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.
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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.
Hussey, N. E. Phenomenology of the normal state in-plane transport properties of high-Tc cuprates. J. Phys. Condens. Matter 20, 123201 (2008).
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).
Stewart, G. R. Non-Fermi-liquid behavior in d- and f-electron metals. Rev. Mod. Phys. 73, 797–855 (2001).
Pippard, A. B. Magnetoresistance in Metals (Cambridge Univ. Press, 2009).
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).
Abrahams, E. & Varma, C. M. Hall effect in the marginal Fermi liquid regime of high-Tc superconductors. Phys. Rev. B 68, 094502 (2003).
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).
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).
Giraldo-Gallo, P. et al. Scale-invariant magnetoresistance in a cuprate superconductor. Science 361, 479–481 (2018).
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).
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).
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).
Sondhi, S. L., Girvin, S. M., Carini, J. P. & Shahar, D. Continuous quantum phase transitions. Rev. Mod. Phys. 69, 315–333 (1997).
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).
Auerbach, A. Equilibrium formulae for transverse magnetotransport of strongly correlated metals. Phys. Rev. B 99, 115115 (2019).
Licciardello, S. et al. Coexistence of orbital and quantum critical magnetoresistance in FeSe1−xSx. Phys. Rev. Res. 1, 023011 (2019).
Varma, C. Quantum-critical fluctuations in 2D metals: strange metals and superconductivity in antiferromagnets and in cuprates. Rep. Prog. Phys. 79, 082501 (2016).
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).
Fanfarillo, L., Cappelluti, E., Castellani, C. & Benfatto, L. Unconventional Hall effect in pnictides from interband interactions. Phys. Rev. Lett. 109, 096402 (2012).
Abdel-Jawad, M. et al. Correlation between the superconducting transition temperature and anisotropic quasiparticle scattering in Tl2Ba2CuO6+δ. Phys. Rev. Lett. 99, 107002 (2007).
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).
Cooper, R. A. et al. Anomalous criticality in the electrical resistivity of La2−xSrxCuO4. Science 323, 603–607 (2009).
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).
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).
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).
Paglione, P. et al. Quantum critical quasiparticle scattering within the superconducting state of CeCoIn5. Phys. Rev. Lett. 117, 016601 (2016).
Mahmood, F., He, X., Božović, I. & Armitage, N. P. Locating the missing superconducting electrons in overdoped cuprates. Phys. Rev. Lett. 122, 027003 (2019).
Moir, C. M. et al. Multi-band mass enhancement towards critical doping in a pnictide superconductor. npj Quant. Mater. 4, 8 (2019).
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).
Hwang, H. Y. et al. Scaling of the temperature dependent Hall effect in La2−xSrxCuO4. Phys. Rev. Lett. 72, 2636–2639 (1994).
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).
Nakajima, Y. et al. Evolution of Hall coefficient in two-dimensional heavy fermion CeCoIn5. J. Phys. Soc. Jpn 75, 023705 (2006).
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).
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).
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).
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.
The authors declare no competing interests.
Peer review information Nature Physics thanks Nigel Hussey and Andrew Schofield for their contribution to the peer review of this work.
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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