Annual Review of Condensed Matter Physics - Volume 7, 2016

This is an account of a professional life in the field that was generally known as solid-state physics when I started working in it; India and the United States of America are the countries in which this life was largely played out. My attempts to understand various things in condensed matter physics, and efforts to put together people and activities in India in this field, are mainly the story.

The study of correlated electronic systems from high-Tc cuprates to heavy-fermion systems continues to motivate the development of experimental tools to probe electronic phenomena in new ways and with increasing precision. In the past two decades, spectroscopic imaging with scanning tunneling microscopy has emerged as a powerful experimental technique. The combination of high energy and spatial resolutions provided by this technique reveals unprecedented detail of the electronic properties of strongly correlated metals and superconductors. This review examines specific experiments, theoretical concepts, and measurement methods that have established the application of these techniques to correlated materials. A wide range of applications, such as the study of collective responses to single atomic impurities, the characterization of quasiparticle-like excitations through their interference, and the identification of competing electronic phases using spectroscopic imaging, are discussed.

Recent decisions of the General Conference on Weights and Measures of the Metre Convention have opened the door to a fundamental change of the International System of Units, the SI, in 2018. The revised SI will be based on fixing the numerical values of seven defining constants corresponding to the seven traditional base units. This will bring about basic modifications in the definition of the kilogram, the ampere, the kelvin, and the mole and will have consequences for units derived from them. In contrast, the second, the meter, and the candela will not be affected. This paper describes the motivation and rationale behind this endeavor, introduces the new definitions, and reviews the requirements for the redefinitions as well as the status of the experiments that are currently being carried out to fulfill them. Benefits and a wide-reaching impact for the realization and dissemination of the units are anticipated because innovative technologies with ever-increasing accuracy will emerge, enabling the direct realization over widespread measurement ranges without the definitions themselves having to be changed.

We overview the wave turbulence approach by example of one physical system: gravity waves on the surface of an infinitely deep fluid. In the theoretical part of our review, we derive the nonlinear Hamiltonian equations governing the water-wave system and describe the premises of the weak wave turbulence theory. We outline derivation of the wave-kinetic equation and the equation for the probability density function, and most important solutions to these equations, including the Kolmogorov-Zakharov spectra corresponding to a direct and an inverse turbulent cascades, as well as solutions for non-Gaussian wave fields corresponding to intermittency. We also discuss strong wave turbulence as well as coherent structures and their interaction with random waves. We describe numerical and laboratory experiments, and field observations of gravity wave turbulence, and compare their results with theoretical predictions.

Life depends as much on the flow of information as on the flow of energy. Here we review the many efforts to make this intuition precise. Starting with the building blocks of information theory, we explore examples where it has been possible to measure, directly, the flow of information in biological networks, or more generally where information-theoretic ideas have been used to guide the analysis of experiments. Systems of interest range from single molecules (the sequence diversity in families of proteins) to groups of organisms (the distribution of velocities in flocks of birds), and all scales in between. Many of these analyses are motivated by the idea that biological systems may have evolved to optimize the gathering and representation of information, and we review the experimental evidence for this optimization, again across a wide range of scales.

We concisely review the recent evolution in the study of parafermions—exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. First we generalize the intimate connection between the -symmetric Ising quantum spin chain and Majorana fermions to -symmetric chains and parafermions. In particular, we highlight how parafermion chains host a topological phase featuring protected edge zero modes. We then tour several blueprints for the laboratory realization of parafermion zero modes—focusing on quantum Hall/superconductor hybrids, quantum Hall bilayers, and two-dimensional topological insulators—and describe striking experimental fingerprints that they provide. Finally, we discuss how coupled parafermion arrays in quantum Hall architectures yield topological phases that potentially furnish hardware for a universal, intrinsically decoherence-free quantum computer.

Collisions between particles suspended in a fluid play an important role in many physical processes. As an example, collisions of microscopic water droplets in clouds are a necessary step in the production of macroscopic raindrops. Collisions of dust grains are also conjectured to be important for planet formation in the gas surrounding young stars and to play a role in the dynamics of sand storms. In these processes, collisions are favored by fast turbulent motions. Here we review recent advances in the understanding of collisional aggregation due to turbulence. We discuss the role of fractal clustering of particles and caustic singularities of their velocities. We also discuss limitations of the Smoluchowski equation for modeling such processes. These advances lead to a semiquantitative understanding on the influence of turbulence on collision rates and point to deficiencies in the current understanding of rainfall and planet formation.

Swimming droplets are artificial microswimmers based on liquid droplets that show self-propelled motion when immersed in a second liquid. These systems are of tremendous interest as experimental models for the study of collective dynamics far from thermal equilibrium. For biological systems, such as bacterial colonies, plankton, or fish swarms, swimming droplets can provide a vital link between simulations and real life. We review the experimental systems and discuss the mechanisms of self-propulsion. Most systems are based on surfactant-stabilized droplets, the surfactant layer of which is modified in a way that leads to a steady Marangoni stress resulting in an autonomous motion of the droplet. The modification of the surfactant layer is caused either by the advection of a chemical reactant or by a solubilization process. Some types of swimming droplets possess a very simple design and long active periods, rendering them promising model systems for future studies of collective behavior.

Recently, the effects of spin-orbit coupling (SOC) in correlated materials have become one of the most actively studied subjects in condensed matter physics, as correlations and SOC together can lead to the discovery of new phases. Examples include unconventional magnetism, spin liquids, and strongly correlated topological phases such as topological superconductivity. Among candidate materials, iridium oxides (iridates) have been an excellent playground to uncover such novel phenomena. In this review, we discuss recent progress in iridates and related materials, focusing on the basic concepts, relevant microscopic Hamiltonians, and unusual properties of iridates in perovskite- and honeycomb-based structures. Perspectives on SOC and correlation physics beyond iridates are also discussed.

We discuss recent research on quantum transport in complex materials, from photosynthetic light-harvesting complexes to photonic circuits. We identify finite, disordered networks as the underlying backbone and as a versatile framework to gain insight into the specific potential of nontrivial quantum dynamical effects to characterize and control transport on complex structures. We discriminate authentic quantum properties from classical aspects of complexity and briefly address the impact of interactions, nonlinearities, and noise. We stress the relevance of what we call the nonasymptotic realm, physical situations in which neither the relevant time- and length-scales, the number of degrees of freedom, or constituents tend to very small or very large values, nor do global symmetries or disorder fully govern the dynamics. Although largely uncharted territory, we argue that novel, intriguing and nontrivial questions for experimental and theoretical work emerge, with the prospect of a unified understanding of complex quantum transport phenomena in diverse physical settings.

This article reviews recent theoretical and experimental work on a new class of topological material—topological Kondo insulators, which develop through the interplay of strong correlations and spin-orbit interactions. The history of Kondo insulators is reviewed along with the theoretical models used to describe these heavy fermion compounds. The Fu-Kane method of topological classification of insulators is used to show that hybridization between the conduction electrons and localized f electrons in these systems gives rise to interaction-induced topological insulating behavior. Finally, some recent experimental results are discussed, which appear to confirm the theoretical prediction of the topological insulating behavior in samarium hexaboride, where the long-standing puzzle of the residual low-temperature conductivity has been shown to originate from robust surface states.

Why do animals move the way they do? Bacteria, insects, birds, and fish share with us the necessity to move so as to live. Although each organism follows its own evolutionary course, it also obeys a set of common laws. At the very least, the movement of animals, like that of planets, is governed by Newton's law: All things fall. On Earth, most things fall in air or water, and their motions are thus subject to the laws of hydrodynamics. Through trial and error, animals have found ways to interact with fluid so they can float, drift, swim, sail, glide, soar, and fly. This elementary struggle to escape the fate of falling shapes the development of motors, sensors, and mind. Perhaps we can deduce parts of their neural computations by understanding what animals must do so as not to fall. Here I discuss recent developments along this line of inquiry in the case of insect flight. Asking how often a fly must sense its orientation in order to balance in air has shed new light on the role of motor neurons and steering muscles responsible for flight stability.

The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without an external magnetic field. The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have potential applications in future electronic devices. In recent years, the quantum anomalous Hall effect was proposed theoretically and realized experimentally. In this review article, we provide a systematic overview of the theoretical and experimental developments in this field.

Cilia and flagella in biological systems often show large scale cooperative behaviors such as the synchronization of their beats in “metachronal waves.” These are beautiful examples of emergent dynamics in biology, and are essential for life, allowing diverse processes from the motility of eukaryotic microorganisms, to nutrient transport and clearance of pathogens from mammalian airways. How these collective states arise is not fully understood, but it is clear that individual cilia interact mechanically, and that a strong and long-ranged component of the coupling is mediated by the viscous fluid. We review here the work by ourselves and others aimed at understanding the behavior of hydrodynamically coupled systems, and particularly a set of results that have been obtained both experimentally and theoretically by studying actively driven colloidal systems. In these controlled scenarios, it is possible to selectively test aspects of living motile cilia, such as the geometrical arrangement, the effects of the driving profile and the distance to no-slip boundaries. We outline and give examples of how it is possible to link model systems to observations on living systems, which can be made on microorganisms, on cell cultures or on tissue sections. This area of research has clear clinical application in the long term, as severe pathologies are associated with compromised cilia function in humans.

Fractional topological insulators (FTIs) are electronic systems that carry fractionally charged excitations, conserve charge, and are symmetric to reversal of time. In this review, we introduce the basic essential concepts of the field and then survey theoretical understanding of FTIs in two and three dimensions. In between, we discuss the case of “two and a half dimensions,” the FTIs that may form on the two-dimensional surface of an unfractionalized three-dimensional topological insulator. We focus on electronic systems and emphasize properties of edges and surfaces, most notably the stability of gapless edge modes to perturbations.

X-ray techniques have been used for more than a century to study the atomic and electronic structure in practically any type of material. The advent of correlated electron systems, in particular complex oxides, brought about new scientific challenges and opportunities for the advancement of conventional X-ray methods. In this context, the need for new approaches capable of selectively sensing new forms of orders involving all degrees of freedom—charge, orbital, spin, and lattice—paved the way for the emergence and success of resonant X-ray scattering, which has become an increasingly popular and powerful tool for the study of electronic ordering phenomena in solids. We review the recent resonant X-ray scattering breakthroughs in the copper oxide high-temperature superconductors, in particular regarding the phenomenon of charge order, a broken-symmetry state occurring when valence electrons self-organize into periodic structures. After a brief historical perspective on charge order, we outline the milestones in the development of resonant X-ray scattering as well as the basic theoretical formalism underlying its unique capabilities. The rest of the review focuses on the recent contributions of resonant scattering to the advancements in our description and understanding of charge order. To conclude, we propose a series of present and upcoming challenges and discuss the future outlook for this technique.