Annual Review of Condensed Matter Physics - Volume 10, 2019

Like The Magic Flute, my career has been paved by wonderful and unexpected stories played by enthusiastic and talented students, in close contact with experiments and industry. I participated in the birth of soft matter physics under the impulse of Pierre-Gilles de Gennes: polymers, liquid crystals, colloids, and wetting, which I later applied to the study of living matter. By teaching in the early days at the Institut Universitaire de Technologies d'Orsay, I came into contact with industry, which gave me the chance to collaborate with several companies: Rhône-Poulenc, Dior, Saint-Gobain, Rhodia, and Michelin. These partners have not only largely financed my research in physical chemistry but they also offered a wealth of innovative research topics. In 1996, when Professor Jacques Prost became the director of the Physico-Chimie Curie laboratory, in the Pavillon Curie built for Marie Curie, I turned to biophysics. I initiated collaborations with biologists, applying soft matter physics to the mechanics of cells and tissues. Pierre-Gilles de Gennes has been a wonderful guide throughout this scientific adventure to build my soft matter garden.

Strontium titanate is a wide-gap semiconductor avoiding a ferroelectric instability thanks to quantum fluctuations. This proximity leads to strong screening of static Coulomb interaction and paves the way for the emergence of a very dilute metal with extremely mobile carriers at liquid-helium temperature. Upon warming, mobility decreases by several orders of magnitude. Yet, metallicity persists above room temperature even when the apparent mean free path falls below the electron wavelength. The superconducting instability survives at exceptionally low concentrations and beyond the boundaries of Migdal–Eliashberg approximation. An intimate connection between dilute superconductivity and aborted ferroelectricity is widely suspected. In this review, we give a brief account of ongoing research on bulk strontium titanate as an insulator, a metal, and a superconductor.

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system constituents. During the past two decades, network science has provided many insights in natural, social, biological, and technological systems. However, real systems are often interconnected, with many interdependencies that are not properly captured by single-layer networks. To account for this source of complexity, a more general framework, in which different networks evolve or interact with each other, is needed. These are known as multilayer networks. Here, we provide an overview of the basic methodology used to describe multilayer systems as well as of some representative dynamical processes that take place on top of them. We round off the review with a summary of several applications in diverse fields of science.

Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high-temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this review, we examine the status of the understanding of metallic quantum criticality and the recent progress made by QMC simulations. We focus on the cases of spin-density wave and Ising nematic criticality. We describe the results obtained so far and their implications for superconductivity, non-Fermi liquid behavior, and transport near metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.

We review recent advances in experimental and theoretical understanding of spin transport in strongly interacting Fermi gases. The central new phenomenon is the observation of a lower bound on the (bare) spin diffusivity in the strongly interacting regime. Transport bounds are of broad interest for the condensed matter community, with a conceptual similarity to observed bounds in shear viscosity and charge conductivity. We discuss the formalism of spin hydrodynamics, how dynamics are parameterized by transport coefficients, the effect of confinement, the role of scale invariance, the quasiparticle picture, and quantum critical transport. We conclude by highlighting open questions, such as precise theoretical bounds, relevance to other phases of matter, and extensions to lattice systems.

When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real world, we need a top-down approach to complexity. In this approach, one may desire to understand general multipoint statistics. Here, such a general approach is presented and discussed based on examples from turbulence and sea waves. Our main idea is based on the cascade picture of turbulence, entangling fluctuations from large to small scales. Inspired by this cascade picture, we express the general multipoint statistics by the statistics of scale-dependent fluctuations of variables and relate it to a scale-dependent process, which finally is a stochastic cascade process. We show how to extract from empirical data a Fokker–Planck equation for this cascade process, which allows the generation of surrogate data to forecast extreme events as well as to develop a nonequilibrium thermodynamics for the complex systems. For each cascade event, an entropy production can be determined. These entropies accurately fulfill a rigorous law, namely the integral fluctuations theorem.

A hallmark of the phase diagrams of quantum materials is the existence of multiple electronic ordered states, which, in many cases, are not independent competing phases, but instead display a complex intertwinement. In this review, we focus on a particular realization of intertwined orders: a primary phase characterized by a multi-component order parameter and a fluctuation-driven vestigial phase characterized by a composite order parameter. This concept has been widely employed to elucidate nematicity in iron-based and cuprate superconductors. Here we present a group-theoretical framework that extends this notion to a variety of phases, providing a classification of vestigial orders of unconventional superconductors and density waves. Electronic states with scalar and vector chiral order, spin-nematic order, Ising-nematic order, time-reversal symmetry-breaking order, and algebraic vestigial order emerge from one underlying principle. The formalism provides a framework to understand the complexity of quantum materials based on symmetry, largely without resorting to microscopic models.

Superfluid ³He is an unconventional neutral superfluid in a p-wave state with three different superfluid phases, each identified by a unique set of characteristic broken symmetries and nontrivial topology. Despite natural immunity of ³He from defects and impurity of any kind, it has been found that they can be artificially introduced with high-porosity silica aerogel. Furthermore, it has been shown that this modified quantum liquid becomes a superfluid with remarkably sharp thermodynamic transitions from the normal state and between its various phases. These phases include new superfluid phases that are stabilized by anisotropy from uniform strain imposed on the silica aerogel framework, and they include new phenomena in a new class of anisotropic aerogels consisting of nematically ordered alumina strands. The study of superfluid ³He in the presence of correlated, quenched disorder from aerogel serves as a model for understanding the effect of impurities on the symmetry and topology of unconventional superconductors.

For a large class of nonequilibrium systems, thermodynamic notions like work, heat, and, in particular, entropy production can be identified on the level of fluctuating dynamical trajectories. Within stochastic thermodynamics various fluctuation theorems relating these quantities have been proven. Their application to experimental systems requires that all relevant mesostates are accessible. Recent advances address the typical situation that only partial, or coarse-grained, information about a system is available. Thermodynamic inference as a general strategy uses consistency constraints derived from stochastic thermodynamics to infer otherwise hidden properties of nonequilibrium systems. An important class in this respect are active particles, for which we resolve the conflicting strategies that have been proposed to identify entropy production. As a paradigm for thermodynamic inference, the thermodynamic uncertainty relation provides a lower bound on the entropy production through measurements of the dispersion of any current in the system. Likewise, it quantifies the cost of precision for biomolecular processes. Generalizations and ramifications allow the inference of, inter alia, model-free upper bounds on the efficiency of molecular motors and of the minimal number of intermediate states in enzymatic networks.

Classical and quantum electronic circuits provide ideal platforms to investigate stochastic thermodynamics, and they have served as a stepping stone to realize Maxwell's Demons with highly controllable protocols. In this article, we first review the central thermal phenomena in quantum nanostructures. Thermometry and basic refrigeration methods are described as enabling tools for thermodynamics experiments. Next, we discuss the role of information in thermodynamics that leads to the concept of Maxwell's Demon. Various Maxwell's Demons realized in single-electron circuits over the past couple of years are described. Currently, true quantum thermodynamics in superconducting circuits is a focus of attention, and we end the review by discussing the ideas and first experiments in this exciting area of research.

Soft-condensed matter physics has provided, in the past decades, many of the relevant concepts and methods allowing successful description of living cells and biological tissues. This recent quantitative physical description of biological systems has profoundly advanced our understanding of life, which is shifting from a descriptive to a predictive level. Like other active materials investigated in condensed matter physics, biological materials still pose great challenges to modern physics as they form a specific class of nonequilibrium systems. Actively driven membranes have been studied for more than two decades, taking advantage of rapid progress in membrane physics and in the experimental development of reconstituted active membranes. The physical description of activity within living biological membranes remains, however, a key challenge that animates a dynamic research community, bringing together physicists and biologists. Here, we first review the past two decades of experimental and theoretical advances that enabled the characterization of mechanical properties and nonequilibrium fluctuations in active membranes. We distinguish active processes originating from membrane proteins or from external interactions, such as cytoskeletal forces. Then, we focus on the emblematic case of red blood cell flickering, the active origin of which has been debated for decades until recently. We finally close this review by discussing future challenges in this ever more interdisciplinary field.

Impurities, defects, and other types of imperfections are ubiquitous in realistic quantum many-body systems and essentially unavoidable in solid state materials. Often, such random disorder is viewed purely negatively as it is believed to prevent interesting new quantum states of matter from forming and to smear out sharp features associated with the phase transitions between them. However, disorder is also responsible for a variety of interesting novel phenomena that do not have clean counterparts. These include Anderson localization of single-particle wave functions, many-body localization in isolated many-body systems, exotic quantum critical points, and glassy ground-state phases. This brief review focuses on two separate but related subtopics in this field. First, we review under what conditions different types of randomness affect the stability of symmetry-broken low-temperature phases in quantum many-body systems and the stability of the corresponding phase transitions. Second, we discuss the fate of quantum phase transitions that are destabilized by disorder as well as the unconventional quantum Griffiths phases that emerge in their vicinity.

Contacting bodies subjected to sufficiently large applied shear will undergo frictional sliding. The onset of this motion is mediated by dynamically propagating fronts, akin to earthquakes, that rupture the discrete contacts that form the interface separating the bodies. Macroscopic motion commences only after these ruptures have traversed the entire interface. Comparison of measured rupture dynamics with the detailed predictions of fracture mechanics reveals that the propagation dynamics, dissipative properties, radiation, and arrest of these “laboratory earthquakes” are in excellent quantitative agreement with the predictions of the theory of brittle fracture. Thus, interface fracture replaces the idea of a characteristic static friction coefficient as a description of the onset of friction. This fracture-based description of friction additionally provides a fundamental description of earthquake dynamics and arrest.

This article focuses on the history of theoretical ideas but also on the developments of experimental tools. The experiments in our laboratory are used to illustrate the various developments associated with Brownian movement. In the first part of this review, we give an overview of the theory. We insist on the pre-Einstein approach to the problem by Lord Rayleigh, Bachelier, and Smoluchowski. In the second part, we detail the achievements of Perrin, measuring Avogadro's number, quantifying the experimental observations of Brownian movement, and introducing the problem of continuous curves without tangent, a precursor to fractal theory. The third part deals with modern application of Brownian movement, escape from a fixed optical trap, particle dynamics on a moving trap, and finally development of Brownian thermal ratchets. Finally, we give a short overview of bacteria motion, presented like an active Brownian movement with very high effective temperature.

Fracton phases constitute a new class of quantum state of matter. They are characterized by excitations that exhibit restricted mobility, being either immobile under local Hamiltonian dynamics or mobile only in certain directions. These phases do not wholly fit into any of the existing paradigms but connect to areas including glassy quantum dynamics, topological order, spin liquids, elasticity theory, quantum information theory, and gravity. We begin by discussing gapped fracton phases, which may be described using exactly solvable lattice spin models. We then introduce the framework of tensor gauge theory, which provides a powerful complementary perspective and allows us to access gapless fracton phases. We discuss the basic properties of gapless fracton phases and their connections to elasticity theory and gravity. We also discuss what is known about the dynamics and thermodynamics of fractons at nonzero density before concluding with a brief survey of some open problems.

Over the past few years, Sr2IrO4, a single-layer member of the Ruddlesden–Popper series iridates, has received much attention as a close analog of cuprate high-temperature superconductors. Although there is not yet firm evidence for superconductivity, a remarkable range of cuprate phenomenology has been reproduced in electron- and hole-doped iridates including pseudogaps, Fermi arcs, and d-wave gaps. Furthermore, many symmetry-breaking orders reminiscent of those decorating the cuprate phase diagram have been reported using various experimental probes. We discuss how the electronic structures of Sr2IrO4 through strong spin-orbit coupling leads to the low-energy physics that had long been unique to cuprates, what the similarities and differences between cuprates and iridates are, and how these advance the field of high-temperature superconductivity by isolating essential ingredients of superconductivity from a rich array of phenomena that surround it. Finally, we comment on the prospect of finding a new high-temperature superconductor based on the iridate series.

Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further our understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically exact and intrinsically unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progress made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.

In this review, we provide an introduction to the physics of a series of frustrated quantum rare-earth pyrochlores. We first give a background on the microscopic single- and two-ion physics of these materials, discussing the origins and properties of their exchange interactions and their minimal low-energy effective models before outlining what is known about their classical and quantum phases. We then make use of this understanding to discuss four important material examples, Er2Ti2O7, Yb2Ti2O7, Tb2Ti2O7, and Pr2Zr2O7, covering in some detail what is known experimentally and theoretically for each and then summarizing some key questions that remain open. Finally, we offer an outlook on some alternative material platforms for realizing similar physics and discuss what we see as prospects for future investigations on these quantum rare-earth pyrochlores.

Floquet engineering, the control of quantum systems using periodic driving, is an old concept in condensed matter physics dating back to ideas such as the inverse Faraday effect. However, there is a renewed interest in this concept owing to (a) the rapid developments in laser and ultrafast spectroscopy techniques, (b) discovery and understanding of various “quantum materials” hosting interesting exotic quantum properties, and (c) communication with different areas of physics such as artificial matter and nonequilibrium quantum statistical physics. Here, starting from a nontechnical introduction with emphasis on the Floquet picture and effective Hamiltonians, we review the recent applications of Floquet engineering in ultrafast, nonlinear phenomena in the solid state. In particular, Floquet topological states and their application to ultrafast spintronics and strongly correlated electron systems are overviewed.

Cuprates exhibit exceptionally strong superconductivity. To understand why, it is essential to elucidate the nature of the electronic interactions that cause pairing. Superconductivity occurs on the backdrop of several underlying electronic phases, including a doped Mott insulator at low doping, a strange metal at high doping, and an enigmatic pseudogap phase in between—inside which a phase of charge-density wave order appears. In this article, we shed light on the nature of these remarkable phases by focusing on the limit as , where experimental signatures and theoretical statements become sharper. We therefore survey the ground-state properties of cuprates once superconductivity has been removed by the application of a magnetic field and distill their key universal features.