Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Unconventional mass enhancement around the Dirac nodal loop in ZrSiS

Abstract

The topological properties of fermions arise from their low-energy Dirac-like band dispersion and associated chirality. Initially confined to points, extensions of the Dirac dispersion to lines, and even loops, have now been uncovered, and semimetals hosting such features have been identified. However, experimental evidence for the enhanced correlation effects predicted to occur in these topological semimetals has been lacking. Here, we report a quantum oscillation study of the nodal-loop semimetal ZrSiS in high magnetic fields that reveals significant enhancement in the effective mass of the quasiparticles residing near the nodal loop. Above a threshold field, magnetic breakdown occurs across gaps in the loop structure with orbits that enclose different windings around its vertices, each winding accompanied by an additional π Berry phase. The amplitudes of these breakdown orbits exhibit an anomalous temperature dependence. These findings demonstrate the emergence of novel, correlation-driven physics in ZrSiS associated with the Dirac-like quasiparticles.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Crystallographic and electronic structure of ZrSiS.
Figure 2: Shubnikov–de Haas oscillations and breakdown orbits in ZrSiS in a perpendicular magnetic field.
Figure 3: Geometrical (Berry) phase around a Dirac cone.
Figure 4: Effective mass and anomalous thermal damping of the oscillation amplitude.

References

  1. 1

    Volovik, G. E. The Universe in a Helium Droplet (Oxford Univ. Press, 2007).

    Google Scholar 

  2. 2

    Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).

    ADS  Google Scholar 

  3. 3

    Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

    ADS  Google Scholar 

  4. 4

    Moore, J. E. & Balents, L. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306 (2007).

    ADS  Google Scholar 

  5. 5

    Konig, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

    ADS  Google Scholar 

  6. 6

    Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012).

    ADS  Google Scholar 

  7. 7

    Young, S. M. & Kane, C. L. Dirac semimetals in two dimensions. Phys. Rev. Lett. 115, 126803 (2015).

    ADS  Google Scholar 

  8. 8

    Weng, H. et al. Topological node-line semimetal in three-dimensional graphene networks. Phys. Rev. B 92, 045108 (2015).

    ADS  Google Scholar 

  9. 9

    Wu, Y. et al. Dirac node arcs in PtSn4 . Nat. Phys. 12, 667–671 (2016).

    Google Scholar 

  10. 10

    Bian, G. et al. Topological nodal-line fermions in spin-orbit metal PbTaSe2 . Nat. Commun. 7, 10556 (2016).

    ADS  Google Scholar 

  11. 11

    Neupane, M. et al. Observation of topological nodal fermion semimetal phase in ZrSiS. Phys. Rev. B 93, 201104(R) (2016).

    ADS  Google Scholar 

  12. 12

    Schoop, L. M. et al. Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS. Nat. Commun. 7, 11696 (2016).

    ADS  Google Scholar 

  13. 13

    Burkov, A. A. Topological semimetals. Nat. Mater. 15, 1145–1148 (2016).

    ADS  Google Scholar 

  14. 14

    Fang, C., Weng, H., Dai, X. & Fang, Z. Topological nodal line semimetals. Chin. Phys. B 25, 117106 (2016).

    ADS  Google Scholar 

  15. 15

    Huh, Y., Moon, E.-G. & Kim, Y.-B. Long-range Coulomb interaction in nodal-ring semimetals. Phys. Rev. B 93, 035138 (2016).

    ADS  Google Scholar 

  16. 16

    Roy, B. Interacting line-node semimetal and spontaneous symmetry breaking. Phys. Rev. B 96, 041113 (2017).

    ADS  Google Scholar 

  17. 17

    Liu, J. & Balents, L. Correlation and transport phenomena in topological nodal-loop semi-metals. Phys. Rev. B 95, 075426 (2017).

    ADS  Google Scholar 

  18. 18

    Wang, X. et al. Evidence of both surface and bulk Dirac bands and anisotropic non-saturating magnetoresistance in ZrSiS. Adv. Electron. Mater. 2, 1600228 (2016).

    Google Scholar 

  19. 19

    Ali, M. N. et al. Butterfly magnetoresistance, quasi-2D Dirac Fermi surfaces and a topological phase transition in ZrSiS. Sci. Adv. 2, e1601742 (2016).

    ADS  Google Scholar 

  20. 20

    Hu, J. et al. Evidence of topological nodal-line fermions in ZrSiSe and ZrSiTe. Phys. Rev. Lett. 117, 016602 (2016).

    ADS  Google Scholar 

  21. 21

    Singha, R., Pariari, A., Satpati, B. & Mandal, P. Large non-saturating magnetoresistance and signature of non-degenerate Dirac nodes in ZrSiS. Proc. Natl Acad. Sci. USA 114, 2468–2473 (2017).

    Google Scholar 

  22. 22

    Hu, J. 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).

    ADS  Google Scholar 

  23. 23

    Topp, A. et al. Non-symmorphic band degeneracy at the Fermi level in ZrSiTe. New J. Phys. 13, 125014 (2016).

    Google Scholar 

  24. 24

    Tan, B. S. et al. Unconventional Fermi surface in an insulating state. Science 349, 287–290 (2015).

    ADS  Google Scholar 

  25. 25

    Klein Haneveld, A. J. & Jellinek, F. Zirconium silicide and germanide chalcogenides preparation and crystal structures. Rec. Trav. Chim. Pays-Bas 83, 776–783 (1964).

    Google Scholar 

  26. 26

    Xu, Q. et al. Two-dimensional oxide topological insulator with iron-pnictide superconductor LiFeAs structure. Phys. Rev. B 92, 205310 (2015).

    ADS  Google Scholar 

  27. 27

    Lv, Y.-Y. et al. Extremely large and significantly anisotropic magnetoresistance in ZrSiS single crystals. Appl. Phys. Lett. 108, 244101 (2016).

    ADS  Google Scholar 

  28. 28

    Matusiak, M., Cooper, J. R. & Kaczorowski, D. Thermoelectric quantum oscillations in ZrSiS. Nat. Commun. 8, 15219 (2017).

    ADS  Google Scholar 

  29. 29

    Gvozdikov, V. M., Pershin, Y. V., Steep, E., Jansen, A. G. M. & Wyder, P. de Haas–van Alphen oscillations in the quasi-two-dimensional organic conductor κ-(ET)2Cu(NCS)2: the magnetic breakdown approach. Phys. Rev. B 65, 165102 (2002).

    ADS  Google Scholar 

  30. 30

    Elias, D. C. et al. Dirac cones reshaped by interaction effects in suspended graphene. Nat. Phys. 7, 701–704 (2011).

    Google Scholar 

  31. 31

    Yu, G. L. et al. Interaction phenomena in graphene seen through quantum capacitance. Proc. Natl Acad. Sci. USA 110, 3282–3286 (2013).

    ADS  Google Scholar 

  32. 32

    Gegenwart, P. et al. Magnetic-field induced quantum critical point in YbRh2Si2 . Phys. Rev. Lett. 89, 056402 (2002).

    ADS  Google Scholar 

  33. 33

    Paglione, J. et al. Field-induced quantum critical point in CeCoIn5 . Phys. Rev. Lett. 91, 246405 (2003).

    ADS  Google Scholar 

  34. 34

    Shoenberg, D. Magnetic Oscillations in Metals (Cambridge Univ. Press, 1984).

    Google Scholar 

  35. 35

    Schrieffer, J. R. Theory of Superconductivity (Perseus Books, 1983).

    Google Scholar 

  36. 36

    Kishigi, K., Nakano, M., Machida, K. & Hori, Y. dHvA effect with quantum interference oscillation due to magnetic breakdown. J. Phys. Soc. Jpn 64, 3043–3059 (1995).

    ADS  Google Scholar 

  37. 37

    Pal, H. K., Piechon, F., Fuchs, J.-N., Goerbig, M. & Montambaux, G. Chemical asymmetry and quantum oscillations in insulators. Phys. Rev. B 94, 125140 (2016).

    ADS  Google Scholar 

  38. 38

    Dzero, M., Sun, K., Galitski, V. & Coleman, P. Topological Kondo insulators. Phys. Rev. Lett. 104, 106408 (2010).

    ADS  Google Scholar 

  39. 39

    Knolle, J. & Cooper, N. R. Quantum oscillations without a Fermi surface and the anomalous de Haas–van Alphen effect. Phys. Rev. Lett. 115, 146401 (2015).

    ADS  Google Scholar 

  40. 40

    Knolle, J. & Cooper, N. R. Anomalous de Haas–van Alphen effect in InAs/GaSb quantum wells. Phys. Rev. Lett. 118, 176801 (2017).

    ADS  Google Scholar 

  41. 41

    Virosztek, A. & Ruvalds, J. Nested Fermi-liquid theory. Phys. Rev. B 42, 4064–4074 (1990).

    ADS  Google Scholar 

  42. 42

    Blaha, P., Schwarz, K., Madsen, G. K. H., Kvasnicka, D. & Luitz, J. WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universität Wien, 2001).

    Google Scholar 

  43. 43

    Perdew, J. P., Burke, S. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge enlightening discussions with Y.-B. Kim and A. McCollam. We also acknowledge the support of the HFML-RU/FOM, member of the European Magnetic Field Laboratory (EMFL). A portion of this work was supported by the Engineering and Physical Sciences Research Council (grant no. EP/K016709/1).

Author information

Affiliations

Authors

Contributions

S.W. initiated the project in collaboration with L.M.S. S.P., M.R.v.D. and S.W. performed the magnetotransport measurements. L.M.S. and B.V.L. synthesized the ZrSiS single crystals. A.C. performed the electronic band-structure calculations. S.P., M.R.v.D., S.W., A.C., M.I.K. and N.E.H. analysed the data. N.E.H. wrote the manuscript with input from all the co-authors.

Corresponding authors

Correspondence to N. E. Hussey or S. Wiedmann.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1081 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Pezzini, S., van Delft, M., Schoop, L. et al. Unconventional mass enhancement around the Dirac nodal loop in ZrSiS. Nat. Phys. 14, 178–183 (2018). https://doi.org/10.1038/nphys4306

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing