Skip to main content

Thank you for visiting 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.

Electrical resistivity across a nematic quantum critical point


Correlated electron systems are highly susceptible to various forms of electronic order. By tuning the transition temperature towards absolute zero, striking deviations from conventional metallic (Fermi-liquid) behaviour can be realized. Evidence for electronic nematicity, a correlated electronic state with broken rotational symmetry, has been reported in a host of metallic systems1,2,3,4,5 that exhibit this so-called quantum critical behaviour. In all cases, however, the nematicity is found to be intertwined with other forms of order, such as antiferromagnetism5,6,7 or charge-density-wave order8, that might themselves be responsible for the observed behaviour. The iron chalcogenide FeSe1−xSx is unique in this respect because its nematic order appears to exist in isolation9,10,11, although until now, the impact of nematicity on the electronic ground state has been obscured by superconductivity. Here we use high magnetic fields to destroy the superconducting state in FeSe1−xSx and follow the evolution of the electrical resistivity across the nematic quantum critical point. Classic signatures of quantum criticality are revealed: an enhancement in the coefficient of the T2 resistivity (due to electron–electron scattering) on approaching the critical point and, at the critical point itself, a strictly T-linear resistivity that extends over a decade in temperature T. In addition to revealing the phenomenon of nematic quantum criticality, the observation of T-linear resistivity at a nematic critical point also raises the question of whether strong nematic fluctuations play a part in the transport properties of other ‘strange metals’, in which T-linear resistivity is observed over an extended regime in their respective phase diagrams.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



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

Fig. 1: Crystal structure and phase diagram of FeSe1−xSx.
Fig. 2: Longitudinal magnetoresistance in FeSe1−xSx.
Fig. 3: T2-resistivity in FeSe1−xSx below the superconducting dome.
Fig. 4: Quantum critical behaviour in the charge transport of FeSe1−xSx.

Data availability

The data that support the findings of this study are available from the authors on reasonable request. See the ‘Author Contributions’ section for specific datasets.


  1. Fradkin, E., Kivelson, S.A., Lawler, M. J., Eisenstein, J. P. & Mackenzie, A. P. Nematic Fermi fluids in condensed matter physics. Annu. Rev. Condens. Matter Phys. 1, 153–178 (2010).

    Article  ADS  CAS  Google Scholar 

  2. Borzi, R. A. et al. Formation of a nematic fluid at high fields in Sr3Ru2O7. Science 315, 214–217 (2007).

    Article  ADS  CAS  Google Scholar 

  3. Chu, J. W. et al. In-plane resistivity anisotropy in an underdoped iron arsenide superconductor. Science 329, 824–826 (2010).

    Article  ADS  CAS  Google Scholar 

  4. Ando, Y., Segawa, K., Komiya, S. & Lavrov, A. N. Electrical resistivity anisotropy from self-organized one dimensionality in high-temperature superconductors. Phys. Rev. Lett. 88, 137005 (2002).

    Article  ADS  Google Scholar 

  5. Ronning, F. et al. Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5. Nature 548, 313–317 (2017).

    Article  ADS  CAS  Google Scholar 

  6. Lester, C. et al. Field-tunable spin-density-wave phases in Sr3Ru2O7. Nat. Mater. 14, 373–378 (2015).

    Article  ADS  CAS  Google Scholar 

  7. Nakai, Y. et al. Unconventional superconductivity and antiferromagnetic quantum critical behavior in the isovalent-doped BaFe2(As1−xPx)2. Phys. Rev. Lett. 105, 107003 (2010).

    Article  ADS  CAS  Google Scholar 

  8. Ramshaw, B. J. et al. Quasiparticle mass enhancement approaching optimal doping in a high-T c superconductor. Science 348, 317–320 (2015).

    Article  ADS  CAS  Google Scholar 

  9. Hosoi, S. et al. Nematic quantum critical point without magnetism in FeSe1−xSx superconductors. Proc. Natl Acad. Sci. USA 113, 8139–8143 (2016).

    Article  ADS  CAS  Google Scholar 

  10. Baek, S.-H. et al. Orbital-driven nematicity in FeSe. Nat. Mater. 14, 210–214 (2015).

    Article  ADS  CAS  Google Scholar 

  11. Watson, M. D. et al. Emergence of the nematic electronic state in FeSe. Phys. Rev. B 91, 155106 (2015).

    Article  ADS  Google Scholar 

  12. Watson, M. D. et al. Suppression of orbital ordering by chemical pressure in FeSe1−xSx. Phys. Rev. B 92, 121108 (2015).

    Article  ADS  Google Scholar 

  13. Terashima, T. et al., Anomalous Fermi surface in FeSe seen by Shubnikov–de Haas oscillation measurements. Phys. Rev. B 90, 144517 (2014).

    Article  ADS  Google Scholar 

  14. Shibauchi, T., Carrington, A. & Matsuda, Y. A quantum critical point lying beneath the superconducting dome in iron pnictides. Annu. Rev. Condens. Matter Phys. 5, 113–135 (2014).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  16. Analytis, J. G. et al. Transport near a quantum critical point in BaFe2(As1−xPx)2. Nat. Phys. 10, 194–197 (2014).

    Article  CAS  Google Scholar 

  17. Urata, T. et al. Non-Fermi liquid behavior of electrical resistivity close to the nematic critical point in Fe1−xCoxSe and FeSe1−ySy. Preprint at (2016).

  18. Hussey, N. E. Non-generality of the Kadowaki–Woods ratio in correlated oxides. J. Phys. Soc. Jpn. 74, 1107–1110 (2005).

    Article  ADS  CAS  Google Scholar 

  19. Hanaguri, T. et al. Two distinct superconducting pairing states divided by the nematic end point in FeSe1−xSx. Sci. Adv. 4, eaar6419 (2018).

    Article  Google Scholar 

  20. Coldea, A. I. et al. Evolution of the Fermi surface of the nematic superconductors FeSe1−xSx. npj Quant. Mater. 4, 2 (2019).

    Article  ADS  Google Scholar 

  21. Pal, H. K. et al. Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids. Lith. J. Phys. 52, 142–164 (2012).

    Article  Google Scholar 

  22. Bendele, M. et al. Pressure induced static magnetic order in superconducting FeSe1−x. Phys. Rev. Lett. 104, 087003 (2010).

    Article  ADS  CAS  Google Scholar 

  23. Wiecki, P. et al. NMR evidence for static local nematicity and its cooperative interplay with low-energy magnetic fluctuations in FeSe under pressure. Phys. Rev. B 96, 180502 (2017).

    Article  ADS  Google Scholar 

  24. Grinenko, V. et al. Close proximity of FeSe to a magnetic quantum critical point as revealed by high-resolution μSR measurements. Phys. Rev. B 97, 201102 (2018).

    Article  ADS  Google Scholar 

  25. Matsuura, K. et al. Maximizing T c by tuning nematicity and magnetism in FeSe1−xSx superconductors. Nat. Commun. 8, 1143 (2017).

    Article  ADS  CAS  Google Scholar 

  26. Maslov, D. L., Yudson, V. I. & Chubukov, A. V. Resistivity of a non-Galilean–invariant Fermi liquid near Pomeranchuk quantum criticality. Phys. Rev. Lett. 106, 106403 (2011).

    Article  ADS  Google Scholar 

  27. Maslov, D. L. & Chubukov, A. V. Fermi liquid near Pomeranchuk quantum criticality. Phys. Rev. B 81, 045110 (2010).

    Article  ADS  Google Scholar 

  28. Hartnoll, S. A., Mahajan, R., Punk, M. & Sachdev, S. Transport near the Ising-nematic quantum critical point of metals in two dimensions. Phys. Rev. B 89, 155130 (2014).

    Article  ADS  Google Scholar 

  29. Lederer, S., Schattner, Y., Berg, E. & Kivelson, A. Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point. Proc. Natl Acad. Sci. USA 114, 4905–4910 (2017).

    Article  ADS  CAS  Google Scholar 

  30. Yu, R. & Si Q. Antiferroquadrupolar and Ising-nematic orders of a frustrated bilinear-biquadratic Heisenberg model and implications for the magnetism of FeSe. Phys. Rev. Lett. 115, 116401 (2015).

    Article  ADS  Google Scholar 

  31. Bruin, J. A. N., Sakai, H., Perry, R. S. & Mackenzie, A. P. Similarity of scattering rates in metals showing T-linear resistivity. Science 339, 804–807 (2013).

    Article  ADS  CAS  Google Scholar 

  32. Audouard, A. et al. Quantum oscillations and upper critical magnetic field of the iron-base superconductor FeSe. Europhys. Lett. 109, 27003 (2015).

    Article  ADS  Google Scholar 

  33. Lin, J.-Y. et al. Coexistence of isotropic and extended s-wave order parameters in FeSe as revealed by low-temperature specific heat. Phys. Rev. B 84, 220507 (2011).

    Article  ADS  Google Scholar 

  34. Bӧhmer, A. et al. Origin of the tetragonal-to-orthorhombic phase transition in FeSe: a combined thermodynamic and NMR study of nematicity. Phys. Rev. Lett. 114, 027001 (2015).

    Article  ADS  Google Scholar 

  35. Hardy, F. et al. Nodal gaps in the nematic superconductor FeSe from heat capacity. Preprint at (2018).

  36. Huynh, K. K. et al. Electric transport of a single-crystal iron chalcogenide FeSe superconductor: evidence of symmetry-breakdown nematicity and additional ultrafast Dirac cone-like carriers. Phys. Rev. B 90, 144516 (2014).

    Article  ADS  Google Scholar 

  37. Watson, M. D. et al. Dichotomy between the hole and electron behavior in multiband superconductor FeSe probed by ultrahigh magnetic fields. Phys. Rev. Lett. 115, 027006 (2015).

    Article  ADS  CAS  Google Scholar 

Download references


We acknowledge discussions with Q. Si, A. Chubukov and J. Schmalian. We also acknowledge the support of the HFML-RU/NWO, a member of the European Magnetic Field Laboratory (EMFL). This work is part of the research programme ‘Strange Metals’ (grant number 16METL01) of the former Foundation for Fundamental Research on Matter (FOM), which is financially supported by the Netherlands Organisation for Scientific Research (NWO). A portion of this work was also supported by the Engineering and Physical Sciences Research Council (grant number EP/L015544/1), by Grants-in-Aid for Scientific Research (KAKENHI) (grant numbers 15H02106, 15H03688, 15KK0160, 18H01177 and 18H05227) and Innovative Areas ‘Topological Material Science’ (grant number 15H05852) from the Japan Society for the Promotion of Science (JSPS).

Reviewer information

Nature thanks E.-A. Kim and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

Authors and Affiliations



N.E.H. initiated the project (in collaboration with Y.M. and T.S.). S.K. synthesized the FeSe1−xSx single crystals. S.L., J.B., J.A. and J.L. performed the magnetotransport measurements. S.L. and N.E.H. analysed the data. N.E.H. and S.L. wrote the manuscript with input from all co-authors.

Corresponding author

Correspondence to N. E. Hussey.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Extended data figures and tables

Extended Data Fig. 1 Calibration of the Cernox temperature sensor in a magnetic field of 35 T between 0.3 K and 30 K.

The coloured symbols in the graph are the data points taken at different constant temperatures as explained in the text. The points were then divided into four temperature intervals to calculate phenomenological fits, plotted here as lines. The inset shows a detail of the lowest temperature range.

Source Data

Extended Data Fig. 2 Low-temperature magnetoresistance of FeSe1−xSx.

a, Field sweeps obtained for a sample with x = 0.2 at several fixed temperatures. The magnetoresistance itself has a negligible temperature dependence over the entire temperature range studied. b, Comparison of a selection of field sweeps for x = 0. Note that the extent of the y scale is different for the 1 K curve because ρab is much smaller than at higher temperatures.

Source Data

Extended Data Fig. 3 Field derivative of the magnetoresistance between 34 T and 35 T at different temperatures for x = 0.13.

The blue symbols represent the slope of linear fits to the magnetoresistance (dρab/dB) curves, while the pink symbols are the difference between the 35 T resistivity and its extrapolated value at zero field. Down to about 1.5 K, the magnitude of the magnetoresistance (MR) is essentially constant. Below 1.5 K, the effect of superconducting (SC) fluctuations on the magnetoresistance can be clearly seen. Vertical error bars represent a compound error of the difference in slope maxima and mimina associated with the scatter in the data and uncertainty in the geometrical factors.

Source Data

Extended Data Fig. 4 Temperature dependence of the in-plane resistivity ρab of FeSe1−xSx.

The plots show ρab(T) curves in zero field and in a 35 T magnetic field B//ab, for all x.

Source Data

Extended Data Fig. 5 Definition of the temperature scales T1 and T2.

For each x value, the temperature derivative of the resistivity curve was obtained after binning and smoothing the 35 T data of Extended Data Fig. 4. The extent of the T-linear behaviour of dρab/dT defines T2, whereas the onset temperature of the constant regime is T1.

Source Data

Extended Data Fig. 6 Determination of the A coefficients from the resistivity curves.

Raw data plotted against T2.

Source Data

Extended Data Fig. 7 Determination of the A coefficients from the resistivity curves.

Binned and smoothed data plotted against T2.

Source Data

Extended Data Fig. 8 Determination of Ts.

The structural phase-transition temperature Ts is determined from the temperature derivatives of the resistivity curves in a broad temperature range of up to about 150 K. The kink in the resistivity curves that can be seen in Fig. 1c corresponds to a dip in the derivatives.

Source Data

Extended Data Fig. 9 The x-dependence of the quantum oscillation frequencies F in FeSe1−xSx.

The black circles and terracotta diamonds represent respectively the evolution, as a function of S substitution x, of the sums α+δ and β+γ of the quantum oscillation frequencies reported in ref. 21. The two dashed lines are linear fits that were used in the determination of kF (at each x) for the renormalization of the A coefficient (to A*) and in the estimate of α, the prefactor in the strength of the T-linear scattering rate. See Methods for more details.

Source Data

Extended Data Fig. 10 Determination of Hc2.

a, Definition of Hc2 at T = 1.35 K for x = 0.25. b, Plotted values of Hc2(T = 1.35 K) as a function of varying x. The black dashed lines are exponential fits. Hc2(T = 1.35 K, x = 0) is much smaller than at higher S concentrations, presumably owing to the lower level of disorder in FeSe. Vertical error bars originate from uncertainties in the determination of Hc2 (as defined in Methods) due to scatter in the raw field sweeps. The larger error bar for x = 0.16 is due to the additional uncertainty caused by having to extrapolate the Hc2 curve below 4.2 K.

Source Data

Extended Data Fig. 11 T-linear resistivity at x ≈ xc.

Estimation of lower limit of A for x = 0.16 from the temperature derivative of the 35 T resistivity curve. The slope of the blue dashed line is 2A = 0.66 μΩ cm K−2. The arrow indicates the temperature at which ρab(T) ceases to be strictly linear. As shown in Fig. 4b, T2 (the temperature below which the T2 resistivity first appears) is approximately half that of T1 (the temperature down to which the resistivity remains T-linear) for all x < 0.16. Thus, it is not unreasonable to assume that the maximum value of T2 for xc = 0.16, if indeed the resistivity does cross over to T2, is a factor of two smaller than the base temperature of our experiment, making our estimate for the minimum value of A twice the absolute minimum plotted in Fig. 3b.

Source Data

Extended Data Table 1 Summary of quantum oscillation measurements on FeSe

Source data

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Licciardello, S., Buhot, J., Lu, J. et al. Electrical resistivity across a nematic quantum critical point. Nature 567, 213–217 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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