- Open Access
Probing the Fermi surface with quantum oscillation measurements in the Dirac semimetal
Phys. Rev. B 112, 195137 – Published 26 November, 2025
DOI: https://doi.org/10.1103/ythr-l17b
Abstract
We report a detailed investigation of the Fermi surface in the layered Dirac semimetal . We probed the magnetization, magnetic torque, and magnetoresistance in high-quality single crystals. Pronounced Shubnikov–de Haas and de Haas–van Alphen oscillations are observed in magnetic fields above and at temperatures of up to . Multiple fundamental frequencies and light effective quasiparticle masses are obtained by fast Fourier transformation (FFT) and Lifshitz-Kosevich formula fits. The high resolution of the low-temperature FFT spectra allows us to investigate individual peaks in detail for the magnetic fields applied along all three crystallographic axes and the planes in between. Our investigation can confirm the density functional theory calculated band structure and its corresponding Fermi surface.
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References (36)
- S. M. Young and C. L. Kane, Dirac semimetals in two dimensions, Phys. Rev. Lett. 115, 126803 (2015).
- M. Yan, H. Huang, K. Zhang, E. Wang, W. Yao, K. Deng, G. Wan, H. Zhang, M. Arita, H. Yang et al., Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide , Nat. Commun. 8, 257 (2017).
- J. Xiong, S. K. Kushwaha, T. Liang, J. W. Krizan, M. Hirschberger, W. Wang, R. J. Cava, and N. P. Ong, Evidence for the chiral anomaly in the Dirac semimetal , Science 350, 413 (2015).
- S. Borisenko, Q. Gibson, D. Evtushinsky, V. Zabolotnyy, B. Büchner, and R. J. Cava, Experimental realization of a three-dimensional Dirac semimetal, Phys. Rev. Lett. 113, 027603 (2014).
- S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang et al., A Weyl fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class, Nat. Commun. 6, 7373 (2015).
- A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, Type-II Weyl semimetals, Nature (London) 527, 495 (2015).
- H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides, Phys. Rev. X 5, 011029 (2015).
- B. Lv, N. Xu, H. Weng, J. Ma, P. Richard, X. Huang, L. Zhao, G. Chen, C. Matt, F. Bisti et al., Observation of Weyl nodes in taas, Nat. Phys. 11, 724 (2015).
- S.-Y. Xu, N. Alidoust, I. Belopolski, Z. Yuan, G. Bian, T.-R. Chang, H. Zheng, V. N. Strocov, D. S. Sanchez, G. Chang et al., Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide, Nat. Phys. 11, 748 (2015).
- S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee et al., Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349, 613 (2015).
- S.-Y. Xu, C. Liu, S. K. Kushwaha, R. Sankar, J. W. Krizan, I. Belopolski, M. Neupane, G. Bian, N. Alidoust, T.-R. Chang et al., Observation of Fermi arc surface states in a topological metal, Science 347, 294 (2015).
- L. Yang, Z. Liu, Y. Sun, H. Peng, H. Yang, T. Zhang, B. Zhou, Y. Zhang, Y. Guo, M. Rahn et al., Weyl semimetal phase in the non-centrosymmetric compound TaAs, Nat. Phys. 11, 728 (2015).
- Z. Liu, L. Yang, Y. Sun, T. Zhang, H. Peng, H. Yang, C. Chen, Y. f. Zhang, Y. Guo, D. Prabhakaran et al., Evolution of the fermi surface of Weyl semimetals in the transition metal pnictide family, Nat. Mater. 15, 27 (2016).
- C. Fang, H. Weng, X. Dai, and Z. Fang, Topological nodal line semimetals, Chin. Phys. B 25, 117106 (2016).
- R. Yu, Z. Fang, X. Dai, and H. Weng, Topological nodal line semimetals predicted from first-principles calculations, Front. Phys. 12, 127202 (2017).
- L. M. Schoop, M. N. Ali, C. Straßer, A. Topp, A. Varykhalov, D. Marchenko, V. Duppel, S. S. Parkin, B. V. Lotsch, and C. R. Ast, Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS, Nat. Commun. 7, 11696 (2016).
- C. Fang, Y. Chen, H.-Y. Kee, and L. Fu, Topological nodal line semimetals with and without spin-orbital coupling, Phys. Rev. B 92, 081201(R) (2015).
- T. Bzdušek, Q. Wu, A. Rüegg, M. Sigrist, and A. A. Soluyanov, Nodal-chain metals, Nature (London) 538, 75 (2016).
- S.-Y. Yang, H. Yang, E. Derunova, S. S. Parkin, B. Yan, and M. N. Ali, Symmetry demanded topological nodal-line materials, Adv. Phys.: X 3, 1414631 (2018).
- J. Hu, Z. Tang, J. Liu, X. Liu, Y. Zhu, D. Graf, K. Myhro, S. Tran, C. N. Lau, J. Wei et al., Evidence of topological nodal-line fermions in ZrSiSe and ZrSiTe, Phys. Rev. Lett. 117, 016602 (2016).
- Z. Hao, W. Chen, Y. Wang, J. Li, X.-M. Ma, Y.-J. Hao, R. Lu, Z. Shen, Z. Jiang, W. Liu et al., Multiple Dirac nodal lines in an in-plane anisotropic semimetal , Phys. Rev. B 104, 115158 (2021).
- C. Xu, Y. Liu, P. Cai, B. Li, W. Jiao, Y. Li, J. Zhang, W. Zhou, B. Qian, X. Jiang et al., Anisotropic transport and quantum oscillations in the quasi-one-dimensional : Evidence for the nontrivial band topology, J. Phys. Chem. Lett. 11, 7782 (2020).
- Z. Chen, M. Wu, Y. Zhang, J. Zhang, Y. Nie, Y. Qin, Y. Han, C. Xi, S. Ma, X. Kan et al., Three-dimensional topological semimetal phase in layered probed by quantum oscillations, Phys. Rev. B 103, 035105 (2021).
- R. Ye, T. Gao, H. Li, X. Liang, and G. Cao, Anisotropic giant magnetoresistance and de Hass–van Alphen oscillations in layered topological semimetal crystals, AIP Adv. 12, 045104 (2022).
- E. W. Liimatta and J. A. Ibers, Synthesis, structures, and conductivities of the new layered compounds and , J. Solid State Chem. 78, 7 (1989).
- P. Blaha, K. Schwarz, G. K. Madsen, D. Kvasnicka, J. Luitz et al., Wien2k: An augmented plane wave+ local orbitals program for calculating crystal properties, 60 (2001).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- S. M. Young, S. Zaheer, J. C. Y. Teo, C. L. Kane, E. J. Mele, and A. M. Rappe, Dirac semimetal in three dimensions, Phys. Rev. Lett. 108, 140405 (2012).
- S. Xiao, W.-H. Jiao, Y. Lin, Q. Jiang, X. Yang, Y. He, Z. Jiang, Y. Yang, Z. Liu, M. Ye et al., Dirac nodal lines in the quasi-one-dimensional ternary telluride , Phys. Rev. B 105, 195145 (2022).
- J. R. Badger, Y. Quan, M. C. Staab, S. Sumita, A. Rossi, K. P. Devlin, K. Neubauer, D. S. Shulman, J. C. Fettinger, P. Klavins et al., Dirac lines and loop at the Fermi level in the time-reversal symmetry breaking superconductor , Commun. Phys. 5, 22 (2022).
- M. Wang, Y. Wang, Z. Yang, J. Fan, B. Zheng, R. Wang, and X. Wu, Symmetry-enforced nodal cage phonons in , Phys. Rev. B 105, 174309 (2022).
- W.-H. Jiao, X.-M. Xie, Y. Liu, X. Xu, B. Li, C.-Q. Xu, J.-Y. Liu, W. Zhou, Y.-K. Li, H.-Y. Yang et al., Topological Dirac states in a layered telluride with quasi-one-dimensional chains, Phys. Rev. B 102, 075141 (2020).
- W.-H. Jiao, S. Xiao, B. Li, C. Xu, X.-M. Xie, H.-Q. Qiu, X. Xu, Y. Liu, S.-J. Song, W. Zhou et al., Anisotropic transport and de Haas–van Alphen oscillations in quasi-one-dimensional , Phys. Rev. B 103, 125150 (2021).
- D. Shoenberg, Magnetic Oscillations in Metals (Cambridge University Press, Cambridge, UK, 1984).
- P. M. C. Rourke and S. Julian, Numerical extraction of de Haas-van Alphen frequencies from calculated band energies, Comput. Phys. Commun. 183, 324 (2012).
- M. Daschner, I. Kokanović, and F. M. Grosche, Mechanical enhancement of quantum oscillations, arXiv:2507.02612.