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.

Many objects in nature and industry are wrapped in a thin sheet to enhance their chemical, mechanical, or optical properties. Similarly, there are a variety of methods for wrapping, from pressing a film onto a hard substrate to inflating a closed membrane, to spontaneously wrapping droplets using capillary forces. Each of these settings raises challenging nonlinear problems involving the geometry and mechanics of a thin sheet, often in the context of resolving a geometric incompatibility between two surfaces. Here, we review recent progress in this area, focusing on highly bendable films that are nonetheless hard to stretch, a class of materials that includes polymer films, metal foils, textiles, and graphene, as well as some biological materials. Significant attention is paid to two recent advances: a novel isometry that arises in the doubly-asymptotic limit of high flexibility and weak tensile forcing, and a simple geometric model for predicting the overall shape of an interfacial film while ignoring small-scale wrinkles, crumples, and folds.

Spin liquids are collective phases of quantum matter that have eluded discovery in correlated magnetic materials for over half a century. Theoretical models of these enigmatic topological phases are no longer in short supply. In experiment there also exist plenty of promising candidate materials for their realization. One of the central challenges for the clear diagnosis of a spin liquid has been to connect the two. From that perspective, this review discusses characteristic features in experiment, resulting from the unusual properties of spin liquids. This takes us to thermodynamic, spectroscopic, transport, and other experiments on a search for traces of emergent gauge fields, spinons, Majorana fermions, and other fractionalized particles.

It has been said that the cell is the test tube of the twenty-first century. If so, the theoretical tools needed to quantitatively and predictively describe what goes on in such test tubes lag sorely behind the stunning experimental advances in biology seen in the decades since the molecular biology revolution began. Perhaps surprisingly, one of the theoretical tools that has been used with great success on problems ranging from how cells communicate with their environment and each other to the nature of the organization of proteins and lipids within the cell membrane is statistical mechanics. A knee-jerk reaction to the use of statistical mechanics in the description of cellular processes is that living organisms are so far from equilibrium that one has no business even thinking about it. But such reactions are probably too hasty given that there are many regimes in which, because of a separation of timescales, for example, such an approach can be a useful first step. In this article, we explore the power of statistical mechanical thinking in the biological setting, with special emphasis on cell signaling and regulation. We show how such models are used to make predictions and describe some recent experiments designed to test them. We also consider the limits of such models based on the relative timescales of the processes of interest.

This autobiographical narrative offers a brief account of my journey and adventures in condensed matter physics (a.k.a. solid state physics) and some of the personal events that shaped my life and my career: my early years in Europe, my family's escape from the Nazis, growing up in Cuba, the difficult road into a field that was essentially closed to women, a personal disaster that knocked the wind out of my sails for more than a decade, and my return to a successful career in physics. In closing, I argue that, although we have made remarkable progress, we know but a thimble-full in our inexhaustible search for an understanding of the laws of nature.

Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples—they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li)2IrO3 iridates and RuCl3. In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.

It is commonly believed that a noninteracting disordered electronic system can undergo only the Anderson metal-insulator transition. It has been suggested, however, that a broad class of systems can display disorder-driven transitions distinct from Anderson localization that have manifestations in the disorder-averaged density of states, conductivity, and other observables. Such transitions have received particular attention in the context of recently discovered 3D Weyl and Dirac materials but have also been predicted in cold-atom systems with long-range interactions, quantum kicked rotors, and all sufficiently high-dimensional systems. Moreover, such systems exhibit unconventional behavior of Lifshitz tails, energy-level statistics, and ballistic-transport properties. Here, we review recent progress and the status of results on non-Anderson disorder-driven transitions and related phenomena.

Entropic forces in classical many-body systems, e.g., colloidal suspensions, can lead to the formation of new phases. Quantum fluctuations can have similar effects: spin fluctuations drive the superfluidity of helium-3, and a similar mechanism operating in metals can give rise to superconductivity. It is conventional to discuss the latter in terms of the forces induced by the quantum fluctuations. However, focusing directly upon the free energy provides a useful alternative perspective in the classical case and can also be applied to study quantum fluctuations. Villain first developed this approach for insulating magnets and coined the term order-by-disorder to describe the observed effect. We discuss the application of this idea to metallic systems, recent progress made in doing so, and the broader prospects for the future.

Spatial patterns are ubiquitous in animate matter. Besides their intricate structure and beauty they generally play functional roles. The capacity of living systems to remain functional in changing environments is a question of utmost importance, but its intimate relationship to pattern formation is largely unexplored. Here, we address this relationship using dryland vegetation as a case study. Following a brief introduction to pattern-formation theory, we describe a mathematical model that captures several mechanisms of vegetation pattern formation and discuss ecological contexts that showcase different mechanisms. Using this model, we unravel the different vegetation patterns that keep dryland ecosystems viable along the rainfall gradient, identify multistability ranges where fronts separating domains of alternative stable states exist, and highlight the roles of front dynamics in mitigating or reversing desertification. The utility of satellite images in testing model predictions is discussed. An outlook on outstanding open problems concludes this paper.

Extensive experimental investigations of the magnetic structures and excitations in the XY pyrochlores have been carried out over the past decade. Three families of XY pyrochlores have emerged: Yb2B2O7, Er2B2O7, and, most recently, Co2F7. In each case, the magnetic cation (either Yb, Er, or Co) exhibits XY anisotropy within the local pyrochlore coordinates, a consequence of crystal field effects. Materials in these families display rich phase behavior and are candidates for exotic ground states, such as quantum spin ice, and exotic ground-state selection via order-by-disorder mechanisms. In this review, we present an experimental summary of the ground-state properties of the XY pyrochlores, including evidence that they are strongly influenced by phase competition. We empirically demonstrate the signatures for phase competition in a frustrated magnet: multiple heat capacity anomalies, suppressed TN or TC, sample- and pressure-dependent ground states, and unconventional spin dynamics.

FeSe is a fascinating superconducting material at the frontier of research in condensed matter physics. Here, we provide an overview of the current understanding of the electronic structure of FeSe, focusing in particular on its low-energy electronic structure as determined from angle-resolved photoemission spectroscopy, quantum oscillations, and magnetotransport measurements of single-crystal samples. We discuss the unique place of FeSe among iron-based superconductors, as it is a multiband system exhibiting strong orbitally dependent electronic correlations and unusually small Fermi surfaces and is prone to different electronic instabilities. We pay particular attention to the evolution of the electronic structure that accompanies the tetragonal-orthorhombic structural distortion of the lattice around 90 K, which stabilizes a unique nematic electronic state. Finally, we discuss how the multiband multiorbital nematic electronic structure impacts our understanding of the superconductivity, and show that the tunability of the nematic state with chemical and physical pressure helps to disentangle the role of different competing interactions relevant for enhancing superconductivity.

Focused ion beam (FIB) machining promises exciting new possibilities for the study of quantum materials through precise control over the shape and geometry of single crystals on the submicrometer scale. It offers viable routes to fabricate high-quality mesoscale structures from materials that cannot yet be grown in thin-film form and to enhance the experimentally accessible signatures of new physical phenomena. Prototype devices can also be produced in a silicon-chip environment to investigate directly the materials application potential for future electronics. This review introduces the concepts of ion beam shaping of matter, discusses the role and extent of surface damage and material disorder inherent to these techniques, and gives an overview of recent experiments on FIB-structured crystals. Given the early stage of the field of FIB-fabricated quantum materials, much is yet to come, and emergent trends and future directions are also discussed.

The interaction of flexible polymers with fluid flows leads to a number of intriguing phenomena observed in laboratory experiments, namely drag reduction, elastic turbulence, and heat transport modification in natural convection, and is one of the most challenging subjects in soft matter physics. In this review, we examine our present knowledge on the subject. Our present knowledge is mostly based on direct numerical simulations performed in the last twenty years, which have successfully explained, at least qualitatively, most of the experimental results. Our goal is to disentangle as much as possible the basic mechanisms acting in the system in order to capture the basic features underlying different theoretical approaches and explanations.

Adaptation refers to the biological phenomenon where living systems change their internal states in response to changes in their environments in order to maintain certain key functions critical for their survival and fitness. Adaptation is one of the most ubiquitous and arguably one of the most fundamental properties of living systems. It occurs throughout all biological scales, from adaptation of populations of species over evolutionary time to adaptation of a single cell to different environmental stresses during its life span. In this article, we review some of the recent progress made in understanding molecular mechanisms of cellular-level adaptation. We take the minimalist (or the physicist) approach and study the simplest systems that exhibit generic adaptive behaviors, namely chemotaxis in bacterium cells (Escherichia coli) and eukaryotic cells (Dictyostelium). We focus on understanding the basic biochemical interaction networks that are responsible for adaptation dynamics. By combining theoretical modeling with quantitative experimentation, we demonstrate universal features in adaptation as well as important differences in different cellular systems. Future work in extending the modeling framework to study adaptation in more complex systems such as sensory neurons is also discussed.

Colloids are abundant in nature, science, and technology, with examples ranging from milk to quantum dots and the colloidal atom paradigm. Similarly, liquid crystal ordering is important in contexts ranging from biological membranes to laboratory models of cosmic strings and liquid crystal displays in consumer devices. Some of the most exciting recent developments in both of these soft matter fields emerge at their interface, in the fast-growing research arena of liquid crystal colloids. Mesoscale self-assembly in such systems may lead to artificial materials and to structures with emergent physical behavior arising from patterning of molecular order and nano- or microparticles into precisely controlled configurations. Liquid crystal colloids show exceptional promise for new discovery that may impinge on composite material fabrication, low-dimensional topology, photonics, and so on. Starting from physical underpinnings, I review the state of the art in this fast-growing field, with a focus on its scientific and technological potential.

Non-Fermi liquids are unconventional metals whose physical properties deviate qualitatively from those of noninteracting fermions due to strong quantum fluctuations near Fermi surfaces. They arise when metals are subject to singular interactions mediated by soft collective modes. In the absence of well-defined quasiparticles, universal physics of non-Fermi liquids is captured by interacting field theories which replace Landau Fermi liquid theory. However, it has been difficult to understand their universal low-energy physics due to a lack of theoretical methods that take into account strong quantum fluctuations in the presence of abundant low-energy degrees of freedom. In this review, we discuss two approaches that have been recently developed for non-Fermi liquid theory with emphasis on two space dimensions. The first is a perturbative scheme based on a dimensional regularization, which achieves a controlled access to the low-energy physics by tuning the codimension of Fermi surface. The second is a nonperturbative approach which treats the interaction ahead of the kinetic term through a non-Gaussian scaling called interaction-driven scaling. Examples of strongly coupled non-Fermi liquids amenable to exact treatments through the interaction-driven scaling are discussed.

Quench dynamics is an active area of study encompassing condensed matter physics and quantum information, with applications to cold-atomic gases and pump-probe spectroscopy of materials. Recent theoretical progress in studying quantum quenches is reviewed. Quenches in interacting one-dimensional systems as well as systems in higher spatial dimensions are covered. The appearance of nontrivial steady states following a quench in exactly solvable models is discussed, and the stability of these states to perturbations is described. Proper conserving approximations needed to capture the onset of thermalization at long times are outlined. The appearance of universal scaling for quenches near critical points and the role of the renormalization group in capturing the transient regime are reviewed. Finally, the effect of quenches near critical points on the dynamics of entanglement entropy and entanglement statistics is discussed. The extraction of critical exponents from the entanglement statistics is outlined.

Raising the superconducting transition temperature to a point where applications are practical is one of the most important challenges in science. In this review, we aim at gaining insights on the Tc controlling factors for a particular high-temperature superconductor family—the FeSe-based superconductors. In particular, we discuss the mechanisms by which the Cooper pairing temperature is enhanced from ∼8 K in bulk FeSe to ∼80 K in the interface between an atomic layer of FeSe and SrTiO3. This includes the experimental hints and the theoretical simulation of the involved mechanisms. We end by applying these insights to suggest some possible high-temperature superconducting systems.

In directed assembly, small building blocks are assembled into an organized structure under the influence of guiding fields. Capillary interactions provide a versatile route for structure formation. Colloids adsorbed on fluid interfaces distort the interface, which creates an associated energy field. When neighboring distortions overlap, colloids interact to minimize interfacial area. Contact line pinning, particle shape, and surface chemistry play important roles in structure formation. Interface curvature acts like an external field; particles migrate and assemble in patterns dictated by curvature gradients. We review basic analysis and recent findings in this rapidly evolving literature. Understanding the roles of assembly is essential for tuning the mechanical, physical, and optical properties of the structure.

Bose condensation is central to our understanding of quantum phases of matter. Here, we review Bose condensation in topologically ordered phases (also called topological symmetry breaking), where the condensing bosons have nontrivial mutual statistics with other quasiparticles in the system. We give a nontechnical overview of the relationship between the phases before and after condensation, drawing parallels with more familiar symmetry-breaking transitions. We then review two important applications of this phenomenon. First, we describe the equivalence between such condensation transitions and pairs of phases with gappable boundaries, as well as examples where multiple types of gapped boundary between the same two phases exist. Second, we discuss how such transitions can lead to global symmetries that exchange or permute anyon types. Finally, we discuss the nature of the critical point, which can be mapped to a conventional phase transition in some—but not all—cases.

The quantum anomalous Hall effect (QAHE) is a quantized Hall effect that occurs at zero magnetic field. Its mechanism and properties are different from those of conventional quantum Hall effects (QHEs) induced by magnetic field. The first theory of a QHE without a magnetic field was proposed in 1988. Yet, it has taken 25 years to be experimentally realized, which has now happened thanks to the development of the topological insulator—a conceptually new topological state of matter. Here, we review QAHE, beginning with the original theoretical idea and concluding with its final implementation using experimentally accessible materials. The current status and future direction of the field are also discussed.

This is an idiosyncratic colloquium-style review of the idea that spacetime and gravity can emerge from entanglement. Drawing inspiration from the conjectured duality between quantum gravity in anti de Sitter space and certain conformal field theories, we argue that tensor networks can be used to define a discrete geometry that encodes entanglement geometrically. With the additional assumption that a continuum limit can be taken, the resulting geometry necessarily obeys Einstein's equations. The discussion takes the point of view that the emergence of spacetime and gravity is a mysterious phenomenon of quantum many-body physics that we would like to understand. We also briefly discuss possible experiments to detect emergent gravity in highly entangled quantum systems.

Weyl metal is the first example of a conducting material with a nontrivial electronic structure topology, making it distinct from an ordinary metal. Unlike in insulators, the nontrivial topology is not related to invariants associated with completely filled bands but with ones associated with the Fermi surface. The Fermi surface of a topological metal consists of disconnected sheets, each enclosing a Weyl node, which is a point of contact between two nondegenerate bands. Such a point contact acts as a source of Berry curvature or a magnetic monopole in momentum space. Its charge, or the flux of the Berry curvature through the enclosing Fermi surface sheet, is a topological invariant. We review the current state of this rapidly growing field with a focus on bulk transport phenomena in topological metals.

Starting with the isolation of a single sheet of graphene, the study of layered materials has been one of the most active areas of condensed matter physics, chemistry, and materials science. Single-layer transition-metal dichalcogenides are direct-gap semiconducting analogs of graphene that exhibit novel electronic and optical properties. These features provide exciting opportunities for the discovery of both new fundamental physical phenomena as well as innovative device platforms. Here, we review the progress associated with the creation and use of a simple microscopic framework for describing the optical and excitonic behavior of few-layer transition-metal dichalcogenides, which is based on symmetry, band structure, and the effective interactions between charge carriers in these materials. This approach provides an often quantitative account of experiments that probe the physics associated with strong electron–hole interactions in these quasi two-dimensional systems and has been successfully employed by many groups to both describe and predict emergent excitonic behavior in these layered semiconducting systems.

We review the recently proposed Dirac composite fermion theory of the half-filled Landau level.

This is a review on the emergent field of topological mechanics, where concepts from electronic topological states of matter are applied to mechanics. We focus on the subcategory of topological mechanics of Maxwell lattices, which are mechanical frames having average coordination numbers equal to twice their spatial dimension, 〈z〉=2d, leaving them on the verge of mechanical instability. We start by introducing examples of Maxwell lattices, describing their elastic properties, and discussing their general classification. We then focus on topological phonon modes of these lattices by reviewing recent theoretical progress on one-dimensional chains and two-dimensional lattices that exhibit topologically protected zero-frequency phonon modes on edges and domain walls. We also propose metamaterials based on Maxwell lattices with unusual topologically protected mechanical properties.

Excitable media are ubiquitous in nature and can be found in physical, chemical, and biological systems that are far from thermodynamic equilibrium. The spatiotemporal self-organization of these systems has long attracted the deep interest of condensed matter physicists and applied mathematicians alike. Spatial inhomogeneity of excitable media leads to nontrivial spatiotemporal dynamics. Here, we report on well-established as well as recent developments in the experimental and theoretical studies of inhomogeneous excitable media.

Recent research on the network modeling of complex systems has led to a convenient representation of numerous natural, social, and engineered systems that are now recognized as networks of interacting parts. Such systems can exhibit a wealth of phenomena that not only cannot be anticipated from merely examining their parts, as per the textbook definition of complexity, but also challenge intuition even when considered in the context of what is now known in network science. Here, we review the recent literature on two major classes of such phenomena that have far-reaching implications: (a) antagonistic responses to changes of states or parameters and (b) coexistence of seemingly incongruous behaviors or properties—both deriving from the collective and inherently decentralized nature of the dynamics. They include effects as diverse as negative compressibility in engineered materials, rescue interactions in biological networks, negative resistance in fluid networks, and the Braess paradox occurring across transport and supply networks. They also include remote synchronization, chimera states, and the converse of symmetry breaking in brain, power-grid, and oscillator networks as well as remote control in biological and bioinspired systems. By offering a unified view of these various scenarios, we suggest that they are representative of a yet broader class of unprecedented network phenomena that ought to be revealed and explained by future research.

Theoretical physics and the institutions that support it have changed greatly during my career. In this article, I recount some of my most memorable experiences as a physicist, first as a graduate student with Rudolf Peierls at the University of Birmingham in England and later as a colleague of Walter Kohn at the Institute for Theoretical Physics in Santa Barbara, California. I use this account to illustrate some of the changes that have occurred in my field and also as a rationale for asserting that theoretical physics has an increasingly vital role to play in modern science.

The unexpected discovery of the quantum Hall effect was the result of basic research on silicon field-effect transistors combined with my experience in metrology, the science of measurements. This personal review demonstrates that condensed matter physics is full of surprises and that access to excellent crystals and materials is a crucial ingredient of the success of experimentalists in condensed matter science.

Arnold Sommerfeld (1868–1951), one of the founders of modern theoretical physics and a pioneer of quantum theory, was no condensed matter physicist. He nevertheless played a crucial role for the history of the field. Besides his important contributions to the study of condensed matter systems, among which his seminal electron gas theory of metallic conduction probably stands out, he influenced the field through his very approach to science, through his way of “doing” physics. Sommerfeld's specific style permeated not only his research but also his teaching and his promoting of physics. This has had a lasting influence on the practices of physicists to this day, and not only, but importantly, on those of condensed matter physicists. This article aims to provide a concise account of Sommerfeld's influence on the study of condensed matter systems, with regard to both his research and his practice.

Ratchet effects can arise for single or collectively interacting Brownian particles on an asymmetric substrate when a net dc transport is produced by an externally applied ac driving force or by periodically flashing the substrate. Recently, a new class of active ratchet systems that do not require the application of external driving has been realized through the use of active matter; they are self-propelled units that can be biological or nonbiological in nature. When active materials such as swimming bacteria interact with an asymmetric substrate, a net dc directed motion can arise even without external driving, opening a wealth of possibilities such as sorting, cargo transport, or micromachine construction. We review the current status of active matter ratchets for swimming bacteria, cells, active colloids, and swarming models, focusing on the role of particle-substrate interactions. We describe ratchet reversals produced by collective effects and the use of active ratchets to transport passive particles. We discuss future directions including deformable substrates or particles, the role of different swimming modes, varied particle–particle interactions, and nondissipative effects.

Nano- and microscale particles, such as colloids, commonly interact over ranges much shorter than their diameters, so it is natural to treat them as “sticky,” interacting only when they touch exactly. The lowest-energy states, free energies, and dynamics of a collection of n particles can be calculated in the sticky limit of a deep, narrow interaction potential. This article surveys the theory of the sticky limit, explains the correspondence between theory and experiments on colloidal clusters, and outlines areas where the sticky limit may bring new insight.

It is widely appreciated that surface tension can dominate the behavior of liquids at small scales. Solids also have surface stresses of a similar magnitude, but they are usually overlooked. However, recent work has shown that these can play a central role in the mechanics of soft solids such as gels. Here, we review this emerging field. We outline the theory of surface stresses, from both mechanical and thermodynamic perspectives, emphasizing the relationship between surface stress and surface energy. We describe a wide range of phenomena at interfaces and contact lines where surface stresses play an important role. We highlight how surface stresses cause dramatic departures from classic theories for wetting (Young–Dupré), adhesion (Johnson–Kendall–Roberts), and composites (Eshelby). A common thread is the importance of the ratio of surface stress to an elastic modulus, which defines a length scale below which surface stresses can dominate.

Quantum-thermal fluctuations of electromagnetic waves are the cornerstone of quantum statistics and inherent to phenomena such as thermal radiation and van der Waals forces. Although the principles are found in elementary texts, recent experimental and technological advances make it necessary to come to terms with counterintuitive consequences at short scales—the so-called near-field regime. We focus on three manifestations: (a) The Stefan–Boltzmann law describes radiation from macroscopic bodies but fails for small objects. (b) The heat transfer between two bodies at close proximity is dominated by evanescent waves and can be orders of magnitude larger than the classical (propagating) contribution. (c) Casimir forces, dominant at submicron separation, are not sufficiently explored for objects at different temperatures (at least experimentally). We explore these phenomena using fluctuational quantum electrodynamics (QED), introduced by Rytov in the 1950s, combined with scattering formalisms. This enables investigation of different material properties, shapes, separations, and arrangements.

Combining the power and possibilities of heterostructure engineering with the collective and emergent properties of quantum materials, quantum-matter heterostructures open a new arena of solid-state physics. Here we provide a review of interfaces and heterostructures made of quantum matter. Unique electronic states can be engineered in these structures, giving rise to unforeseeable opportunities for scientific discovery and potential applications. We discuss the present status of this nascent field of quantum-matter heterostructures and its limitations, perspectives, and challenges.

Origami has emerged as a tool for designing three-dimensional structures from flat films. Because they can be fabricated by lithographic or roll-to-roll processing techniques, they have great potential for the manufacture of complicated geometries and devices. This article discusses the mechanics of origami and kirigami with a view toward understanding how to design self-folding origami structures. Whether an origami structure can be made to fold autonomously depends strongly on the geometry and kinematics of the origami fold pattern. This article collects some of the results on origami rigidity into a single framework, and discusses how these aspects affect the foldability of origami. Despite recent progress, most problems in origami and origami design remain completely open.

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were extended to continuous phase transitions separating distinct nonequilibrium stationary states in driven classical and quantum systems. In concordance with detailed numerical simulations and laboratory experiments, several prominent dynamical universality classes have emerged that govern large-scale, long-time scaling properties both near and far from thermal equilibrium. These pertain to genuine specific critical points as well as entire parameter space regions for steady states that display generic scale invariance. The exploration of nonstationary relaxation properties and associated physical aging scaling constitutes a complementary potent means to characterize cooperative dynamics in complex out-of-equilibrium systems. This review describes dynamic scaling features through paradigmatic examples that include near-equilibrium critical dynamics, driven lattice gases and growing interfaces, correlation-dominated reaction-diffusion systems, and basic epidemic models.

The phenomena associated with topological defects have had an enormous impact in condensed matter physics for more than 50 years. Beginning with an understanding of topological defects in ordered phases, the field is now sharply focused on defects in topological phases of matter. In this review, we cover aspects of defects in conventional ordered media, bound states on defects in strong topological insulators (TIs) and topological superconductors (TSCs), and bound states on defects in crystalline topological phases protected by spatial symmetries. As a unifying theme, we present the structure of many types of index theorems that relate the existence of topological bound states to the bulk topology of the host phase of matter and the topological charge of the relevant defects.

Dynamic processes in living cells are highly organized in space and time. Unraveling the underlying molecular mechanisms of spatiotemporal pattern formation remains one of the outstanding challenges at the interface between physics and biology. A fundamental recurrent pattern found in many different cell types is that of self-sustained oscillations. They are involved in a wide range of cellular functions, including second messenger signaling, gene expression, and cytoskeletal dynamics. Here, we review recent developments in the field of cellular oscillations and focus on cases where concepts from physics have been instrumental for understanding the underlying mechanisms. We consider biochemical and genetic oscillators as well as oscillations that arise from chemo-mechanical coupling. Finally, we highlight recent studies of intracellular waves that have increasingly moved into the focus of this research field.

Despite decades of work, gaining a first-principles understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution of a microscopic glass-forming model in the mean-field limit of infinite spatial dimension. Numerical simulations have remarkably confirmed the dimensional robustness of some of the predictions. This review describes these latest advances. More specifically, we consider the dynamical and thermodynamic descriptions of hard spheres around the dynamical, Gardner, and jamming transitions. Comparing mean-field predictions with the finite-dimensional simulations, we identify robust aspects of the theory and uncover its more sensitive features. We conclude with a brief overview of ongoing research.