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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. Classical nematics generally 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 Sr(3)Ru(2)O(7) 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 Sr(3)Ru(2)O(7) 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

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.

The concept of quantum criticality is proving to be central to attempts to understand the physics of strongly correlated electrons. Here, we argue that observations on the itinerant metamagnet Sr3Ru2O7 represent good evidence for a new class of quantum critical point, arising when the critical end point terminating a line of first-order transitions is depressed toward zero temperature. This is of interest both in its own right and because of the convenience of having a quantum critical point for which the tuning parameter is the magnetic field. The relationship between the resultant critical fluctuations and novel behavior very near the critical field is discussed.

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.

In a quantum fluid without an associated lattice, such as ! He, the momentum of the fluid is conserved except where it interacts with the walls of a channel through which it is flowing. As the temperature decreases and the quasiparticle--quasiparticle mean free path within the fluid increases because of the decrease of its quasiparticle scattering rate, interactions with the walls become more probable, and the viscosity and flow resistance increase. This is intuitively at odds with the behavior seen for electrons moving in a crystalline lattice, whose flow resistance decreases as increases. The resolution of this apparent paradox is that coupling to the lattice and its excitations means that the large majority of collisions in the electron fluid (electron--impurity, normal electron--phonon, Umklapp electron--electron and Umklapp electron--phonon) relax momentum, taking the fluid far from the hydrodynamic limit. At least some of these momentum--relaxing collisions are inevitable in any real material. Strictly speaking, momentum of the electron fluid can never be conserved, even in a bulk sample for which boundary scattering is insignificant. This does not, however, mean that the electronic viscosity needs to play no role in determining electrical resistance. A pragmatic benchmark is whether momentum--conserving processes are faster or slower than momentum--relaxing ones. If the electron fluid's momentum is relaxed slowly, it can be thought of as being quasi--conserved, and hydrodynamic signatures might be observable (1--9).The search for hydrodynamic effects in electrons in solids has been given extra impetus by the introduction of the "holographic correspondence" to condensed matter physics (10).This technique introduced the concept of a minimum viscosity, argued to be applicable to strongly interacting fluids as diverse as the quark--gluon plasma and cold atomic gases (11). 3Hydrodynamic effects have also been postulated to be at the root of the T--linear resistivity of the high temperature superconductors (6, 7), but because momentum--relaxing scattering is strong in those materials, it is difficult to perform an analysis of the experimental data that unambiguously separates the two effects. In a pioneering experiment, unusual current--voltage relationships in a semiconductor wire were convincingly ascribed to hydrodynamic effects (3), but that avenue of research has not been widely pursued, even though the large difference between transport and electron--electron scattering rates in semiconductors was subsequently demonstrated by direct non--equilibrium measurements (12).Here we sought to identify a material in which momentum--relaxing scattering is anomalously suppressed in order to investigate whether a hydrodynamic contribution to electrical transport could be clearly separated from the more standard contributions from momentum--relaxing processes. The material that we chose was PdCoO ! , a layered metal with a series of unusual properties (13--21). Its electronic structure is deceptively simple, with one ...

We report a comprehensive study of magneto-oscillatory phenomena in the normal state of Sr 2 RuO 4 , the first layered perovskite superconductor ͑T c Х 1 K͒ not based on copper. The form of the quasiparticle spectrum observed may be interpreted in terms of an almost two-dimensional Fermi liquid model which is consistent with Luttinger's theorem and successfully predicts bulk thermodynamic and transport properties at low temperatures. A study of the spectra and transport along the c axis provides insights into the different normal state and superconducting behavior of Sr 2 RuO 4 and the cuprates.[S0031-9007(96)00174-3] PACS numbers: 71.18.+y, 71.27.+a, 74.25.Jb A decade of intensive research on the cuprate superconductors and related systems has raised fundamental challenges to our understanding of the metallic state. A surprising development is the realization that not only the superconducting but also the normal phases can exhibit properties which are difficult to reconcile with the standard (Fermi liquid) description. A number of mechanisms for the breakdown of at least some of the predictions of the usual Fermi liquid model have been proposed, but their applicability to the cuprates remains controversial. Some of the proposals stress the unique chemistry of the planar Cu-O bond [1] while a common theme in many of the others is the importance of reduced dimensionality. The latter favors long range effective interactions between the quasiparticles which can lead to an instability of the standard Fermi liquid state or at least to temperature ͑T ͒ dependences of physical properties at variance with those normally associated with this state. Perhaps the most novel of these proposals is that of Anderson [2] in which a singular quasiparticle pseudopotential arises quite generally in a two-dimensional system at not too low a density due to the reduced phase space available for recoil in collisions, an effect which in higher dimensions tends to stabilize the normal Fermi liquid.Experimental constraints on these models come not only from studies of the cuprates, but also of other related layered perovskites which share with them a quasi-twodimensional structure, but differ in other details. Of particular interest is the recently discovered superconductor Sr 2 RuO 4 [3] which has a similar crystal structure to the parent compound, La 2 CuO 4 , of one of the best studied families of the cuprate superconductors, La 22x Sr x CuO 4 , but has four valence electrons (for Ru 41 ) instead of one hole per formula unit.In stoichiometric La 2 CuO 4 the holes in a starting half filled d͑x 2 2 y 2 ͒-p s band undergo a transition to a Mott insulating state with spin 1͞2 per formula unit, and finite conductivity is achieved only upon doping. For a corresponding description of Sr 2 RuO 4 , it is convenient to begin with the isostructural and isoelectronic relative Sr 2 FeO 4 in which the four valence electrons that in a starting model occupy three d͑xy, xz, yz͒-p p orbitals undergo a Mott transition to an insulator with a high spin. ...

Condensed systems of strongly interacting electrons are ideal for the study of quantum complexity. It has become possible to promote the formation of new quantum phases by explicitly tuning systems toward special low-temperature quantum critical points. So far, the clearest examples have been appearances of superconductivity near pressure-tuned antiferromagnetic quantum critical points. We present experimental evidence for the formation of a nonsuperconducting phase in the vicinity of a magnetic field-tuned quantum critical point in ultrapure crystals of the ruthenate metal Sr3Ru2O7, and we discuss the possibility that the observed phase is due to a spin-dependent symmetry-breaking Fermi surface distortion.