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.

Violation of Ohm’s law in a Weyl metal

Abstract

Ohm’s law is a fundamental paradigm in the electrical transport of metals1. Any transport signatures violating Ohm’s law would give an indisputable fingerprint for a novel metallic state. Here, we uncover the breakdown of Ohm’s law owing to a topological structure of the chiral anomaly in the Weyl metal phase. We observe nonlinear IV characteristics in Bi0.96Sb0.04 single crystals in the diffusive limit, which occurs only for a magnetic-field-aligned electric field (EB). The Boltzmann transport theory with the charge pumping effect reveals the topological-in-origin nonlinear conductivity, and it leads to a universal scaling function of the longitudinal magnetoconductivity, which completely describes our experimental results. As a hallmark of Weyl metals, the nonlinear conductivity provides a venue for nonlinear electronics, optical applications, and the development of a topological Fermi-liquid theory beyond the Landau Fermi-liquid theory.

This is a preview of subscription content

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: The charge pumping effect and signature of nonlinear transport phenomena in longitudinal magnetoresistance.
Figure 2: The field-temperature dependence of nonlinear conductance and its fit with a universal scaling formula.

References

  1. 1

    Ohm, G. S. Die galvanische Kette, mathematisch bearbeitet (TH Riemann, 1827).

    Book  Google Scholar 

  2. 2

    Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–1976 (2010).

    CAS  Article  Google Scholar 

  3. 3

    Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539 (2010).

    Article  Google Scholar 

  4. 4

    Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045 (2010).

    CAS  Article  Google Scholar 

  5. 5

    Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011).

    CAS  Article  Google Scholar 

  6. 6

    Nielsen, H. B. & Ninomiya, M. The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal. Phys. Lett. 130B, 389 (1983).

    CAS  Article  Google Scholar 

  7. 7

    Kim, K.-S., Kim, H.-J., Sasaki, M., Wang, J.-F. & Li, L. Anomalous transport phenomena in Weyl metal beyond the Drude model for Landau’s Fermi liquids. Sci. Technol. Adv. Mater. 15, 064401 (2014).

    Article  Google Scholar 

  8. 8

    Hosur, P. & Qi, X. L. Recent developments in transport phenomena in Weyl semimetals. C. R. Phys. 14, 857 (2013).

    CAS  Article  Google Scholar 

  9. 9

    Haldane, F. D. M. Berry curvature on the Fermi surface: anomalous Hall effect as a topological Fermi-liquid property. Phys. Rev. Lett. 93, 206602 (2004).

    CAS  Article  Google Scholar 

  10. 10

    Murakami, S. Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase. New J. Phys. 9, 356 (2007).

    Article  Google Scholar 

  11. 11

    Burkov, A. A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011).

    CAS  Article  Google Scholar 

  12. 12

    Kim, H.-J. et al. Dirac versus Weyl fermions in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena. Phys. Rev. Lett. 111, 246603 (2013).

    Article  Google Scholar 

  13. 13

    Xiong, J. et al. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350, 413–416 (2015).

    CAS  Article  Google Scholar 

  14. 14

    Li, C. et al. Giant negative magnetoresistance induced by the chiral anomaly in individual Cd3As2 nanowires. Nat. Commun. 6, 10137 (2015).

    CAS  Article  Google Scholar 

  15. 15

    Liang, T. et al. Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2 . Nat. Mater. 14, 280 (2015).

    CAS  Article  Google Scholar 

  16. 16

    Li, H. et al. Negative magnetoresistance in the Dirac semimetal Cd3As2 . Nat. Commun. 7, 10301 (2016).

    CAS  Article  Google Scholar 

  17. 17

    Arnold, F. et al. Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP. Nat. Commun. 7, 11615 (2016).

    CAS  Article  Google Scholar 

  18. 18

    Huang, X. et al. Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs. Phys. Rev. X 5, 031023 (2015).

    Google Scholar 

  19. 19

    Li, Q. et al. Chiral magnetic effect in ZrTe5 . Nat. Phys. 12, 550–554 (2016).

    Article  Google Scholar 

  20. 20

    Goswami, P. & Tewari, S. Axionic field theory of (3+1)-dimensional Weyl semimetals. Phys. Rev. B 88, 245107 (2013).

    Article  Google Scholar 

  21. 21

    Zyuzin, A. A. & Burkov, A. A. Topological response in Weyl semimetals and the chiral anomaly. Phys. Rev. B 86, 115133 (2012).

    Article  Google Scholar 

  22. 22

    Son, D. T. & Spivak, B. Z. Chiral anomaly and classical negative magnetoresistance of Weyl metals. Phys. Rev. B 88, 104412 (2013).

    Article  Google Scholar 

  23. 23

    Kim, K.-S., Kim, H.-J. & Sasaki, M. Boltzmann equation approach to anomalous transport in a Weyl metal. Phys. Rev. B 89, 195137 (2014).

    Article  Google Scholar 

  24. 24

    Kim, K.-S. Role of axion electrodynamics in a Weyl metal: violation of Wiedemann-Franz law. Phys. Rev. B 90, 121108(R) (2014).

    Article  Google Scholar 

  25. 25

    Sharma, G., Goswami, P. & Tewari, S. Nernst and magnetothermal conductivity in a lattice model of Weyl fermions. Phys. Rev. B 93, 035116 (2016).

    Article  Google Scholar 

  26. 26

    Son, D. T. & Yamamoto, N. Berry curvature, triangle anomalies, and the chiral magnetic effect in Fermi liquids. Phys. Rev. Lett. 109, 181602 (2012).

    Article  Google Scholar 

  27. 27

    Stephanov, M. A. & Yin, Y. Chiral kinetic theory. Phys. Rev. Lett. 109, 162001 (2012).

    CAS  Article  Google Scholar 

  28. 28

    Manuel, C. & Torres-Rincon, J.-M. Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory. Phys. Rev. D 90, 076007 (2014).

    Google Scholar 

  29. 29

    Fukushima, K., Kharzeev, D. E. & Warringa, H. J. Chiral magnetic effect. Phys. Rev. D 78, 074033 (2008).

    Article  Google Scholar 

  30. 30

    Chen, Y., Wu, S. & Burkov, A. A. Axion response in Weyl semimetals. Phys. Rev. B 88, 125105 (2013).

    Article  Google Scholar 

  31. 31

    Jho, Y.-S., Han, J.-H. & Kim, K.-S. Topological Fermi-liquid theory for interacting Weyl metals with time reversal symmetry breaking. Phys. Rev. B 95, 205113 (2017).

    Article  Google Scholar 

Download references

Acknowledgements

D.S. and J.K. were supported by the Ministry of Education, Science, and Technology (No. NRF-2017R1A2B4012482) and by the Institute for Basic Science (IBS), Grant No. IBS-R014-D1. D.S. and J.K. are grateful to J. Jeong and H. Chang for TEM measurement. K.-S.K. was supported by the Ministry of Education, Science, and Technology (No. NRF-2015R1C1A1A01051629 and No. 2011-0030046) of the National Research Foundation of Korea (NRF) and by TJ Park Science Fellowship of the POSCO TJ Park Foundation. K.-S.K. was also supported by the POSTECH Basic Science Research Institute Grant (2016). Work at LANL was supported by the National Science Foundation under Grant NSF-DMR-1157490. H.-J.K. was supported by the Basic Science Research Program and National Nuclear R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT, and Future Planning (No. NRF-2014R1A1A1002263, NRF-2011-0031558 (mpk)). Y.L. and Y.H.J. were supported by NRF (2011- 0030786 and 2015R1D1A1A02062239). We would like to acknowledge fruitful discussions in the APCTP Focus programme ‘Lecture series on Beyond Landau Fermi liquid and BCS superconductivity near quantum criticality’ in 2016 and the BK21 plus project.

Author information

Affiliations

Authors

Contributions

J.K. supervised the project. D.S. and K.-S.K. performed the analytical and numerical work. D.S. and Y.L. performed the experiments at low magnetic fields. F.W. and J.B.B. carried out measurements in high pulsed fields at LANL. M.S. made single-crystal samples. D.S., H.-J.K., K.-S.K. and J.K. analysed the data. D.S., H.-J.K., K.-S.K. and J.K. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Heon-Jung Kim, Ki-Seok Kim or Jeehoon Kim.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 1370 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shin, D., Lee, Y., Sasaki, M. et al. Violation of Ohm’s law in a Weyl metal. Nature Mater 16, 1096–1099 (2017). https://doi.org/10.1038/nmat4965

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