Correlated electron fluids can exhibit a startling array of complex phases, among which one of the more surprising is the electron nematic, a translationally invariant metallic phase with a spontaneously generated spatial anisotropy. Classicalnematicsgenerally occur in liquids of rod-like molecules; given that electrons are point like, the initial theoretical motivation for contemplating electron nematics came from thinking of the electron fluid as a quantum melted electron crystal, rather than a strongly interacting descendent of a Fermi gas. Dramatic transport experiments in ultra-clean quantum Hall systems in 1999 and in Sr3Ru2O7 in a strong magnetic field in 2007 established that such phases exist in nature. In this article, we briefly review the theoretical considerations governing nematic order, summarize the quantum Hall and Sr3Ru2O7 experiments that unambiguously establish the existence of this phase, and survey some of the current evidence for such a phase in the cuprate and Fe-based high temperature superconductors.

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Nematic Fermi Fluids in Condensed Matter Physics

Many exotic compounds, such as cuprate superconductors and heavy fermion materials, exhibit a linear in temperature (T) resistivity, the origin of which is not well understood. We found that the resistivity of the quantum critical metal Sr(3)Ru(2)O(7) is also T-linear at the critical magnetic field of 7.9 T. Using the precise existing data for the Fermi surface topography and quasiparticle velocities of Sr(3)Ru(2)O(7), we show that in the region of the T-linear resistivity, the scattering rate per kelvin is well approximated by the ratio of the Boltzmann constant to the Planck constant divided by 2π. Extending the analysis to a number of other materials reveals similar results in the T-linear region, in spite of large differences in the microscopic origins of the scattering.

http://science.sciencemag.org/content/sci/339/6121/804.full.pdf

Similarity of Scattering Rates in Metals Showing T-Linear Resistivity

In principle, a complex assembly of strongly interacting electrons can self-organize into a wide variety of collective states, but relatively few such states have been identified in practice. We report that, in the close vicinity of a metamagnetic quantum critical point, high-purity strontium ruthenate Sr3Ru2O7 possesses a large magnetoresistive anisotropy, consistent with the existence of an electronic nematic fluid. We discuss a striking phenomenological similarity between our observations and those made in high-purity two-dimensional electron fluids in gallium arsenide devices.

https://science.sciencemag.org/content/sci/315/5809/214.full.pdf

Formation of a Nematic Fluid at High Fields in Sr3Ru2O7

This review presents a summary and evaluations of the superconducting properties of the layered ruthenate Sr 2 RuO 4 as they are known in the autumn of 2011. This paper appends the main progress th...

Evaluation of Spin-Triplet Superconductivity in Sr2RuO4

A sensitive probe of unconventional order is its response to a symmetry-breaking field. To probe the proposed px ± ipy topological superconducting state of Sr2RuO4, we have constructed an apparatus capable of applying both compressive and tensile strains of up to 0.23%. Strains applied along 〈 100 〉 crystallographic directions yield a strong, strain-symmetric increase in the superconducting transition temperature Tc. 〈 110 〉 strains give a much weaker, mostly antisymmetric response. As well as advancing the understanding of the superconductivity of Sr2RuO4, our technique has potential applicability to a wide range of problems in solid-state physics.

https://science.sciencemag.org/content/sci/344/6181/283.full.pdf

Strong Increase of Tc of Sr2RuO4 Under Both Tensile and Compressive Strain

101Ru-Knight shift (101K) in the spin-triplet superconductor Sr2RuO4 was measured under magnetic fields parallel to the c axis (perpendicular to the RuO2 plane), which is the promising superconducting (SC) d-vector direction in a zero field. We succeeded in measuring K(c) in the field range from 200 to 1200 Oe and at temperatures down to 80 mK, using nuclear-quadrupole-resonance spectra. We found that (101)K(c) is invariant with respect to the field and temperature on passing through H(c2) and T(c) above 200 Oe. This indicates that the spin susceptibility along the c axis does not change in the SC state, at least, in the field greater than 200 Oe. The results imply that the SC d vector is in the RuO2 plane when the magnetic field is applied to the c axis.

Measurement of the 101Ru-Knight shift of superconducting Sr2RuO4 in a parallel magnetic field.

Co nuclear-quadrupole-resonance (NQR) studies were performed in the recently discovered superconductor Na x CoO 2 · y H 2 O to investigate physical properties in the superconducting (SC) and normal states. Two samples from the same Na x CoO 2 were examined, a SC bilayer-hydrate sample with T c ∼4.7 K and a non-SC monolayer-hydrate sample. From the measurement of nuclear-spin lattice relaxation rate 1/ T 1 in the SC sample, it was found that the coherence peak is absent just below T c and that 1/ T 1 is proportional to temperature far below T c . These results, which are in qualitative agreement with the previous result by Fujimoto et al. , suggest strongly that unconventional superconductivity is realized in this compound. In the normal state, 1/ T 1 T of the SC sample shows a gradual increase below 100 K down to T c , whereas 1/ T 1 T of the non-SC sample shows the Korringa behavior in this temperature range. From the comparison between 1/ T 1 T and χ bulk in the SC sample, the increase in 1/ T 1 T is at...

Unconventional Superconductivity and Nearly Ferromagnetic Spin Fluctuations in NaxCoO2·yH2O

We report 59Co NMR studies on magnetically oriented powder samples of Co oxide superconductors, NaxCoO2·yH2O, with Tc~4.7 K. From the two-dimensional powder pattern in the NMR spectrum, the ab-plane Knight shift in the normal state was estimated from the magnetic field dependence of the second-order quadrupole shifts at various temperatures. Below 50 K, the Knight shift shows a Curie–Weiss-like temperature dependence, similarly to the bulk magnetic susceptibility χ. From the analysis of the so-called K–χ plot, the spin and the orbital components of K and the positive hyperfine coupling constant were estimated. The onset temperature of the superconducting transition in the Knight shift does not change much in an applied magnetic field up to 7 T, which is consistent with the reported high upper critical field Hc2. The Knight shift at 7 T shows an invariant behaviour below Tc. No coherence peak just below Tc was observed in the temperature dependence of the nuclear spin–lattice relaxation rate 1/T1 in either case (NMR, nuclear quadrupole resonance). We conclude that the invariant behaviour of the Knight shift below Tc and unconventional behaviours of 1/T1 may indicate spin triplet superconductivity with p- or f-wave symmetry.

https://iopscience.iop.org/article/10.1088/0953-8984/18/2/022/pdf

Possible spin triplet superconductivity in NaxCoO2?yH2O ?59Co NMR studies

The electrical conductivity σ and the thermoelectric power S have been measured for liquid Te–Se mixtures in a wide temperature and pressure range. Substantial changes in σ and S are induced by a slight application of pressure. The region where such changes occur is determined can the concentration-temperature plane. It is suggested that the observed semiconductor to metal transition is originated from the structural change.

Electrical Properties of Liquid Te–Se Mixtures at High Temperatures and High Pressures

We have investigated the spin dynamics using $^{17}\mathrm{O}\mathrm{\text{\ensuremath{-}}}\mathrm{NMR}$ in the bilayered perovskite ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$, which sits close to a metamagnetic quantum critical point. The nuclear spin-lattice relaxation rate divided by temperature $1/{T}_{1}T$ is enhanced on approaching the metamagnetic critical field of $\ensuremath{\sim}7.9\text{ }\text{ }\mathrm{T}$, and at the critical field $1/{T}_{1}T$ continues to increase and does not show Fermi-liquid behavior down to 0.3 K. The temperature dependence of ${T}_{1}T$ in this region suggests the critical temperature $\ensuremath{\Theta}$ to be $\ensuremath{\sim}0\text{ }\text{ }\mathrm{K}$, which is strong evidence that the spin dynamics possesses a quantum critical character. Comparison between uniform susceptibility and $1/{T}_{1}T$ reveals that antiferromagnetic fluctuations instead of two-dimensional ferromagnetic fluctuations dominate the spin fluctuation spectrum at the critical field, which is unexpected for itinerant metamagnetism.

K Ishida

Papers

Measurement of the 101Ru-Knight shift of superconducting Sr2RuO4 in a parallel magnetic field.

Unconventional Superconductivity and Nearly Ferromagnetic Spin Fluctuations in NaxCoO2·yH2O

Possible spin triplet superconductivity in NaxCoO2?yH2O ?59Co NMR studies

Electrical Properties of Liquid Te–Se Mixtures at High Temperatures and High Pressures

Metamagnetic quantum criticality revealed by 17O-NMR in the itinerant metamagnet Sr3Ru2O7.