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This article investigates the potential of the point contact Andreev reflection spectroscopy (PCARS) technique for measuring the symmetry of the energy gap and other key parameters of various 0-, 1-, and 2-dimensional superconducting systems. It begins with a brief description of PCARS, explaining what a point contact is and how it can be made and the conditions under which a PC is ballistic, as well as why and to what extent a PC between normal metals is spectroscopic. It then discusses the basics of Andreev reflection and the length scales in mesoscopic systems before considering the limits of applicability of PCARS for spectroscopy of ‘small’ superconductors. Finally, it reviews some examples of PCARS in quasi-0D, quasi-1D and quasi-2D superconductors.

This article considers Josephson junction barriers, focusing on barriers made from insulators, metals, semiconductors, magnets, and nanowires. The main characteristic of Josephson junctions is the local reduction or even suppression of the critical current in the barrier. These barriers affect the static and dynamics properties of Josephson junctions, including coupling strength, ground state, phase damping, and tunability of the critical current. The article first provides an overview of the fundamental physics of Josephson junctions, with particular emphasis on the Josephson effect, before describing the properties of two coupled superconductors. It then discusses tunnel barriers, metallic barriers, semiconducting barriers, and magnetic barriers.

This article examines the properties of biological fluid interfaces and membranes, with particular emphasis on monolayers and bilayers. There are several examples of interfaces between biological fluids; the most relevant to human physiology are probably the liquid/air interfaces in the lungs and on the surface of the eyes. Both of these feature films with remarkable properties of compressibility and self-healing. After providing an overview of the constituent molecules of biological interfaces, this article reviews the current knowledge on surface films and membranes, giving context for their role in biology, but paying special attention to the basic physical ideas that underpin fundamental studies of in-vitro model systems. It also considers isolated membranes, characterized by tension, elasticity and viscous damping, as well as closed vesicles and cells where the membrane separates the cytoskeleton from the extracellular matrix.

This article explores the dynamics, thermodynamics, and small-angle scattering of block copolymers. The goal is to determine what drives the applications of block copolymers, i.e. how block copolymers behave and how they are characterized. The article begins with a summary of the experimental data and various theories that comprise our understanding of block copolymer thermodynamics, with particular emphasis on phase behavior and especially the theory of microphase separation. It then considers topics related to block copolymer dynamics, including diffusion, viscoelasticity and rheology, shear-processing, and the kinetics of self-assembly. It also discusses small-angle scattering techniques as applied to block copolymer characterization, including scattering from ordered block copolymer melts.

This article examines the ‘active’ part of the cell cytoskeleton — which mostly corresponds to actin and tubulin polymers and associated molecular motors — using theoretical tools derived from a soft matter physics coarse-grained approach. It begins with an overview of the cytoskeleton and its components, which include actin filaments and gels, microtubules and specialized microtubule-based organelles, molecular motors, intermediate filaments, the plasma membrane and glycocalix, the cell wall, and the extracellular matrix. It then describes coarse-grained models of the cytoskeleton and gives two examples of models for important cellular functions, namely cell migration and cell polarity. It also proposes a new kind of soft matter model providing a coarse-grained description of cytoskeletal polymers and associated molecular motors.

This article deals with the fundamentals of colloid science, with particular emphasis on the interplay of energy and entropy factors in forming colloidal suspensions. It first considers when a colloidal suspension changes from a liquid at low colloid concentration to various equilibrium, along with metastable (including kinetically arrested) structures at higher concentrations. active driven matter and the selectivity of binding in protein-based colloids. It then discusses a number of key ideas and some recent developments in colloid physics by focusing on the work of Albert Einstein and Jean Perrin. It also explores the physics of entropy, how the liquid state is formed, strategies for tuning colloidal interactions, kinetic arrest and glass transition, and mode coupling theory. Finally, it describes gelation, colloid rheology, concentration effects in colloidal fluids, the rheology of solids, and proteins as ‘a mysterious sort of colloids’.

This article discusses some applications of concepts from random matrix theory (RMT) to condensed matter physics, with emphasis on phenomena, predicted or explained by RMT, that have actually been observed in experiments on quantum wires and quantum dots. These observations range from universal conductance fluctuations (UCF) to weak localization, non-Gaussian thermopower distributions, and sub-Poissonian shot noise. The article first considers the UCF phenomenon, nonlogarithmic eigenvalue repulsion, and sub-Poissonian shot noise in quantum wires before analysing level and wave function statistics, scattering matrix ensembles, conductance distribution, and thermopower distribution in quantum dots. It also examines the effects (not yet observed) of superconductors on the statistics of the Hamiltonian and scattering matrix.

This article explores the dynamics of entangled polymers, with particular emphasis on how the unusual and often dramatic mechanical properties of concentrated polymer systems are determined by the physics of entanglements. It begins with an overview of the foundations of entangled polymer dynamics, organized around tubes and slip links used in modeling entanglements, the packing length and concentration effects, the results of computer simulations on entanglements, topological contacts, and the effects of large deformations. The focus is on the nature of ‘entanglement’, both from a bottom-up molecular view, and from a phenomenological one. The discussion then turns to the linear viscoelasticity of entangled polymer solutions and melts, along with nonlinear viscoelasticity. Models of polymer dynamics in the linear regime are also described, including the ‘standard tube model’. The article concludes with suggestions for future work.

This article focuses on the rubberlike elasticity of elastomers, with particular emphasis on rubberlike materials that exhibit high deformability and recoverability. It begins with a discussion of the variety of practical ways to form and characterize a rubber-elastic network, including random chemical crosslinking, highly specific chemical end-linking, polymerizations with multi-functional monomers, physical aggregation, and crosslinking in solution and in the deformed state. It then considers the effects of network structure on elastomeric properties, along with the results of elasticity experiments regarding the mechanical properties of elastomeric materials. It also examines the evolution of theories of rubber elasticity describes the specific properties of swollen polymer gels where the possibility of solvent exchange leads to some dramatic transformations in the system. Finally, it evaluates new emerging classes of rubber-elastic materials, such as liquid crystalline elastomers, where the internal microstructure added to the random network leads to some unique mechanical properties.

This article examines fluid transport and solvent dynamics in polymer gels, in equilibrium and under mechanical stress, and the effect of fluids on gel deformation. It also introduces a continuum model that describes the coupled phenomena of electric current, solvent flux, and deformation of gel network. This model is a generalization of the diffusio-mechanical coupling model of non-ionic gels. The discussion begins with an overview of the equilibrium state of non-ionic gels under the action of mechanical forces. This is followed by an analysis of the dynamics of non-ionic gels, especially the relaxation of mechanical responses caused by solvent flow. The article concludes with an assessment of the dynamics of ionic gels as well as the effect of electric field on solvent flow and the gel deformation.

This article focuses on foams, which consist of gas bubbles surrounded by liquid and closely packed together so that they are in contact with each other. As a mixture of two fluids, a foam is paradoxically a solid, at least under a small enough stress — surface tension and gas pressure maintain it in equilibrium when deformed. The corresponding mixture of two liquids is an emulsion, rendered stiff by surface tension under low stress. After explaining what a foam is, this article discusses various applications of foams. It then considers the statics and dynamics of foams, the simple rules that govern local equilibrium, and the structure of foams. It also examines the key properties of foams, such as coarsening due to diffusion, coalescence, drainage, foamability, rheology and rheometry, shear localization, conductivity, and light scattering. Finally, it describes the role of surfactants in foam stability and evaluates analogous systems such as emulsions.

This article describes the fabrication of high-temperature superconducting nanowires and their characterization by magnetic and electric transport measurements. In the literature, nanowires of high-temperature superconductors (HTSc) are obtained by means of lithography, using thin film material as a base. However, there are two main problems with this approach: first, the substrate often influences the HTSc nanowire, and second, only electric transport measurements can be performed. This article explains how nanowires and nanobelts of high-temperature superconducting cuprates can be prepared by the template method and by electrospinning. It also considers the possibilities for employing substrate-free HTSc nanowires as building blocks to realize new, nanoporous bulk superconducting materials for a variety of applications.

This article reviews the experimental progress in hybrid superconducting devices based on quantum wires, in the form of semiconductor nanowires or carbon nanotubes, which are coupled to superconducting electrodes. It also presents a series of recent examples which illustrate the key phenomena that have allowed detailed investigations of important scenarios, including individual impurities on superconductors and proximitized systems that may hold Majorana quasiparticles. After describing experimental aspects of hybrid devices, including materials and fabrication techniques, the article considers superconducting junctions with normal quantum dots (QDs). It then turns to experiments on superconductivity-enhanced QD spectroscopy, sub-gap states in hybrid QDs, and non-local signals in Cooper pair splitter devices. Finally, it discusses the growth of epitaxial semiconductor–superconductor nanowire hybrids.

This article discusses modern directions of research in liquid crystals (LCs). LCs represent one of the best studied classes of soft matter, along with colloids, polymer solutions and melts, gels, and foams. Phenomena observed in LCs and approaches developed for their description become of heuristic value in other branches of science. This article considers the basic properties of low-molecular weight thermotropic LCs, with an additional emphasis on the developments of the last decade, such as LC colloids. It begins with an overview of thermotropic and lyotropic systems, followed by a review of the concept of order parameter, elasticity, surface anchoring, and topological defects. It also evaluates hybrid systems combining LCs with polymers or colloids, along with new ways of creating mesomorphic systems and the dynamics of LCs, including anisotropic viscosity, director dynamics and the Frederiks transition, and flow induced by thermal expansion. Finally, it describes various applications of LCs.

This article examines the vortex matter of mesoscopic superconductors with numerous vortex states that do not exist in bulk superconductors. Using scanning tunneling microscopy/spectroscopy, it investigates the organization of vortex cores at different levels of confinement. The article begins with a discussion of the basic properties of quantum vortices in superconductors and experimental requirements for studying vortex confinement phenomena. It then considers the effect of sample size and shape on vortex distribution and pinning, along with the resulting ultra-dense configurations that cannot be achieved in bulk superconductors. It also describes the peculiar features of vortices in atomically thin superconductors having mixed Abrikosov–Josephson vortices.

This article examines the practical problem of thermally driven high-speed flux avalanches occurring in superconducting thin films with mesoscopic artificial patterns. The thin films are synthesized with artificial pins in the form of sub-micrometric antidots (ADs). The article first provides an overview of magnetic flux avalanches in superconductors, with particular emphasis on thermally driven avalanches, before discussing the occurrence and morphology of flux avalanches in superconducting thin films comprised of AD arrays. It analyses the influence of lattice symmetry and different AD geometries on the guidance and consequently the branching of flux avalanches. It also explores how artificial pinning centers inserted in superconducting films affect vortex dynamics.

This article examines the occurrence of mesoscopic effects in superconductor-ferromagnet hybrids. It begins with an overview of theories underpinning superconducting/ferromagnetic (S/F) hybrid structures, focusing on their vortex nucleation conditions and vortex behavior as well as the localized nucleation of superconductivity in an ideal S/F system. It then presents experimental measurements of the localized superconducting state in the cases of domain wall and reverse domain superconductivity, along with the vortex state in planar S/F hybrids. In particular, it considers nucleation thresholds for superconducting vortices and equilibrium vortex configurations. Finally, it discusses the results of local scanning probe measurements of the novel mesoscopic effects that emerge in magnetically coupled S/F hybrid structures in the absence of proximity effects.

This article presents the results of model calculations carried out to determine the mesoscopic structural features of high-temperature superconducting (HTS) crystal structures, and especially their characteristic high critical temperature (Tc) and anisotropy. The crystal structure of high-temperature superconductors (HTSc) is unique in having some mesoscopic features. For example, the structures of a majority of cuprite superconductors are comprised of two structural blocks, perovskite and rock salt, stacked along the c-direction. This article calculates the interaction between the perovskite and rock salt blocks in the form of combinative energy in order to elucidate the effects of mesoscopic structures on high-Tc superconductivity. Both X-ray diffraction and Raman spectroscopy show that a ‘fixed triangle’ exists in the samples under investigation. The article also examines the importance of electron–phonon coupling in high-Tc superconductors.

This article examines the behavior of superconductivity in mesoscopic type-I superconductors based on micromagnetic measurements on two electrochemically grown mesoscopic superconductors, namely lead and tin. It first provides an overview of the basic properties of mesoscopic superconductivity and the interface between two different superconductors that are in close contact with one another. It then describes the electrochemical preparation of β-tin samples in a variety of shapes and sizes in the mesoscopic regime. It also presents the results of micromagnetic measurements, carried out using micro-Hall probes, including observations of the vortex states in mesoscopic tin and lead triangles and of proximity effects in lead/tin core–shell structures.

This article investigates multi-vortex states in mesoscopic amorphous superconductors with different geometries by means of scanning SQUID microscopy. It first describes the setup of the scanning SQUID microscope used in magnetic imaging of superconducting vortices before discussing the physical properties of amorphous superconducting thin films. It then presents the results of experiments showing the formation of multi-vortex states in mesoscopic dots of weak pinning, amorphous MoGe thin films, along with the formation of vortex polygons and concentric vortex rings in mesoscopic disks. It also considers the concept of multiple vortex shells and its applicability to vortex patterns observed in mesoscopic circle and square dots. The article highlights some of the key features of mesoscopic superconducting dots, including commensurability effect, multiple shell structures, repeated packing sequences, inclusion structural hierarchy, and pinning effect.