Abstract
Electronic nematic materials are characterized by a lowered symmetry of the electronic system compared to the underlying lattice, in analogy to the directional alignment without translational order in nematic liquid crystals1. Such nematic phases appear in the copper- and iron-based high-temperature superconductors2,3,4, and their role in establishing superconductivity remains an open question. Nematicity may take an active part, cooperating or competing with superconductivity, or may appear accidentally in such systems. Here we present experimental evidence for a phase of fluctuating nematic character in a heavy-fermion superconductor, CeRhIn5 (ref. 5). We observe a magnetic-field-induced state in the vicinity of a field-tuned antiferromagnetic quantum critical point at Hc ≈ 50 tesla. This phase appears above an out-of-plane critical field H* ≈ 28 tesla and is characterized by a substantial in-plane resistivity anisotropy in the presence of a small in-plane field component. The in-plane symmetry breaking has little apparent connection to the underlying lattice, as evidenced by the small magnitude of the magnetostriction anomaly at H*. Furthermore, no anomalies appear in the magnetic torque, suggesting the absence of metamagnetism in this field range. The appearance of nematic behaviour in a prototypical heavy-fermion superconductor highlights the interrelation of nematicity and unconventional superconductivity, suggesting nematicity to be common among correlated materials.
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Acknowledgements
We thank A. Mackenzie, B. Batlogg, S. Kivelson, E. Fradkin, C. Geibel and J. Thompson for discussions. We also thank B. Zeng for supporting the torque measurements. L.B. is supported by DOE-BES through award DE-SC0002613. The project was supported by the Max Planck Society and funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — MO 3077/1-1. Work at Los Alamos National Laboratory was performed under the auspices of the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Work at the National High Magnetic Field Laboratory was supported by National Science Foundation Cooperative Agreement no. DMR-1157490, the State of Florida, and the US DOE. M.J. acknowledges support from the IMS Rapid Response program at LANL. M.K.C. was supported by funds from US DOE BES ‘Science at 100T’.
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P.J.W.M. and F.R. designed the experiment. P.J.W.M., K.R.S., T.H. and M.D.B. fabricated the microstructured devices. P.J.W.M., T.H., M.K.C., B.J.R., R.D.M. and F.F.B. performed the pulsed field experiments and P.J.W.M., K.R.S. and L.B. the dc-field experiments. E.D.B. and F.R. grew the crystals. M.J. performed the magnetostriction measurements and their analysis. All authors contributed to the manuscript.
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Extended data figures and tables
Extended Data Figure 1 Sketch of the focussed ion beam fabrication process.
a, Precutting of the lamella from the large single crystal. Red arrow in all panels shows the position of the focussed ion beam (FIB). b, Undercutting the lamella to disconnect it from the crystal for the ex situ transfer. c, Transfer of the lamella onto a silicon substrate and electric contacting with gold (Au). d, Final fine structuring into the shapes shown in Fig. 1.
Extended Data Figure 2 Quantum critical transport.
a, In-plane resistivity as a function of field H || [010] for different temperatures (labels on curves, in K). The transition into the AFM state is clearly visible as a kink in the curve moving to higher fields at lower temperatures. At the lowest temperatures, the signature turns into a step-like transition. b, Temperature dependence of in-plane resistivity at fixed field (see key: Hc, critical field) extracted from the data in a. Whereas the resistivity above and below Hc cannot be described by a simple power law, at Hc a slightly sublinear power law ρ ≈ T0.91 describes the measured resistivity over a temperature range up to 10 K.
Extended Data Figure 3 Angle dependence of the anisotropy.
Main panel, measurements of the field angle dependence of in-plane resistivity in a static field (35 T applied along the c direction to ensure the sample is in the high-field phase) and at fixed temperature (300 mK). The samples were rotated in the field towards 20° at which the maximum anisotropy occurs. Two different samples were used to probe this anisotropy. The triangular one shown in Fig. 1 probes the anisotropy developing along the [110], 
channel (dashed line; also shown in Fig. 2), while a second similar sample featuring resistance bars along [100], [010] probed the other orientation (solid line). The emergent anisotropy of the two devices with similar dimensions is remarkably similar. The field configuration during the rotation is sketched on the right. The top sketch indicates the rotation of the magnetic field towards one in-plane direction (red arrow) while the orthogonal in-plane direction defines the axis of rotation (blue). The same colour-code is used consistently in the main panel. The middle (bottom) sketch indicates the configuration for the concrete case of the [110], 
([100], [010]) device. Owing to the off-axis field during the rotation, an in-plane field Bip emerges and its direction in the individual devices is indicated by the green arrow.
Extended Data Figure 4 Lattice response to temperature and magnetic field.
a, Measured zero field coefficient of thermal expansion α(T) of CeRhIn5 in 3He gas. The lambda-type anomaly at the second order AFM phase transition is evident (TN, Néel temperature). b, Magnetostriction ΔL/L(H) measured along the c direction in pulsed magnetic fields at 510 mK. The pulsed field measurement was performed on the same needle-like crystal of CeRhIn5 that is shown in the zero-field measurement in a. The high-field measurement was taken using the same experimental set-up as the temperature-dependent measurement. The crystal was immersed in liquid 3He with the magnetic field applied 11° off the c axis. These raw data show a typical smooth and roughly quadratic behaviour in the magnetic field. Both pulse upsweep (red) and downsweep (blue) overlap well and are barely distinguishable in the raw data. c, Same magnetostriction ΔL/L as in b but after subtraction of a smooth background. In the downsweep, a small but sharp feature appears at H ≈ 30 T that may indicate c-axis shrinkage as the sample transitions into the nematic phase.
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Ronning, F., Helm, T., Shirer, K. et al. Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5. Nature 548, 313–317 (2017). https://doi.org/10.1038/nature23315
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DOI: https://doi.org/10.1038/nature23315
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