Steven A. Kivelson

How to detect fluctuating stripes in the high-temperature superconductors

We discuss fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies for extracting information concerning such local order from experiments are derived with emphasis on neutron scattering and scanning tunneling microscopy. These ideas are tested by application to two model systems - the exactly solvable one dimensional electron gas with an impurity, and a weakly-interacting 2D electron gas. We extensively review experiments on the cuprate high-temperature superconductors which can be analyzed using these strategies. We adduce evidence that stripe correlations are widespread in the cuprates. Finally, we compare and contrast the advantages of two limiting perspectives on the high-temperature superconductor: weak coupling, in which correlation effects are treated as a perturbation on an underlying metallic (although renormalized) Fermi liquid state, and strong coupling, in which the magnetism is associated with well defined localized spins, and stripes are viewed as a form of micro-phase separation. We present quantitative indicators that the latter view better accounts for the observed stripe phenomena in the cuprates.

Electronic Liquid Crystal Phases of a Doped Mott Insulator

The character of the ground state of an antiferromagnetic insulator is fundamentally altered following addition of even a small amount of charge. The added charge is concentrated into domain walls across which a π phase shift in the spin correlations of the host material is induced. In two dimensions, these domain walls are ‘stripes’ which can be insulating, or conducting — that is, metallic ‘rivers’ with their own low-energy degrees of freedom. However, in arrays of one-dimensional metals, which occur in materials such as organic conductors, interactions between stripes typically drive a transition to an insulating ordered charge-density-wave (CDW) state at low temperatures. Here it is shown that such a transition is eliminated if the zero-point energy of transverse stripe fluctuations is sufficiently large compared tothe CDW coupling between stripes. As a consequence, there should exist electronic quantum liquid-crystal phases, which constitute new states of matter, and which can be either high-temperature superconductors or two-dimensional anisotropic ‘metallic’ non-Fermi liquids. Neutron scattering and other experiments in the copper oxide superconductor La1.6−xNd0.4SrxCuO4 already provide evidence for the existence of these phases in at least one class of materials.

From quantum matter to high-temperature superconductivity in copper oxides

The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the ‘normal’ state at elevated temperatures.

Frustrated electronic phase separation and high-temperature superconductors

Abstract There is a strong tendency for dilute holes in an antiferromagnet to phase separate. (This is a generic feature of doping into a commensurate correlated insulating state.) We review the general and model-specific theoretical arguments that support this conclusion for neutral holes. In the presence of long-range Coulomb interactions, there is frustrated phase separation leading to large-amplitude, low-energy fluctuations in the hole density at intermediate length scales, provided the dielectric constant is sufficiently large. We describe extensive experimental evidence showing that such “clumping” of the holes is an important feature of the cuprate superconductors. We also summarize theoretical results which suggest that frustrated phase separation may account for the anomalous properties of the normal state and give rise to high-temperature superconductivity.

A thermodynamic theory of supercooled liquids

A novel thermodynamic theory of the properties of supercooled liquids as they get glassy is presented. It is based on the postulated existence of a narrowly avoided thermodynamic phase transition at a temperature T∗ ⩾ Tm, where Tm is the melting point, and the “avoidance” is due to geometric frustration. We show that as a consequence two large emergent length scales develop at temperatures less than T∗, and we also show that this picture is consistent with appropriate statistical mechanical models. A theoretical expression is obtained which permits collapse of the viscosity versus temperature of all known glass-formers onto a single master-curve.

Intrinsic conductivity of conducting polymers

Because the charged dopant ions are spatially separated from the quasi-one-dimensional conduction path in conducting polymers, resistive back scattering is suppressed. In the case of high molecular weight and relatively few sp3 defects, even relatively weak interchain coupling is sufficient to avoid one-dimensional localization; this leads to coherent transport with a mean free path that is limited by either the mean separation between chain imperfections or by phonon scattering. Because of the large π-electron bandwidth and the relatively small number of thermally excited 2κF phonons, nph ≈ exp(−hω0/κBT) where ω0 is the 2κF phonon frequency, the intrinsic room temperature conductivity is estimated to be greater than that of copper.

Stripe phases in high-temperature superconductors

Stripe phases are predicted and observed to occur in a class of strongly correlated materials describable as doped antiferromagnets, of which the copper-oxide superconductors are the most prominent representatives. The existence of stripe correlations necessitates the development of new principles for describing charge transport and especially superconductivity in these materials.

Nematic Fermi Fluids in Condensed Matter Physics

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.

Electronic correlation effects and superconductivity in doped fullerenes.

A theory of the electronic properties of doped fullerenes is proposed in which electronic correlation effects within single fullerene molecules play a central role, and qualitative predictions are made which, if verified, would support this hypothesis. Depending on the effective intrafulllerene electron-electron repulsion and the interfullerene hopping amplitudes (which should depend on the dopant species, among other things), the calculations indicate the possibilities of singlet superconductivity and ferromagnetism.

Colloquium : Theory of intertwined orders in high temperature superconductors

Understanding high temperature superconductors is a central problem in condensed matter physics. Many experiments have uncovered ordering tendencies which are responsible for the complex phase diagram of high temperature superconductors. This Colloquium discusses the interplay between different order parameters in these materials. Considering the intertwining of these orders leads to new experimentally observable consequences, shedding new light into the physics of these fascinating materials.