. R. K. Kumar et al., High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices, Science 357, 181 (2017).
  25. M. Drienovsky et al., Commensurability oscillations in one-dimensional graphene superlattices, Phys. Rev. Lett. 121, 026806 (2018).
  26. R. Huber et al., Band conductivity oscillations in a gate-tunable graphene superlattice, Nat. Commun. 13, 2856 (2022).
  27. H. Silberbauer, Magnetic minibands in lateral semiconductor superlattices, J. Phys. Condens. Matter 4, 7355 (1992).
  28. R. Fleischmann, T. Geisel, and R. Ketzmerick, Magnetoresistance due to chaos and nonlinear resonances in lateral surface superlattices, Phys. Rev. Lett. 68, 1367 (1992).
  29. G. Datseris, T. Geisel, and R. Fleischmann, Robustness of ballistic transport in antidot superlattices, New J. Phys. 21, 043051 (2019).
  30. D. Q. Wang et al., Formation of artificial Fermi surfaces with a triangular superlattice on a conventional two-dimensional electron gas, Nano Lett. 23, 1705 (2023).
  31. A. Sandner et al., Ballistic transport in graphene antidot lattices, Nano Lett. 15, 8402 (2015).
  32. R. Yagi et al., Ballistic transport in graphene antidot lattices, Phys. Rev. B 92, 195406 (2015).
  33. B. S. Jessen et al., Lithographic band structure engineering of graphene, Nat. Nanotechnol. 14, 340 (2019).
  34. H. Maier et al., Ballistic geometric resistance resonances in a single surface of a topological insulator, Nat. Commun. 8, 2023 (2017).
  35. A. Devarakonda et al., Evidence of striped electronic phases in a structurally modulated superlattice, Nature (London) 631, 526 (2024).
  36. W. Kang, H. L. Stormer, L. N. Pfeiffer, K. W. Baldwin, and K. W. West, How real are composite fermions? Phys. Rev. Lett. 71, 3850 (1993).
  37. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
  38. P. J. W. Moll, Focused ion beam microstructuring of quantum matter, Annu. Rev. Condens. Matter Phys. 9, 147 (2018).
  39. Z. K. Liu et al., Evolution of the Fermi surface of Weyl semimetals in the transition metal pnictide family, Nat. Mater. 15, 27 (2016).
  40. See Supplemental Material at http://link.aps.org/supplemental/10.1103/l4b4-qzjz for additional data and processing methods.
  41. Z. Wang et al., Helicity-protected ultrahigh mobility Weyl fermions in NbP, Phys. Rev. B 93, 121112 (2016).
  42. P. H. Beton et al., Temperature dependence of magnetoresistance oscillations in a two-dimensional electron gas subjected to a periodic potential, Phys. Rev. B 42, 9689 (1990).
  43. F. M. Peeters and P. Vasilopoulos, Electrical and thermal properties of a two-dimensional electron gas in a one-dimensional periodic potential, Phys. Rev. B 46, 4667 (1992).
  44. C. Shekhar et al., Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP, Nat. Phys. 11, 645 (2015).
  45. F. Balduini et al., Origin of the extreme and anisotropic magnetoresistance in the Weyl semimetal NbP, Phys. Rev. B 109, 045148 (2024).
  46. J. Klotz et al., Quantum oscillations and the Fermi surface topology of the Weyl semimetal NbP, Phys. Rev. B 93, 121105 (2016).
  47. D. Shoenberg, Magnetic Oscillations in Metals, Cambridge Monographs on Physics (Cambridge University Press, Cambridge, 1984).
  48. J.-K. Yu, S. Mitrovic, D. Tham, J. Varghese, and J. R. Heath, Reduction of thermal conductivity in phononic nanomesh structures, Nat. Nanotechnol. 5, 718 (2010).
  49. S. Alaie et al., Thermal transport in phononic crystals and the observation of coherent phonon scattering at room temperature, Nat. Commun. 6, 7228 (2015).
  50. M. N. Luckyanova et al., Coherent phonon heat conduction in superlattices, Science 338, 936 (2012).
  51. B. Skinner and L. Fu, Large nonsaturating thermopower in a quantizing magnetic field, Sci. Adv. 4, eaat2621 (2018).
  52. F. Han et al., Quantized thermoelectric Hall effect induces giant power factor in a topological semimetal, Nat. Commun. 11, 6167 (2020).
  53. S. N. Guin et al., Anomalous Nernst effect beyond the magnetization scaling relation in the ferromagnetic Heusler compound Co2MnGa, NPG Asia Mater. 11, 16 (2019).
  54. T. Asaba et al., Colossal anomalous Nernst effect in a correlated noncentrosymmetric kagome ferromagnet, Sci. Adv. 7, eabf1467 (2021).
  55. E. Zhai et al., The rise of semi-metal electronics, Nat. Rev. Electr. Eng. 1, 497 (2024).

Outline

Information

Phys. Rev. Research 8, 033023– Published 6 July, 2026
  • Received 12 January 2026
  • Accepted 5 June 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation