Elihu Abrahams

Strong correlations and magnetic frustration in the high Tc iron pnictides.

We consider the iron pnictides in terms of a proximity to a Mott insulator. The superexchange interactions contain competing nearest-neighbor and next-nearest-neighbor components. In the undoped parent compound, these frustrated interactions lead to a two-sublattice collinear antiferromagnet (each sublattice forming a Néel ordering), with a reduced magnitude for the ordered moment. Electron or hole doping, together with the frustration effect, suppresses the magnetic ordering and allows a superconducting state. The exchange interactions favor a d-wave superconducting order parameter; in the notation appropriate for the Fe square lattice, its orbital symmetry is dxy. A number of existing and future experiments are discussed in light of the theoretical considerations.

Correlated electrons in δ-plutonium within a dynamical mean-field picture

Given the practical importance of metallic plutonium, there is considerable interest in understanding its fundamental properties. Plutonium undergoes a 25 per cent increase in volume when transformed from its α-phase (which is stable below 400 K) to the δ-phase (stable at around 600 K), an effect that is crucial for issues of long-term storage and disposal. It has long been suspected that this unique property is a consequence of the special location of plutonium in the periodic table, on the border between the light and heavy actinides—here, electron wave–particle duality (or itinerant versus localized behaviour) is important. This situation has resisted previous theoretical treatment. Here we report an electronic structure method, based on dynamical mean-field theory, that enables interpolation between the band-like and atomic-like behaviour of the electron. Our approach enables us to study the phase diagram of plutonium, by providing access to the energetics and one-electron spectra of strongly correlated systems. We explain the origin of the volume expansion between the α- and δ-phases, predict the existence of a strong quasiparticle peak near the Fermi level and give a new viewpoint on the physics of plutonium, in which the α- and δ-phases are on opposite sides of the interaction-driven localization–delocalization transition.

The Metal-Insulator Transition in Correlated Disordered Systems

Some materials are metals and conduct electricity well; others are insulators and do not. In some cases, metals can be converted to insulators and vice versa by changing some fundamental parameter, such as pressure. In their Perspective, Abrahams and Kotliar discuss results reported in the same issue by Husmann et al. (p. 1874) in which a continuous metal-insulator transition has been observed in a nickel selenide-sulfide compound. Understanding such transitions, which have posed puzzles for years, may help unravel the physics of highly correlated electrons, as well as lead to new materials.

SCALING THEORY OF TWO-DIMENSIONAL METAL-INSULATOR TRANSITIONS

We discuss the recently discovered two-dimensional metal-insulator transition in zero magnetic field in the light of the scaling theory of localization. We demonstrate that the observed symmetry relating conductivity and resistivity follows directly from the quantum critical behavior associated with such a transition. In addition, we show that very general scaling considerations imply that any disordered two dimensional metal is a perfect metal, but most likely not a Fermi liquid.

Charge transfer excitations and superconductivity in “ionic” metals

Abstract The newly discovered high T c oxide metals have a low enough electron density that the charge transfer excitations between the nearest neighbor cations and anions are unscreened. Excitonic resonances with large oscillator strengths are then possible. It is suggested that the high T c is due to scattering of electrons from such resonances rather than from photons.

Iron pnictides as a new setting for quantum criticality

Two major themes in the physics of condensed matter are quantum critical phenomena and unconventional superconductivity. These usually occur in the context of competing interactions in systems of strongly correlated electrons. All this interesting physics comes together in the behavior of the recently discovered iron pnictide compounds that have generated enormous interest because of their moderately high-temperature superconductivity. The ubiquity of antiferromagnetic ordering in their phase diagrams naturally raises the question of the relevance of magnetic quantum criticality, but the answer remains uncertain both theoretically and experimentally. Here, we show that the undoped iron pnictides feature a unique type of magnetic quantum critical point, which results from a competition between electronic localization and itinerancy. Our theory provides a mechanism to understand the experimentally observed variation of the ordered moment among the undoped iron pnictides. We suggest P substitution for As in the undoped iron pnictides as a means to access this example of magnetic quantum criticality in an unmasked fashion. Our findings point to the iron pnictides as a much-needed setting for quantum criticality, one that offers a unique set of control parameters.

High-temperature superconductivity in iron pnictides and chalcogenides

Superconductivity develops in metals upon the formation of a coherent macroscopic quantum state of electron pairs. Iron pnictides and chalcogenides are materials that have high superconducting transition temperatures. In this Review, we describe the advances in the field that have led to higher superconducting transition temperatures in iron-based superconductors and the wide range of materials that form them. We summarize both the essential aspects of the normal state and the mechanism for superconductivity. We emphasize the degree of electron-electron correlations and their manifestation in properties of the normal state. We examine the nature of magnetism, analyse its role in driving the electronic nematicity, and discuss quantum criticality at the border of magnetism in the phase diagram. Finally, we review the amplitude and structure of the superconducting pairing, and survey the potential settings for optimizing superconductivity.

Properties of odd-gap superconductors

We discuss the class of superconductors that have pairing correlations which are odd in frequency, as introduced originally by Berezinskii and more recently by Balatsky and Abrahams. As follows from the equations of motion, a natural definition of the thermodynamic order parameter of the odd-pairing state is the expectation value of a composite operator which couples a Cooper pair to a spin or charge fluctuation. We use a model pairing Hamiltonian to describe properties of the odd-pairing composite-operator condensate. We show that the superfluid stiffness is positive, we discuss superconductive tunneling with an ordinary superconductor, and we derive other thermodynamic and transport properties.

Thermal and electrical transport across a magnetic quantum critical point

A quantum critical point (QCP) arises when a continuous transition between competing phases occurs at zero temperature. Collective excitations at magnetic QCPs give rise to metallic properties that strongly deviate from the expectations of Landau’s Fermi-liquid description, which is the standard theory of electron correlations in metals. Central to this theory is the notion of quasiparticles, electronic excitations that possess the quantum numbers of the non-interacting electrons. Here we report measurements of thermal and electrical transport across the field-induced magnetic QCP in the heavy-fermion compound YbRh2Si2 (refs 2, 3). We show that the ratio of the thermal to electrical conductivities at the zero-temperature limit obeys the Wiedemann–Franz law for magnetic fields above the critical field at which the QCP is attained. This is also expected for magnetic fields below the critical field, where weak antiferromagnetic order and a Fermi-liquid phase form below 0.07 K (at zero field). At the critical field, however, the low-temperature electrical conductivity exceeds the thermal conductivity by about 10 per cent, suggestive of a non-Fermi-liquid ground state. This apparent violation of the Wiedemann–Franz law provides evidence for an unconventional type of QCP at which the fundamental concept of Landau quasiparticles no longer holds. These results imply that Landau quasiparticles break up, and that the origin of this disintegration is inelastic scattering associated with electronic quantum critical fluctuations—these insights could be relevant to understanding other deviations from Fermi-liquid behaviour frequently observed in various classes of correlated materials.

Anisotropic in-plane resistivity in the nematic phase of the iron pnictides.

We show that the interference between scattering by impurities and by critical spin fluctuations gives rise to anisotropic transport in the Ising-nematic state of the iron pnictides. The effect is closely related to the non-Fermi-liquid behavior of the resistivity near an antiferromagnetic quantum critical point. Our theory not only explains the observed sign of the resistivity anisotropy Δρ in electron-doped systems but also predicts a sign change of Δρ upon sufficient hole doping. Furthermore, our model naturally addresses the changes in Δρ upon sample annealing and alkaline-earth substitution.