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

Tuning the Chern number of a Kitaev quantum spin liquid

Seong Jun Kwon1,2, Kyusung Hwang3,*, and Suk Bum Chung2,4,5,†

  • 1Department of Applied Physics, The University of Tokyo, Bunkyo, Tokyo 113-8656, Japan
  • 2Department of Physics and Natural Science Research Institute, University of Seoul, Seoul 02504, Republic of Korea
  • 3Department of Applied Physics, Kyung Hee University, Yongin 17104, Republic of Korea
  • 4School of Physics, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
  • 5Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

  • *Contact author: kyusung.hwang@khu.ac.kr
  • †Contact author: sbchung0@uos.ac.kr

Phys. Rev. B 113, 024416 – Published 16 January, 2026

DOI: https://doi.org/10.1103/1qmb-c69z

Abstract

It is now well understood that non-Kitaev spin interactions can be added to the Kitaev quantum spin liquid by applying external fields. Recent years have seen intensive discussion on the possible phase transitions that these spin interactions induce. In this paper, we will show through the perturbation theory the possibility of accessing a gapped spin liquid phase with a higher Chern number through, in contrast to the cases studied in literature, a continuous phase transition. Such a transition may be induced by external tuning parameters such as electric field and hydrostatic pressure.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (56)

  1. A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. (NY) 321, 2 (2006).
  2. L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
  3. Y. Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states, Rev. Mod. Phys. 89, 025003 (2017).
  4. J. Knolle and R. Moessner, A field guide to spin liquids, Annu. Rev. Condens. Matter Phys. 10, 451 (2019).
  5. C. Broholm, R. J. Cava, S. A. Kivelson, D. G. Nocera, M. R. Norman, and T. Senthil, Quantum spin liquids, Science 367, eaay0668 (2020).
  6. G. Jackeli and G. Khaliullin, Mott insulators in the strong spin-orbit coupling limit: From Heisenberg to a quantum compass and Kitaev models, Phys. Rev. Lett. 102, 017205 (2009).
  7. J. Chaloupka, G. Jackeli, and G. Khaliullin, Kitaev-Heisenberg model on a honeycomb lattice: Possible exotic phases in iridium oxides A2IrO3, Phys. Rev. Lett. 105, 027204 (2010).
  8. S. M. Winter, A. A. Tsirlin, M. Daghofer, J. van den Brink, Y. Singh, P. Gegenwart, and R. Valentí, Models and materials for generalized Kitaev magnetism, J. Phys.: Condens. Matter 29, 493002 (2017).
  9. H. Takagi, T. Takayama, G. Jackeli, G. Khaliullin, and S. E. Nagler, Concept and realization of Kitaev quantum spin liquids, Nat. Rev. Phys. 1, 264 (2019).
  10. Y. Motome and J. Nasu, Hunting Majorana fermions in Kitaev magnets, J. Phys. Soc. Jpn. 89, 012002 (2020).
  11. Y. Matsuda, T. Shibauchi, and H.-Y. Kee, Kitaev quantum spin liquids, Rev. Mod. Phys. 97, 045003 (2025).
  12. Y. Kasahara, T. Ohnishi, Y. Mizukami, O. Tanaka, S. Ma, K. Sugii, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, T. Shibauchi, and Y. Matsuda, Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid, Nature (London) 559, 227 (2018).
  13. T. Yokoi, S. Ma, Y. Kasahara, S. Kasahara, T. Shibauchi, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, C. Hickey, S. Trebst, and Y. Matsuda, Half-integer quantized anomalous thermal Hall effect in the Kitaev material candidate α−RuCl3, Science 373, 568 (2021).
  14. O. Tanaka, Y. Mizukami, R. Harasawa, K. Hashimoto, K. Hwang, N. Kurita, H. Tanaka, S. Fujimoto, Y. Matsuda, E. G. Moon, and T. Shibauchi, Thermodynamic evidence for a field-angle-dependent Majorana gap in a Kitaev spin liquid, Nat. Phys. 18, 429 (2022).
  15. K. Imamura, S. Suetsugu, Y. Mizukami, Y. Yoshida, K. Hashimoto, K. Ohtsuka, Y. Kasahara, N. Kurita, H. Tanaka, P. Noh, J. Nasu, E.-G. Moon, Y. Matsuda, and T. Shibauchi, Majorana-fermion origin of the planar thermal Hall effect in the Kitaev magnet α−RuCl3, Sci. Adv. 10, eadk3539 (2024).
  16. J. G. Rau, E. K.-H. Lee, and H.-Y. Kee, Generic spin model for the honeycomb iridates beyond the Kitaev limit, Phys. Rev. Lett. 112, 077204 (2014).
  17. V. M. Katukuri, S. Nishimoto, V. Yushankhai, A. Stoyanova, H. Kandpal, S. Choi, R. Coldea, I. Rousochatzakis, L. Hozoi, and J. van den Brink, Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: Insights from ab initio quantum chemistry calculations, New J. Phys. 16, 013056 (2014).
  18. S. K. Choi, R. Coldea, A. N. Kolmogorov, T. Lancaster, I. I. Mazin, S. J. Blundell, P. G. Radaelli, Y. Singh, P. Gegenwart, K. R. Choi, S.-W. Cheong, P. J. Baker, C. Stock, and J. Taylor, Spin waves and revised crystal structure of honeycomb iridate Na2IrO3, Phys. Rev. Lett. 108, 127204 (2012).
  19. J. A. Sears, M. Songvilay, K. W. Plumb, J. P. Clancy, Y. Qiu, Y. Zhao, D. Parshall, and Y.-J. Kim, Magnetic order in α−RuCl3: A honeycomb-lattice quantum magnet with strong spin-orbit coupling, Phys. Rev. B 91, 144420 (2015).
  20. R. D. Johnson, S. C. Williams, A. A. Haghighirad, J. Singleton, V. Zapf, P. Manuel, I. I. Mazin, Y. Li, H. O. Jeschke, R. Valentí, and R. Coldea, Monoclinic crystal structure of α−RuCl3 and the zigzag antiferromagnetic ground state, Phys. Rev. B 92, 235119 (2015).
  21. H.-S. Kim, V. Shankar V, A. Catuneanu, and H.-Y. Kee, Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling, Phys. Rev. B 91, 241110(R) (2015).
  22. H. B. Cao, A. Banerjee, J.-Q. Yan, C. A. Bridges, M. D. Lumsden, D. G. Mandrus, D. A. Tennant, B. C. Chakoumakos, and S. E. Nagler, Low-temperature crystal and magnetic structure of α−RuCl3, Phys. Rev. B 93, 134423 (2016).
  23. S. M. Winter, Y. Li, H. O. Jeschke, and R. Valentí, Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales, Phys. Rev. B 93, 214431 (2016).
  24. J. Wang, B. Normand, and Z.-X. Liu, One proximate Kitaev spin liquid in the K−J−Γ model on the honeycomb lattice, Phys. Rev. Lett. 123, 197201 (2019).
  25. J. Wang, Q. Zhao, X. Wang, and Z.-X. Liu, Multinode quantum spin liquids on the honeycomb lattice, Phys. Rev. B 102, 144427 (2020).
  26. L. N. Bulaevskii, C. D. Batista, M. V. Mostovoy, and D. I. Khomskii, Electronic orbital currents and polarization in Mott insulators, Phys. Rev. B 78, 024402 (2008).
  27. S. Miyahara and N. Furukawa, Theory of antisymmetric spin-pair-dependent electric polarization in multiferroics, Phys. Rev. B 93, 014445 (2016).
  28. A. Bolens, Theory of electronic magnetoelectric coupling in d5 Mott insulators, Phys. Rev. B 98, 125135 (2018).
  29. R. Chari, R. Moessner, and J. G. Rau, Magnetoelectric generation of a Majorana-Fermi surface in Kitaev's honeycomb model, Phys. Rev. B 103, 134444 (2021).
  30. P. Noh, K. Hwang, and E.-G. Moon, Manipulating topological quantum phase transitions of Kitaev's quantum spin liquids with electric fields, Phys. Rev. B 109, L201105 (2024).
  31. T. Koyama, Y. Nakatani, J. Ieda, and D. Chiba, Electric field control of magnetic domain wall motion via modulation of the Dzyaloshinskii-Moriya interaction, Sci. Adv. 4, eaav0265 (2018).
  32. J. Chaloupka and G. Khaliullin, Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for the honeycomb-lattice iridates A2IrO3, Phys. Rev. B 92, 024413 (2015).
  33. D. Takikawa and S. Fujimoto, Impact of off-diagonal exchange interactions on the Kitaev spin-liquid state of α−RuCl3, Phys. Rev. B 99, 224409 (2019).
  34. D. I. Khomskii and S. V. Streltsov, Orbital effects in solids: Basics, recent progress, and opportunities, Chem. Rev. 121, 2992 (2021).
  35. H. Liu, J. Chaloupka, and G. Khaliullin, Exchange interactions in d5 Kitaev materials: From Na2IrO3 to α−RuCl3, Phys. Rev. B 105, 214411 (2022).
  36. B. Wolf, D. A. S. Kaib, A. Razpopov, S. Biswas, K. Riedl, S. M. Winter, R. Valentí, Y. Saito, S. Hartmann, E. Vinokurova, T. Doert, A. Isaeva, G. Bastien, A. U. B. Wolter, B. Büchner, and M. Lang, Combined experimental and theoretical study of hydrostatic He-gas pressure effects in α−RuCl3, Phys. Rev. B 106, 134432 (2022).
  37. X. Wang, F. Zhu, N. Qureshi, K. Beauvois, J. Song, T. Mueller, T. Brückel, and Y. Su, Hydrostatic pressure effects in the Kitaev quantum magnet α−RuCl3: A single-crystal neutron diffraction study, arXiv:2304.00632.
  38. A. Hauspurg, S. Singh, T. Yanagisawa, V. Tsurkan, J. Wosnitza, W. Brenig, N. B. Perkins, and S. Zherlitsyn, Spin-strain interactions under hydrostatic pressure in α−RuCl3, Phys. Rev. B 112, 134405 (2025).
  39. J. G. Rau and H.-Y. Kee, Trigonal distortion in the honeycomb iridates: Proximity of zigzag and spiral phases in Na2IrO3, arXiv:1408.4811.
  40. F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett. 61, 2015 (1988).
  41. K. Hwang, A. Go, J. H. Seong, T. Shibauchi, and E.-G. Moon, Identification of a Kitaev quantum spin liquid by magnetic field angle dependence, Nat. Commun. 13, 323 (2022).
  42. D. Takikawa and S. Fujimoto, Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state, Phys. Rev. B 102, 174414 (2020).
  43. S.-S. Zhang, C. D. Batista, and G. B. Halász, Toward Kitaev's sixteenfold way in a honeycomb lattice model, Phys. Rev. Res. 2, 023334 (2020).
  44. J.-N. Fuchs, S. Patil, and J. Vidal, Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way, Phys. Rev. B 102, 115130 (2020).
  45. Y. Liu, K. Slagle, K. S. Burch, and J. Alicea, Dynamical anyon generation in Kitaev honeycomb non-Abelian spin liquids, Phys. Rev. Lett. 129, 037201 (2022).
  46. K. Klocke, Y. Liu, G. B. Halász, and J. Alicea, Spin-liquid-based topological qubits, arXiv:2411.08093.
  47. M. Gohlke, R. Moessner, and F. Pollmann, Dynamical and topological properties of the kitaev model in a [111] magnetic field, Phys. Rev. B 98, 014418 (2018).
  48. S.-S. Zhang, Z. Wang, G. B. Halász, and C. D. Batista, Vison crystals in an extended Kitaev model on the honeycomb lattice, Phys. Rev. Lett. 123, 057201 (2019).
  49. J. Nasu, Majorana quasiparticles emergent in Kitaev spin liquid, Prog. Theor. Exp. Phys. 2024, 08C104 (2024).
  50. D. Sticlet and F. Piéchon, Distant-neighbor hopping in graphene and Haldane models, Phys. Rev. B 87, 115402 (2013).
  51. D. Sticlet, F. Piéchon, J.-N. Fuchs, P. Kalugin, and P. Simon, Geometrical engineering of a two-band Chern insulator in two dimensions with arbitrary topological index, Phys. Rev. B 85, 165456 (2012).
  52. C. Bena and L. Simon, Dirac point metamorphosis from third-neighbor couplings in graphene and related materials, Phys. Rev. B 83, 115404 (2011).
  53. M. Hermanns, K. O'Brien, and S. Trebst, Weyl spin liquids, Phys. Rev. Lett. 114, 157202 (2015).
  54. A. P. Joy and A. Rosch, Dynamics of visons and thermal Hall effect in perturbed Kitaev models, Phys. Rev. X 12, 041004 (2022).
  55. N. Read and D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B 61, 10267 (2000).
  56. S. C. Furuya and M. Sato, Electric-field control of magnetic anisotropies: Applications to Kitaev spin liquids and topological spin textures, Phys. Rev. Res. 6, 013228 (2024).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation