# 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.

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## References

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## 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

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.

Correspondence to Heon-Jung Kim or 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)

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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

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