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
  • Letter
  • Open Access

Intrinsic orbital Hall effect in degenerate spin-32 systems driven by the quantum metric

Rhonald Burgos Atencia

Phys. Rev. B 114, L231405 – Published 14 October, 2026

DOI: https://doi.org/10.1103/c6kd-njr5

Abstract

We show that in rotationally invariant spin-3/2 systems, the orbital Hall effect originates from interband matrix elements of the orbital magnetic moment. The resulting Hall response is governed by the quantum metric, rather than by the Berry curvature, revealing a purely geometric transport mechanism. Conventional intraband contributions associated with the orbital magnetic moment and Berry curvature are shown to vanish identically in the doubly degenerate two-band structure of the Luttinger model. These results identify the quantum metric as the key geometric quantity controlling orbital Hall transport in degenerate spin-3/2 systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (60)

  1. M.-C. Chang and Q. Niu, Berry curvature, orbital moment, and effective quantum theory of electrons in electromagnetic fields, J. Phys.: Condens. Matter 20, 193202 (2008).
  2. D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
  3. R. B. Atencia, A. Agarwal, and D. Culcer, Orbital angular momentum of Bloch electrons: Equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect, Adv. Phys.: X 9, 2371972 (2024).
  4. T. Yoda, T. Yokoyama, and S. Murakami, Orbital Edelstein effect as a condensed-matter analog of solenoids, Nano Lett. 18, 916 (2018).
  5. S. Zhong, J. E. Moore, and I. Souza, Gyrotropic magnetic effect and the magnetic moment on the Fermi surface, Phys. Rev. Lett. 116, 077201 (2016).
  6. T. P. Cysne, F. S. M. Guimarães, L. M. Canonico, T. G. Rappoport, and R. B. Muniz, Orbital magnetoelectric effect in zigzag nanoribbons of p-band systems, Phys. Rev. B 104, 165403 (2021).
  7. T. P. Cysne, F. S. M. Guimarães, L. M. Canonico, M. Costa, T. G. Rappoport, and R. B. Muniz, Orbital magnetoelectric effect in nanoribbons of transition metal dichalcogenides, Phys. Rev. B 107, 115402 (2023).
  8. Z. Zhang, X.-Z. Li, and W.-Y. He, Orbital magnetization as the origin of the nonlinear Hall effect, Phys. Rev. Res. 7, L042064 (2025).
  9. W. Gao, L. Liao, H. Isshiki, N. Budai, J. Kim, H.-W. Lee, K.-J. Lee, D. Go, Y. Mokrousov, S. Miwa, and Y. Otani, Nonlocal electrical detection of reciprocal orbital Edelstein effect, Nat. Commun. 16, 6380 (2025).
  10. J. H. Cullen and D. Culcer, Ge as an orbitronic platform: Giant in-plane orbital magneto-electric effect in a two-dimensional hole gas, J. Appl. Phys. 139, 093905 (2026).
  11. B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Orbitronics: The intrinsic orbital current in p-doped silicon, Phys. Rev. Lett. 95, 066601 (2005).
  12. L. M. Canonico, T. P. Cysne, T. G. Rappoport, and R. B. Muniz, Two-dimensional orbital Hall insulators, Phys. Rev. B 101, 075429 (2020).
  13. L. M. Canonico, T. P. Cysne, A. Molina-Sanchez, R. B. Muniz, and T. G. Rappoport, Orbital Hall insulating phase in transition metal dichalcogenide monolayers, Phys. Rev. B 101, 161409(R) (2020).
  14. D. Go, D. Jo, H.-W. Lee, M. Kläui, and Y. Mokrousov, Orbitronics: Orbital currents in solids, Europhys. Lett. 135, 37001 (2021).
  15. T. P. Cysne, S. Bhowal, G. Vignale, and T. G. Rappoport, Orbital Hall effect in bilayer transition metal dichalcogenides: From the intra-atomic approximation to the Bloch states orbital magnetic moment approach, Phys. Rev. B 105, 195421 (2022).
  16. A. Pezo, D. García Ovalle, and A. Manchon, Orbital Hall effect in crystals: Interatomic versus intra-atomic contributions, Phys. Rev. B 106, 104414 (2022).
  17. T. P. Cysne, M. Costa, L. M. Canonico, M. B. Nardelli, R. B. Muniz, and T. G. Rappoport, Disentangling orbital and valley Hall effects in bilayers of transition metal dichalcogenides, Phys. Rev. Lett. 126, 056601 (2021).
  18. A. Pezo, D. García Ovalle, and A. Manchon, Orbital Hall physics in two-dimensional Dirac materials, Phys. Rev. B 108, 075427 (2023).
  19. J. M. Lee, M. J. Park, and H.-W. Lee, Orbital Edelstein effect of electronic itinerant orbital motion at edges, Phys. Rev. B 110, 134436 (2024).
  20. M. Costa, B. Focassio, L. M. Canonico, T. P. Cysne, G. R. Schleder, R. B. Muniz, A. Fazzio, and T. G. Rappoport, Connecting higher-order topology with the orbital Hall effect in monolayers of transition metal dichalcogenides, Phys. Rev. Lett. 130, 116204 (2023).
  21. R. B. Atencia, Da. P. Arovas, and D. Culcer, Intrinsic torque on the orbital angular momentum in an electric field, Phys. Rev. B 110, 035427 (2024).
  22. A. L. R. Barbosa, L. M. Canonico, J. H. García, and T. G. Rappoport, Orbital Hall effect and topology on a two-dimensional triangular lattice: From bulk to edge, Phys. Rev. B 110, 085412 (2024).
  23. T. P. Cysne, W. J. M. Kort-Kamp, and T. G. Rappoport, Controlling the orbital Hall effect in gapped bilayer graphene in the terahertz regime, Phys. Rev. Res. 6, 023271 (2024).
  24. J. H. Cullen, H. Liu, and D. Culcer, Giant orbital Hall effect due to the bulk states of 3D topological insulators, npj Spintron. 3, 22 (2025).
  25. H. Liu, J. H. Cullen, D. P. Arovas, and D. Culcer, Quantum correction to the orbital Hall effect, Phys. Rev. Lett. 134, 036304 (2025).
  26. K. Ando, Orbitronics: Harnessing orbital currents in solid-state devices, J. Phys. Soc. Jpn. 94, 092001 (2025).
  27. P. Wang, F. Chen, Y. Yang, S. Hu, Y. Li, W. Wang, D. Zhang, and Y. Jiang, Orbitronics: Mechanisms, materials and devices, Adv. Electron. Mater. 11, 2400554 (2025).
  28. S. Bhowal and G. Vignale, Orbital Hall effect as an alternative to valley Hall effect in gapped graphene, Phys. Rev. B 103, 195309 (2021).
  29. H. Liu and D. Culcer, Dominance of extrinsic scattering mechanisms in the orbital Hall effect: Graphene, transition metal dichalcogenides, and topological antiferromagnets, Phys. Rev. Lett. 132, 186302 (2024).
  30. T. P. Cysne, R. B. Muniz, and T. G. Rappoport, Transport of orbital currents in systems with strong intervalley coupling: The case of Kekulé distorted graphene, SciPost Phys. Core 7, 046 (2024).
  31. P. Tang and G. E. W. Bauer, Role of disorder in the intrinsic orbital Hall effect, Phys. Rev. Lett. 133, 186302 (2024).
  32. 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).
  33. F. Wilczek and A. Zee, Appearance of gauge structure in simple dynamical systems, Phys. Rev. Lett. 52, 2111 (1984).
  34. F. D. M. Haldane, Berry curvature on the Fermi surface: Anomalous Hall effect as a topological Fermi-liquid property, Phys. Rev. Lett. 93, 206602 (2004).
  35. J. M. Luttinger and W. Kohn, Motion of electrons and holes in perturbed periodic fields, Phys. Rev. 97, 869 (1955).
  36. J. M. Luttinger, Quantum theory of cyclotron resonance in semiconductors: General theory, Phys. Rev. 102, 1030 (1956).
  37. S. Murakami, N. Nagaosa, and S. C. Zhang, SU(2) non-Abelian holonomy and dissipationless spin current in semiconductors, Phys. Rev. B 69, 235206 (2004).
  38. J. P. Provost and G. Vallee, Riemannian structure on manifolds of quantum states, Commun. Math. Phys. 76, 289 (1980).
  39. Y. Jiang, T. Holder, and B. Yan, Revealing quantum geometry in nonlinear quantum materials, Rep. Prog. Phys. 88, 076502 (2025).
  40. J. Yu, B. A. Bernevig, R. Queiroz, E. Rossi, P. Törmä, and B.-J. Yang, Quantum geometry in quantum materials, npj Quantum Mater. 10, 101 (2025).
  41. G. Sala, M. T. Mercaldo, K. Domi, S. Gariglio, M. Cuoco, C. Ortix, and A. D. Caviglia, The quantum metric of electrons with spin-momentum locking, Science 389, 822 (2025).
  42. G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B 59, 14915 (1999).
  43. J. C. W. Song and G. Vignale, Low-dissipation edge currents without edge states, Phys. Rev. B 99, 235405 (2019).
  44. Ó. P. Ocaña and I. Souza, Multipole theory of optical spatial dispersion in crystals, SciPost Phys. 14, 118 (2023).
  45. R. B. Atencia, Quantum geometry and linear orbital response in arbitrary SU(2) representation, Phys. Rev. B 113, 075422 (2026).
  46. K. Wen, H.-Y. Xie, A. Auerbach, and B. Uchoa, Thermal and thermoelectric transport in flat bands with nontrivial quantum geometry, Phys. Rev. B 111, 205140 (2025).
  47. T. P. Cysne, I. Souza, and T. G. Rappoport, Orbital Hall effect from orbital magnetic moments of Bloch states: The role of a new correction term, Phys. Rev. Res. 8, 033086 (2026).
  48. D. Culcer, A. Sekine, and A. H. MacDonald, Interband coherence response to electric fields in crystals: Berry-phase contributions and disorder effects, Phys. Rev. B 96, 035106 (2017).
  49. R. B. Atencia, Q. Niu, and D. Culcer, Semiclassical response of disordered conductors: Extrinsic carrier velocity and spin and field-corrected collision integral, Phys. Rev. Res. 4, 013001 (2022).
  50. R. G. Winkler, Spin-Orbit Coupling Effects in Two-dimensional Electron and Hole Systems, Springer Tracts in Modern Physics Vol. 191 (Springer-Verlag, Berlin, 2003).
  51. H. Kontani, T. Tanaka, D. S. Hirashima, K. Yamada, and J. Inoue, Giant intrinsic spin and orbital Hall effects in Sr2MO4 (M=Ru, Rh, Mo), Phys. Rev. Lett. 100, 096601 (2008).
  52. H. Kontani, T. Tanaka, D. S. Hirashima, K. Yamada, and J. Inoue, Giant orbital Hall effect in transition metals: Origin of large spin and anomalous Hall effects, Phys. Rev. Lett. 102, 016601 (2009).
  53. D. Jo, D. Go, and H.-W. Lee, Gigantic intrinsic orbital Hall effects in weakly spin-orbit coupled metals, Phys. Rev. B 98, 214405 (2018).
  54. M. Rang and P. J. Kelly, Orbital Hall effect in transition metals from first-principles scattering calculations, Phys. Rev. B 111, 125121 (2025).
  55. I. Baek and H.-W. Lee, Negative intrinsic orbital Hall effect in group XIV materials, Phys. Rev. B 104, 245204 (2021).
  56. S. Murakami, N. Nagaosa, and S.-C. Zhang, Dissipationless quantum spin current at room temperature, Science 301, 1348 (2003).
  57. J. H. Cullen, Z. Wang, and D. Culcer, Orbital Hall effect in spin-3/2 hole-doped semiconductors and its implications for orbitronics, Commun. Phys. 9, 209 (2026).
  58. G. Sala and P. Gambardella, Giant orbital Hall effect and orbital-to-spin conversion in 3d, 5d, and 4f metallic heterostructures, Phys. Rev. Res. 4, 033037 (2022).
  59. E. Santos, J. E. Abrão, J. L. Costa, J. G. S. Santos, G. Rodrigues-Junior, J. B. S. Mendes, and A. Azevedo, Negative orbital Hall effect in germanium, Phys. Rev. Appl. 22, 064071 (2024).
  60. A. Manchon, C. Sun, X. Ning, T. Sato, T. Kato, and T. G. Rappoport, Multipolar orbital relaxation of the t2g states, Phys. Rev. Lett. 136, 226801 (2026).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation