Spin Hall effects are a collection of relativistic spin-orbit coupling phenomena in which electrical currents can generate transverse spin currents and vice versa. Despite being observed only a decade ago, these effects are already ubiquitous within spintronics, as standard spin-current generators and detectors. Here the theoretical and experimental results that have established this subfield of spintronics are reviewed. The focus is on the results that have converged to give us the current understanding of the phenomena, which has evolved from a qualitative to a more quantitative measurement of spin currents and their associated spin accumulation. Within the experimental framework, optical-, transport-, and magnetization-dynamics-based measurements are reviewed and linked to both phenomenological and microscopic theories of the effect. Within the theoretical framework, the basic mechanisms in both the extrinsic and intrinsic regimes are reviewed, which are linked to the mechanisms present in their closely related phenomenon in ferromagnets, the anomalous Hall effect. Also reviewed is the connection to the phenomenological treatment based on spin-diffusion equations applicable to certain regimes, as well as the spin-pumping theory of spin generation used in many measurements of the spin Hall angle. A further connection to the spin-current-generating spin Hall effect to the inverse spin galvanic effect is given, in which an electrical current induces a nonequilibrium spin polarization. This effect often accompanies the spin Hall effect since they share common microscopic origins. Both can exhibit the same symmetries when present in structures comprising ferromagnetic and nonmagnetic layers through their induced current-driven spin torques or induced voltages. Although a short chronological overview of the evolution of the spin Hall effect field and the resolution of some early controversies is given, the main body of this review is structured from a pedagogical point of view, focusing on well-established and accepted physics. In such a young field, there remains much to be understood and explored, hence some of the future challenges and opportunities of this rapidly evolving area of spintronics are outlined.

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.

Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks of topological materials is the existence of protected gapless surface states, which arise due to a nontrivial topology of the bulk wave functions. This review provides a pedagogical introduction into the field of topological quantum matter with an emphasis on classification schemes. Both fully gapped and gapless topological materials and their classification in terms of nonspatial symmetries, such as time reversal, as well as spatial symmetries, such as reflection, are considered. Furthermore, the classification of gapless modes localized on topological defects is surveyed. The classification of these systems is discussed by use of homotopy groups, Clifford algebras, K theory, and nonlinear sigma models describing the Anderson (de) localization at the surface or inside a defect of the material. Theoretical model systems and their topological invariants are reviewed together with recent experimental results in order to provide a unified and comprehensive perspective of the field. While the bulk of this article is concerned with the topological properties of noninteracting or mean-field Hamiltonians, a brief overview of recent results and open questions concerning the topological classifications of interacting systems is also provided.

This paper gives the 2014 self-consistent set of values of the constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA). These values are based on a least-squares adjustment that takes into account all data available up to 31 December 2014. Details of the data selection and methodology of the adjustment are described. The recommended values may also be found at physics.nist.gov/constants.

Optical atomic clocks represent the state of the art in the frontier of modern measurement science. In this article a detailed review on the development of optical atomic clocks that are based on trapped single ions and many neutral atoms is provided. Important technical ingredients for optical clocks are discussed and measurement precision and systematic uncertainty associated with some of the best clocks to date are presented. An outlook on the exciting prospect for clock applications is given in conclusion.

Photonic nanostructures provide a means of tailoring the interaction between light and matter and the past decade has witnessed tremendous experimental and theoretical progress on this subject. In particular, the combination with semiconductor quantum dots has proven successful. This manuscript reviews quantum optics with excitons in single quantum dots embedded in photonic nanostructures. The ability to engineer the light-matter interaction strength in integrated photonic nanostructures enables a range of fundamental quantum-electrodynamics experiments on, e.g., spontaneous-emission control, modified Lamb shifts, and enhanced dipole-dipole interaction. Furthermore, highly efficient single-photon sources and giant photon nonlinearities may be implemented with immediate applications for photonic quantum-information processing. This review summarizes the general theoretical framework of photon emission including the role of dephasing processes and applies it to photonic nanostructures of current interest, such as photonic-crystal cavities and waveguides, dielectric nanowires, and plasmonic waveguides. The introduced concepts are generally applicable in quantum nanophotonics and apply to a large extent also to other quantum emitters, such as molecules, nitrogen vacancy centers, or atoms. Finally, the progress and future prospects of applications in quantum-information processing are considered.

Ettore Majorana (1906-1938) disappeared while traveling by ship from Palermo to Naples in 1938. His fate has never been fully resolved and several articles have been written that explore the mystery itself. His demise intrigues us still today because of his seminal work, published the previous year, that established symmetric solutions to the Dirac equation that describe a fermionic particle that is its own antiparticle. This work has long had a significant impact in neutrino physics, where this fundamental question regarding the particle remains unanswered. But the formalism he developed has found many uses as there are now a number of candidate spin-1/2 neutral particles that may be truly neutral with no quantum number to distinguish them from their antiparticles. If such particles exist, they will influence many areas of nuclear and particle physics. Most notably the process of neutrinoless double beta decay can exist only if neutrinos are massive Majorana particles. Hence, many efforts to search for this process are underway. Majorana's influence does not stop with particle physics, however, even though that was his original consideration. The equations he derived also arise in solid-state physics where they describe electronic states in materials with superconducting order. Of special interest here is the class of solutions of the Majorana equation in one and two spatial dimensions at exactly zero energy. These Majorana zero modes are endowed with some remarkable physical properties that may lead to advances in quantum computing and, in fact, there is evidence that they have been experimentally observed. This Colloquium first summarizes the basics of Majorana's theory and its implications. It then provides an overview of the rich experimental programs trying to find a fermion that is its own antiparticle in nuclear, particle, and solid-state physics.

High-transition temperature (high-T-c) superconductivity in the iron pnictides or chalcogenides emerges from the suppression of the static antiferromagnetic order in their parent compounds, similar to copper oxide superconductors. This raises a fundamental question concerning the role of magnetism in the superconductivity of these materials. Neutron scattering, a powerful probe to study the magnetic order and spin dynamics, plays an essential role in determining the relationship between magnetism and superconductivity in high-T-c superconductors. The rapid development of modern neutron time-of-flight spectrometers allows a direct determination of the spin dynamical properties of iron-based superconductors throughout the entire Brillouin zone. In this paper, an overview is presented of the neutron scattering results on iron-based superconductors, focusing on the evolution of spin-excitation spectra as a function of electron and hole doping and isoelectronic substitution. Spin dynamical properties of iron-based superconductors are compared with those of copper oxide and heavy fermion superconductors and the common features of spin excitations in these three families of unconventional superconductors and their relationship with superconductivity are discussed.

In little more than 20 years, the number of applications of the density functional (DF) formalism in chemistry and materials science has grown in an astonishing fashion. The number of publications alone shows that DF calculations make up a huge success story, and many younger colleagues are surprised to learn that the widespread application of density functional methods, particularly in chemistry, began only after 1990. This is indeed unexpected, because the origins are usually traced to the papers of Hohenberg, Kohn, and Sham more than a quarter of a century earlier. The DF formalism, its applications, and prospects were reviewed for this journal in 1989. About the same time, the combination of DF calculations with molecular dynamics promised to provide an efficient way to study structures and reactions in molecules and extended systems. This paper reviews the development of density-related methods back to the early years of quantum mechanics and follows the breakthrough in their application after 1990. The two examples from biochemistry and materials science are among the many current applications that were simply far beyond expectations in 1990. The reasons why-50 years after its modern formulation and after two decades of rapid expansion-some of the most cited practitioners in the field are concerned about its future are discussed.

Surface nanobubbles are nanoscopic gaseous domains on immersed substrates which can survive for days. They were first speculated to exist about 20 years ago, based on stepwise features in force curves between two hydrophobic surfaces, eventually leading to the first atomic force microscopy (AFM) image in 2000. While in the early years it was suspected that they may be an artifact caused by AFM, meanwhile their existence has been confirmed with various other methods, including through direct optical observation. Their existence seems to be paradoxical, as a simple classical estimate suggests that they should dissolve in microseconds, due to the large Laplace pressure inside these nanoscopic spherical-cap-shaped objects. Moreover, their contact angle (on the gas side) is much smaller than one would expect from macroscopic counterparts. This review will not only give an overview on surface nanobubbles, but also on surface nanodroplets, which are nanoscopic droplets (e.g., of oil) on (hydrophobic) substrates immersed in water, as they show similar properties and can easily be confused with surface nanobubbles and as they are produced in a similar way, namely, by a solvent exchange process, leading to local oversaturation of the water with gas or oil, respectively, and thus to nucleation. The review starts with how surface nanobubbles and nanodroplets can be made, how they can be observed (both individually and collectively), and what their properties are. Molecular dynamic simulations and theories to account for the long lifetime of the surface nanobubbles are then reported on. The crucial element contributing to the long lifetime of surface nanobubbles and nanodroplets is pinning of the three-phase contact line at chemical or geometric surface heterogeneities. The dynamical evolution of the surface nanobubbles then follows from the diffusion equation, Laplace’s equation, and Henry’s law. In particular, one obtains stable surface nanobubbles when the gas influx from the gas-oversaturated water and the outflux due to Laplace pressure balance. This is only possible for small enough surface bubbles. It is therefore the gas or oil oversaturation ζ that determines the contact angle of the surface nanobubble or nanodroplet and not the Young equation. The review also covers the potential technological relevance of surface nanobubbles and nanodroplets, namely, in flotation, in (photo)catalysis and electrolysis, in nanomaterial engineering, for transport in and out of nanofluidic devices, and for plasmonic bubbles, vapor nanobubbles, and energy conversion. Also given is a discussion on surface nanobubbles and nanodroplets in a nutshell, including theoretical predictions resulting from it and future directions. Studying the nucleation, growth, and dissolution dynamics of surface nanobubbles and nanodroplets will shed new light on the problems of contact line pinning and contact angle hysteresis on the submicron scale.

The electronic phase diagrams of many highly correlated systems, and, in particular, the cuprate high temperature superconductors, are complex, with many different phases appearing with similar (sometimes identical) ordering temperatures even as material properties, such as dopant concentration, are varied over wide ranges. This complexity is sometimes referred to as "competing orders." However, since the relation is intimate, and can even lead to the existence of new phases of matter such as the putative "pair-density wave," the general relation is better thought of in terms of " intertwined orders." Some of the experiments in the cuprates which suggest that essential aspects of the physics are reflected in the intertwining of multiple orders, not just in the nature of each order by itself, are selectively analyzed. Several theoretical ideas concerning the origin and implications of this complexity are also summarized and critiqued.

Distributed quantum networks will allow users to perform tasks and to interact in ways which are not possible with present-day technology. Their implementation is a key challenge for quantum science and requires the development of stationary quantum nodes that can send and receive as well as store and process quantum information locally. The nodes are connected by quantum channels for flying information carriers, i.e., photons. These channels serve both to directly exchange quantum information between nodes and to distribute entanglement over the whole network. In order to scale such networks to many particles and long distances, an efficient interface between the nodes and the channels is required. This article describes the cavity-based approach to this goal, with an emphasis on experimental systems in which single atoms are trapped in and coupled to optical resonators. Besides being conceptually appealing, this approach is promising for quantum networks on larger scales, as it gives access to long qubit coherence times and high light-matter coupling efficiencies. Thus, it allows one to generate entangled photons on the push of a button, to reversibly map the quantum state of a photon onto an atom, to transfer and teleport quantum states between remote atoms, to entangle distant atoms, to detect optical photons nondestructively, to perform entangling quantum gates between an atom and one or several photons, and even provides a route toward efficient heralded quantum memories for future repeaters. The presented general protocols and the identification of key parameters are applicable to other experimental systems.

Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The Levy-walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, biophysics, and behavioral science demonstrate that this particular type of random walk provides significant insight into complex transport phenomena. This review gives a self-consistent introduction to Levy walks, surveys their existing applications, including latest advances, and outlines further perspectives.

Quantum Monte Carlo methods have proved valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab initio calculations reproduce many low-lying states, moments, and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. The nuclear interactions and currents are reviewed along with a description of the continuum quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. A variety of results are presented, including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. Low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars are also described. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.

This is a review on theoretical and experimental studies on dielectric microcavities, which play a significant role in fundamental and applied research. The basic concepts and theories are introduced. Experimental techniques for fabrication of microcavities and optical characterization are described. Starting from undeformed cavities, the review moves on to weak deformation, intermediate deformation with mixed phase space, and then strong deformation with full ray chaos. Non-Hermitian physics such as avoided resonance crossings and exceptional points are covered along with various dynamical tunneling phenomena. Some specific topics such as unidirectional output, beam shifts, wavelength-scale microcavities, and rotating microcavities are discussed. The open microdisk and microsphere cavities are ideal model systems for the studies on wave chaos and non-Hermitian physics.

Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review the formalism of qubit stabilizer and subsystem stabilizer codes and their possible use in protecting quantum information in a quantum memory are considered. The theory of fault tolerance and quantum error correction is reviewed, and examples of various codes and code constructions, the general quantum error-correction conditions, the noise threshold, the special role played by Clifford gates, and the route toward fault-tolerant universal quantum computation are discussed. The second part of the review is focused on providing an overview of quantum error correction using two-dimensional (topological) codes, in particular, the surface code architecture. The complexity of decoding and the notion of passive or self-correcting quantum memories are discussed. The review does not focus on a particular technology but discusses topics that will be relevant for various quantum technologies.

Stationary nonequilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics approach, these states have been the subject of several theoretical investigations, both analytic and numerical. The macroscopic fluctuation theory, based on a formula for the probability of joint space-time fluctuations of thermodynamic variables and currents, provides a unified macroscopic treatment of such states for driven diffusive systems. A detailed review of this theory including its main predictions and most relevant applications is given.

Recent advances in the generation of well-characterized subfemtosecond laser pulses have opened up unpredicted opportunities for the real-time observation of ultrafast electronic dynamics in matter. Such attosecond chronoscopy allows a novel look at a wide range of fundamental photophysical and photochemical processes in the time domain, including Auger and autoionization processes, as well as photoemission from atoms, molecules, and surfaces, complementing conventional energy-domain spectroscopy. Attosecond chronoscopy raises fundamental conceptual and theoretical questions as to which novel information becomes accessible and which dynamical processes can be controlled and steered. Several of these questions, currently a matter of lively debate, are addressed in this review. The focus is placed on one prototypical case, the chronoscopy of the photoelectric effect by attosecond streaking. Is photoionization instantaneous or is there a finite response time of the electronic wave function to the photoabsorption event? Answers to this question turn out to be far more complex and multifaceted than initially thought. They touch upon fundamental issues of time and time delay as observables in quantum theory. Recent progress of our understanding of time-resolved photoemission from atoms, molecules, and solids is reviewed. Unresolved and open questions are highlighted and future directions are discussed addressing the observation and control of electronic motion in more complex nanoscale structures and in condensed matter.

Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty principle and, hence, play an important role in quantum foundations. More recently, entropic uncertainty relations have emerged as the central ingredient in the security analysis of almost all quantum cryptographic protocols, such as quantum key distribution and two-party quantum cryptography. This review surveys entropic uncertainty relations that capture Heisenberg's idea that the results of incompatible measurements are impossible to predict, covering both finite- and infinite-dimensional measurements. These ideas are then extended to incorporate quantum correlations between the observed object and its environment, allowing for a variety of recent, more general formulations of the uncertainty principle. Finally, various applications are discussed, ranging from entanglement witnessing to wave-particle duality to quantum cryptography.

Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike in conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and valley freedom. The interplay between the two is the focus of this review. The energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are explained, together with their consequences for transport measurements through nanotube quantum dots. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behavior. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, open questions for the field are also clearly stated. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a low level.