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.

  • Letter
  • Published:

Superconductivity and quantum criticality linked by the Hall effect in a strange metal

Abstract

Many unconventional superconductors exhibit a common set of anomalous charge transport properties that characterize them as ‘strange metals’, which provides hope that there is a single theory that describes them1,2,3. However, model-independent connections between the strange metals and superconductivity have remained elusive. Here, we show that the Hall effect of the unconventional superconductor BaFe2(As1−xPx)2 contains an anomalous contribution arising from the correlations within the strange metal. This term has a distinctive dependence on the magnetic field, which allows us to track its behaviour across the doping–temperature phase diagram, even under the superconducting dome. These measurements demonstrate that the strange metal Hall component emanates from a quantum critical point and, in the zero-temperature limit, decays together with the superconducting critical temperature. This empirically reveals the structure of the connection between superconductivity and quantum criticality, which may be common to the physics of many strange metal superconductors.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Strange metal behaviour in BaFe2(As1−xPx)2.
Fig. 2: Low-temperature Hall coefficient of BaFe2(As1−xPx)2.
Fig. 3: Low-field enhancement of the Hall number across the critical fan.

Similar content being viewed by others

Data availability

Source data are available for this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

References

  1. Hussey, N. E. Phenomenology of the normal state in-plane transport properties of high-Tc cuprates. J. Phys. Condens. Matter 20, 123201 (2008).

    Article  ADS  Google Scholar 

  2. Kasahara, S. et al. Evolution from non-Fermi- to Fermi-liquid transport via isovalent doping in BaFe2(As1−xPx)2 superconductors. Phys. Rev. B 81, 184519 (2010).

    Article  ADS  Google Scholar 

  3. Stewart, G. R. Non-Fermi-liquid behavior in d- and f-electron metals. Rev. Mod. Phys. 73, 797–855 (2001).

    Article  ADS  Google Scholar 

  4. Pippard, A. B. Magnetoresistance in Metals (Cambridge Univ. Press, 2009).

  5. Casey, P. A. & Anderson, P. W. Hidden Fermi liquid: self-consistent theory for the normal state of high-Tc superconductors. Phys. Rev. Lett. 106, 097002 (2011).

    Article  ADS  Google Scholar 

  6. Abrahams, E. & Varma, C. M. Hall effect in the marginal Fermi liquid regime of high-Tc superconductors. Phys. Rev. B 68, 094502 (2003).

    Article  ADS  Google Scholar 

  7. Coleman, P., Schofield, A. J. & Tsvelik, A. M. How should we interpret the two transport relaxation times in the cuprates? J. Phys. Condens. Matter 8, 9985–10015 (1996).

    Article  ADS  Google Scholar 

  8. Hayes, I. M. et al. Scaling between magnetic field and temperature in the high temperature superconductor BaFe2(As1−x Px)2. Nat. Phys. 12, 916–919 (2016).

    Article  Google Scholar 

  9. Giraldo-Gallo, P. et al. Scale-invariant magnetoresistance in a cuprate superconductor. Science 361, 479–481 (2018).

    Article  ADS  Google Scholar 

  10. Sarkar, T., Mandal, P. R., Poniatowski, N. R., Chan, M. K. & Greene, R. L. Correlation between scale-invariant normal state resistivity and superconductivity in an electron-doped cuprate. Sci. Adv. 5, eaav6753 (2019).

    Article  ADS  Google Scholar 

  11. Analytis, J. G., Chu, J., McDonald, R. D., Riggs, S. C. & Fisher, I. R. Enhanced Fermi-surface nesting in superconducting BaFe2(As1−x Px)2 revealed by the de Haas−van Alphen effect. Phys. Rev. Lett. 105, 207004 (2010).

    Article  ADS  Google Scholar 

  12. Shishido, H. et al. Evolution of the Fermi surface of BaFe2(As1−x Px)2 on entering the superconducting dome. Phys. Rev. Lett. 104, 057008 (2010).

    Article  ADS  Google Scholar 

  13. Sondhi, S. L., Girvin, S. M., Carini, J. P. & Shahar, D. Continuous quantum phase transitions. Rev. Mod. Phys. 69, 315–333 (1997).

    Article  ADS  Google Scholar 

  14. Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).

    Article  ADS  Google Scholar 

  15. Auerbach, A. Equilibrium formulae for transverse magnetotransport of strongly correlated metals. Phys. Rev. B 99, 115115 (2019).

    Article  ADS  Google Scholar 

  16. Licciardello, S. et al. Coexistence of orbital and quantum critical magnetoresistance in FeSe1−xSx. Phys. Rev. Res. 1, 023011 (2019).

    Article  Google Scholar 

  17. Varma, C. Quantum-critical fluctuations in 2D metals: strange metals and superconductivity in antiferromagnets and in cuprates. Rep. Prog. Phys. 79, 082501 (2016).

    Article  ADS  Google Scholar 

  18. Lederer, S. et al. Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point. Proc. Natl Acad. Sci. USA 114, 4905–4910 (2017).

    Article  ADS  Google Scholar 

  19. Fanfarillo, L., Cappelluti, E., Castellani, C. & Benfatto, L. Unconventional Hall effect in pnictides from interband interactions. Phys. Rev. Lett. 109, 096402 (2012).

    Article  ADS  Google Scholar 

  20. Abdel-Jawad, M. et al. Correlation between the superconducting transition temperature and anisotropic quasiparticle scattering in Tl2Ba2CuO6+δ. Phys. Rev. Lett. 99, 107002 (2007).

    Article  ADS  Google Scholar 

  21. Dorion-Leyraud, N. et al. Correlation between linear resistivity and Tc in the Bechgaard salts and the pnictide superconductor BaFe2(As1−x Px)2. Phys. Rev. B 80, 214531 (2009).

    Article  ADS  Google Scholar 

  22. Cooper, R. A. et al. Anomalous criticality in the electrical resistivity of La2−xSrxCuO4. Science 323, 603–607 (2009).

    Article  ADS  Google Scholar 

  23. Jin, K., Butch, N. P., Kirshenbaum, K., Paglione, J. & Greene, R. L. Link between spin fluctuations and electron pairing in copper oxide superconductors. Nature 476, 73–75 (2011).

    Article  Google Scholar 

  24. Mandal, P. R., Sarkar, T. & Greene, R. L. Anomalous quantum criticality in the electron-doped cuprates. Proc. Natl Acad. Sci. USA 116, 5991–5994 (2019).

    Article  ADS  Google Scholar 

  25. Božović, I., He, X., Wu, J. & Bollinger, A. T. Dependence of the critical temperature in overdoped copper oxides on superfluid density. Nature 536, 309–311 (2016).

    Article  ADS  Google Scholar 

  26. Paglione, P. et al. Quantum critical quasiparticle scattering within the superconducting state of CeCoIn5. Phys. Rev. Lett. 117, 016601 (2016).

    Article  ADS  Google Scholar 

  27. Mahmood, F., He, X., Božović, I. & Armitage, N. P. Locating the missing superconducting electrons in overdoped cuprates. Phys. Rev. Lett. 122, 027003 (2019).

    Article  ADS  Google Scholar 

  28. Moir, C. M. et al. Multi-band mass enhancement towards critical doping in a pnictide superconductor. npj Quant. Mater. 4, 8 (2019).

    Article  ADS  Google Scholar 

  29. Chien, T. R., Wang, Z. Z. & Ong, N. P. Effect of Zn impurities on the normal-state Hall angle in single-crystal YBa2Cu3−xO7−δ. Phys. Rev. Lett. 67, 2088–2091 (1991).

    Article  ADS  Google Scholar 

  30. Hwang, H. Y. et al. Scaling of the temperature dependent Hall effect in La2−xSrxCuO4. Phys. Rev. Lett. 72, 2636–2639 (1994).

    Article  ADS  Google Scholar 

  31. Putzke, C. et al. Reduced Hall carrier density in the overdoped strange metal regime of cuprate superconductors. Preprint at https://arxiv.org/abs/1909.08102 (2019).

  32. Nakajima, Y. et al. Evolution of Hall coefficient in two-dimensional heavy fermion CeCoIn5. J. Phys. Soc. Jpn 75, 023705 (2006).

    Article  ADS  Google Scholar 

  33. Ando, Y., Komiya, S., Segawa, K., Ono, S. & Kurita, Y. Electronic phase diagram of High-Tc cuprate superconductors from a mapping of the in-plane resistivity curvature. Phys. Rev. Lett. 93, 267001 (2004).

    Article  ADS  Google Scholar 

  34. Hussey, N. E., Buhot, J. & Licciardello, S. A tale of two metals: contrasting criticalities in the pnictides and hole-doped cuprates. Rep. Prog. Phys. 81, 052501 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  35. Nakajima, M. et al. Growth of BaFe2(As1−xPx)2 single crystals (0≤x≤1) by Ba2As3/Ba2P3-flux method. J. Phys. Soc. Jpn 81, 104710 (2012).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank D.-H. Lee and C. Varma for fruitful discussions. This work is supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant number GBMF9067. Materials synthesis by N.M. was performed as part of the Quantum Materials programme supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division of the US Department of Energy under contract number DE-AC02-05CH11231. A portion work was performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative Agreement Numbers DMR-1157490 and DMR-1644779 and the State of Florida. B.J.R., M.K.C. and R.D.M. acknowledge funding from the US Department of Energy Office of Basic Energy Sciences Science under the 100 T programme.

Author information

Authors and Affiliations

Authors

Contributions

I.M.H. and J.G.A. conceived the project. I.M.H. and N.M. synthesized the samples. I.M.H., N.M., M.K.C., G.N.L., B.J.R. and R.D.M. performed the measurements. I.M.H. and J.G.A. analysed the data and wrote the manuscript with input from all of the authors.

Corresponding author

Correspondence to James G. Analytis.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Nigel Hussey and Andrew Schofield for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1 and 2 and discussion sections I and II.

Source data

Source Data Fig. 1

Hall coefficient numerical values plotted in Fig. 1.

Source Data Fig. 2

Hall coefficient numerical values plotted in Fig. 2.

Source Data Fig. 3

Hall coefficient numerical values plotted in Fig. 3.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hayes, I.M., Maksimovic, N., Lopez, G.N. et al. Superconductivity and quantum criticality linked by the Hall effect in a strange metal. Nat. Phys. 17, 58–62 (2021). https://doi.org/10.1038/s41567-020-0982-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-020-0982-x

This article is cited by

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