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.
Access optionsAccess options
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
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.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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).
Borzi, R. A. et al. Formation of a nematic fluid at high fields in Sr3Ru2O7. Science 315, 214–217 (2007).
Chu, J. W. et al. In-plane resistivity anisotropy in an underdoped iron arsenide superconductor. Science 329, 824–826 (2010).
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).
Ronning, F. et al. Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5. Nature 548, 313–317 (2017).
Lester, C. et al. Field-tunable spin-density-wave phases in Sr3Ru2O7. Nat. Mater. 14, 373–378 (2015).
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).
Ramshaw, B. J. et al. Quasiparticle mass enhancement approaching optimal doping in a high-T c superconductor. Science 348, 317–320 (2015).
Hosoi, S. et al. Nematic quantum critical point without magnetism in FeSe1−xSx superconductors. Proc. Natl Acad. Sci. USA 113, 8139–8143 (2016).
Baek, S.-H. et al. Orbital-driven nematicity in FeSe. Nat. Mater. 14, 210–214 (2015).
Watson, M. D. et al. Emergence of the nematic electronic state in FeSe. Phys. Rev. B 91, 155106 (2015).
Watson, M. D. et al. Suppression of orbital ordering by chemical pressure in FeSe1−xSx. Phys. Rev. B 92, 121108 (2015).
Terashima, T. et al., Anomalous Fermi surface in FeSe seen by Shubnikov–de Haas oscillation measurements. Phys. Rev. B 90, 144517 (2014).
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).
Cooper, R. A. et al. Anomalous criticality in the electrical resistivity of La2−xSrxCuO4. Science 323, 603–607 (2009).
Analytis, J. G. et al. Transport near a quantum critical point in BaFe2(As1−xPx)2. Nat. Phys. 10, 194–197 (2014).
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 https://arxiv.org/abs/1608.01044 (2016).
Hussey, N. E. Non-generality of the Kadowaki–Woods ratio in correlated oxides. J. Phys. Soc. Jpn. 74, 1107–1110 (2005).
Hanaguri, T. et al. Two distinct superconducting pairing states divided by the nematic end point in FeSe1−xSx. Sci. Adv. 4, eaar6419 (2018).
Coldea, A. I. et al. Evolution of the Fermi surface of the nematic superconductors FeSe1−xSx. npj Quant. Mater. 4, 2 (2019).
Pal, H. K. et al. Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids. Lith. J. Phys. 52, 142–164 (2012).
Bendele, M. et al. Pressure induced static magnetic order in superconducting FeSe1−x. Phys. Rev. Lett. 104, 087003 (2010).
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).
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).
Matsuura, K. et al. Maximizing T c by tuning nematicity and magnetism in FeSe1−xSx superconductors. Nat. Commun. 8, 1143 (2017).
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).
Maslov, D. L. & Chubukov, A. V. Fermi liquid near Pomeranchuk quantum criticality. Phys. Rev. B 81, 045110 (2010).
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).
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).
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).
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).
Audouard, A. et al. Quantum oscillations and upper critical magnetic field of the iron-base superconductor FeSe. Europhys. Lett. 109, 27003 (2015).
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).
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).
Hardy, F. et al. Nodal gaps in the nematic superconductor FeSe from heat capacity. Preprint at https://arxiv.org/abs/1807.07907 (2018).
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).
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).
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).
Nature thanks E.-A. Kim and the other anonymous reviewer(s) for their contribution to the peer review of this work.
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
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
The plots show ρab(T) curves in zero field and in a 35 T magnetic field B//ab, for all x. Source Data
Raw data plotted against T2. Source Data
Binned and smoothed data plotted against T2. Source Data
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
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
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