- 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

Fermi surface and Berry phase analysis for Dirac nodal line semimetals: Cautionary tale from SrGa2 and BaGa2

Yuxiang Gao1,*, Yichen Zhang1,*, Shiming Lei1,†, Neil Harrison2, Mun Keat Chan2, Jonathan D. Denlinger3, Sergey Gorovikov4, Sanu Mishra1, Yan Sun5 et al.

Ming Yi1 and Emilia Morosan1,‡

  • *These authors contributed equally to this work.
  • †Present address: Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China.
  • ‡Contact author: emorosan@rice.edu
PDF

Phys. Rev. Research 7, 043028 – Published 7 October, 2025

DOI: https://doi.org/10.1103/6tq6-sr6w

Abstract

A Berry phase of odd multiples of π inferred from quantum oscillations (QOs) has often been treated as evidence for nontrivial reciprocal space topology. However, disentangling the Berry phase values from the Zeeman effect and the orbital magnetic moment is often challenging. In centrosymmetric compounds, the case is simpler as the orbital magnetic moment contribution is negligible. Although the Zeeman effect can be significant, it is usually overlooked in most studies of QOs in centrosymmetric compounds. Here, we present a detailed study on the nonmagnetic centrosymmetric SrGa2 and BaGa2, which are predicted to be Dirac nodal line semimetals based on density functional theory (DFT) calculations. Evidence of the nontrivial topology is found in magnetotransport measurements. The Fermi surface topology and band structure are carefully studied through a combination of angle-dependent QOs, angle-resolved photoemission spectroscopy (ARPES), and DFT calculations, where the nodal line is observed in the vicinity of the Fermi level. Strong de Haas–van Alphen fundamental oscillations associated with higher harmonics are observed in both compounds, which are well fitted by the Lifshitz-Kosevich (LK) formula. However, even with the inclusion of higher harmonics in the fitting, we found that the Berry phases cannot be unambiguously determined when the Zeeman effect is included. We revisit the LK formula and analyze the phenomena and outcomes that were associated with the Zeeman effect in previous studies. Our experimental results confirm that SrGa2 and BaGa2 are Dirac nodal line semimetals. Additionally, we highlight the often overlooked role of spin-damping terms in Berry phase analysis.

View figure in article

Physics Subject Headings (PhySH)

Corrections

22 December, 2025

Correction: A minor change has been made to the title. The previously published Fig. 11 contained errors and has been replaced.

Article Text

References (56)

  1. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  2. A. A. Burkov, Weyl metals, Annu. Rev. Condens. Matter Phys. 9, 359 (2017).
  3. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
  4. A. Bernevig et al., Recent progress in the study of topological semimetals, J. Phys. Soc. Jpn. 87, 041001 (2017).
  5. J. Hu et al., Transport of topological semimetals, Annu. Rev. Mater. Res. 49, 207 (2019).
  6. B. Bradlyn et al., Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals, Science 353, 6299 (2016).
  7. C. Fang et al., Topological nodal line semimetals, Chinese Phys. B 25, 117106 (2016).
  8. G. Chang et al., Topological quantum properties of chiral crystals, Nat. Mater. 17, 978 (2018).
  9. Y. M. Xie et al., Kramers nodal line metals, Nat. Commun. 12, 3064 (2021).
  10. S. Lei et al., Weyl nodal ring states and Landau quantization with very large magnetoresistance in square-net magnet EuGa4, Nat. Commun. 14, 5812 (2023).
  11. Y. Zhang et al., Kramers nodal lines and Weyl fermions in SmAlSi, Commun. Phys. 6, 134 (2023).
  12. Y. Zhang et al., Kramers nodal lines in intercalated TaS2 superconductors, Nat. Commun. 16, 4984 (2025).
  13. L. Schoop et al., Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS, Nat. Commun. 7, 11696 (2016).
  14. J. Hu et al., Evidence of topological nodal-line fermions in ZrSiSe and ZrSiTe, Phys. Rev. Lett. 117, 016602 (2016).
  15. M. Ali et al., Butterfly magnetoresistance, quasi-2D Dirac Fermi surface and topological phase transition in ZrSiS, Sci. Adv. 2, 1601742 (2016).
  16. R. Singha et al., Large nonsaturating magnetoresistance and signature of nondegenerate Dirac nodes in ZrSiS, Proc. Natl. Acad. Sci. USA 114, 2468 (2017).
  17. R. Singha et al., Magnetotransport properties and evidence of a topological insulating state in LaSbTe, Phys. Rev. B 96, 245138 (2017).
  18. L. Schoop et al., Tunable Weyl and Dirac states in the nonsymmorphic compound CeSbTe, Sci. Adv. 4, eaar2317 (2018).
  19. Y. C. Chiu et al., Origin of the butterfly magnetoresistance in a Dirac nodal-line system, Phys. Rev. B 100, 125112 (2019).
  20. L. P. He et al., Quantum transport evidence for the three-dimensional Dirac semimetal phase in Cd3As2, Phys. Rev. Lett. 113, 246402 (2014).
  21. F. Fei et al., Nontrivial Berry phase and type-II Dirac transport in the layered material PdTe2, Phys. Rev. B 96, 041201(R) (2017).
  22. S. Huang et al., Nontrivial Berry phase in magnetic BaMnSb2 semimetal, Proc. Natl. Acad. Sci. USA 114, 6256 (2017).
  23. J. Wang et al., Vanishing quantum oscillations in Dirac semimetal ZrTe5, Proc. Natl. Acad. Sci. USA 115, 9145 (2018).
  24. W. Ma et al., Rare earth engineering in RMn6Sn6 (R = Gd-Tm, Lu) topological kagome magnets, Phys. Rev. Lett. 126, 246602 (2021).
  25. E. Cheng et al., Magnetism-induced topological transition in EuAs3, Nat. Commun. 12, 6970 (2021).
  26. L. Tian et al., Anomalous Hall effect in ZrTe5, Nat. Phys. 14, 451 (2018).
  27. L. K. Zeng et al., Compensated semimetal LaSb with Unsaturated Magnetoresistance, Phys. Rev. Lett. 117, 217204 (2016).
  28. L. Guo et al., Extreme magnetoresistance and SdH oscillation in compensated semimetals of NbSb2 single crystals, J. Appl. Phys. 123, 155103 (2018).
  29. F. Arnold et al., Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP, Nat. Commun. 7, 11615 (2016).
  30. S. Liang et al., Experimental tests of the chiral anomaly magnetoresistance in the Dirac-Weyl semimetals Na3Bi and GdPtBi, Phys. Rev. X 8, 031002 (2018).
  31. C. Li et al., Rules for phase shifts of quantum oscillations in topological nodal-line semimetals, Phys. Rev. Lett. 120, 146602 (2018).
  32. Y. Yang et al., Anisotropic Berry phase in the Dirac nodal-line semimetal ZrSiS: The effect of spin-orbit coupling, Phys. Rev. B 103, 125160 (2021).
  33. A. A. Taskin and Y. Ando, Berry phase of nonideal Dirac fermions in topological insulators, Phys. Rev. B 84, 035301 (2011).
  34. G. P. Mikitik and Y. V. Sharlai, Manifestation of Berry’s phase in metal physics, Phys. Rev. Lett. 82, 2147 (1999).
  35. H. Lu et al., Massive Dirac fermions and spin physics in an ultrathin film of topological insulator, Phys. Rev. B 81, 115407 (2010).
  36. A. R. Wright and R. H. McKenzie, Quantum oscillations and Berry’s phase in topological insulator surface states with broken particle-hole symmetry, Phys. Rev. B 87, 085411 (2013).
  37. D. Shoenberg et al., Magnetic Oscillations in Metals (Cambridge University Press, Cambridge, England, 1984).
  38. Y. Kwan et al., Quantum oscillations probe the Fermi surface topology of the nodal-line semimetal CaAgAs, Phys. Rev. Res. 2, 012055(R) (2020).
  39. A. Alexandradinata et al., Revealing the topology of Fermi-surface wave functions from magnetic quantum oscillations, Phys. Rev. X 8, 011027 (2018).
  40. J. Y. Liu et al., A magnetic topological semimetal Sr1−yMn1−zSb2 (y, z < 0.1), Nat. Mater. 16, 905 (2017).
  41. S. Nimori et al., de Haas-van Alphen effect of singlet ground state TmSb, Phys. B: Condens. Matter 201, 111 (1994).
  42. A. Narayananan et al., Linear magnetoresistance caused by mobility fluctuations in n-doped Cd3As2, Phys. Rev. Lett. 114, 117201 (2015).
  43. J. Cao et al., Landau level splitting in Cd3As2 under high magnetic fields, Nat. Commun. 6, 7779 (2015).
  44. J. Hu et al., π Berry phase and Zeeman splitting of Weyl semimetal TaP, Sci. Rep. 6, 18674 (2016).
  45. Y. Liu et al., Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5, Nat. Commun. 7, 12516 (2016).
  46. M. Martin et al., Extremely large magnetoresistance induced by Zeeman effect-driven electron-hole compensation and topological protection in MoSi2, Phys. Rev. B 97, 205130 (2018).
  47. Z. Xiang et al., Unusual high-field metal in a Kondo insulator, Nat. Phys. 17, 788 (2021).
  48. G. Kresse, and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  49. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  50. S. Xu et al., Interlayer quantum transport in Dirac semimetal BaGa2, Nat. Commun. 11, 2370 (2020).
  51. J. Hu et al., Nearly massless Dirac fermions and strong Zeeman splitting in the nodal-line semimetal ZrSiS probed by de Haas–van Alphen quantum oscillations, Phys. Rev. B 96, 045127 (2017).
  52. O. Pavlosiuk et al., Giant magnetoresistance, Fermi-surface topology, Shoenberg effect, and vanishing quantum oscillations in the type-II Dirac semimetal candidates MoSi2 and WSi2, Phys. Rev. B 105, 075141 (2022).
  53. O. Vogt and B. R. Copper, Anisotropic magnetization of TmSb, J. Appl. Phys. 39, 1202 (1968).
  54. S. Nimori et al., Field induced magnetization of TmSb, J. Magn. Magn. Mater. 140–144, 1167 (1995).
  55. S. Zhang et al., VASP2KP: k·p Models and Landé g-factors from ab initio calculations, Chinese Phys. Lett. 40, 127101 (2023).
  56. R. Bi et al., Spin zero and large Landé g-factor in WTe2, New J. Phys. 20, 063026 (2018).

Outline

Information

Phys. Rev. Research 7, 043028– Published 7 October, 2025
  • Received 24 June 2025
  • Accepted 15 September 2025
  • Corrected 22 December 2025
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