Annual Review of Condensed Matter Physics - Volume 15, 2024

The thermal Green's function formalism bridging between macroscopic observables and microscopic processes via linear response theory was established in the early 1960s, when I started my research career. I recall stimulating experiences with the help of this technique in exploring transport and thermodynamic properties of Bloch electrons in magnetic fields, especially orbital magnetism and the Hall effect, and this technique is useful for understanding narrow gap systems like Dirac and Weyl electrons, which are of current interest. Recent ongoing challenges on thermoelectricity based on the Kubo–Luttinger formula are briefly introduced; it is an important scientific issue in view of sustainable development goals that awaits contributions from condensed matter physics, where the thermal Green's function is again a powerful tool.

The “flow” of electric currents and heat in standard metals is diffusive with electronic motion randomized by impurities. However, for ultraclean metals, electrons can flow like water with their flow being described by the equations of hydrodynamics. While theoretically postulated, this situation was highly elusive for decades. In the past decade, several experimental groups have found strong indications for this type of flow, especially in graphene-based devices. In this review, we give an overview of some of the recent key developments, on both the theoretical and experimental sides.

Underwater soft robots are typically constructed from soft and flexible materials, which enable them to adapt to aquatic environments where the terrain can be complex. They are often inspired by soft-bodied aquatic animals and can be used for a range of tasks, such as underwater exploration, environmental monitoring, and rescue operations. However, the design of these robots presents significant challenges, as it requires soft materials and systems that can withstand the harsh and varied conditions of ocean environments. This review delves into the physics of soft materials and outlines the constitutive models for such materials. Through an exploration of the muscle structures in aquatic creatures like octopuses and stingrays, we highlight the interplay between the materials that make up artificial muscles and how these muscles interact with their external surroundings. Finally, we conclude by outlining unresolved challenges and providing potential avenues for future research.

In noncentrosymmetric materials, the responses (for example, electrical and optical) generally depend on the direction of the external stimuli, called nonreciprocal phenomena. In quantum materials, these nonreciprocal responses are governed by the quantum geometric properties and symmetries of the electronic states. In particular, spatial inversion () and time-reversal () symmetries play crucial roles, which are also relevant to the geometric Berry phase. Here, we give a comprehensive review of the nonreciprocal transport and optical responses including (a) the magnetochiral anisotropy, i.e., the nonlinear resistivity with respect to the electric field, in semiconductors and metals, (b) the nonreciprocal transport in superconductors such as the nonreciprocal paraconductivity and the superconducting diode effect in bulk and Josephson junctions, and (c) the second-order nonlinear optical effects in the electric field of light, including the geometric shift current in nonmagnetic systems, magnetic systems, and superconductors.

Magnetoelectric multiferroics, which display both ferroelectric and magnetic orders, are appealing because of their rich fundamental physics and promising technological applications. The revival of multiferroics since 2003 led to a comprehensive understanding of the mechanisms that facilitate the coexistence of electric and magnetic orders and conceptually new design strategies for device architectures, which brought us an important step closer to multiferroic-based technology. In the past thirty years, first-principles calculations based on the laws of quantum mechanics played a crucial role in understanding the electronic, magnetic, and structural properties of multiferroics and guided the design of new multiferroics with improved properties. In this review, we provide a comprehensive overview of first-principles approaches to magnetoelectric multiferroics, especially in low-dimensional forms. In particular, we discuss methods to build an effective Hamiltonian from first principles for magnets, ferroelectrics, and multiferroics. The recently developed machine learning potential approach for multiferroics is also outlined. Furthermore, we present the unified model for spin-induced ferroelectricity and methods for computing the linear magnetoelectric coupling tensor. Finally, recent progress in multiferroic systems and the applications of first-principles approaches to these systems are reviewed.

We review aspects of the evolution from Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) in two dimensions, which have now become relevant in systems with low densities, such as gated superconductors LixZrNCl, magic-angle twisted trilayer graphene, FeSe, FeSe1−xSx, and ultracold Fermi superfluids. We emphasize the important role played by chemical potentials in determining crossovers or topological quantum phase transitions during the BCS–BEC evolution in one-band and two-band superfluids and superconductors. We highlight that crossovers from BCS to BEC occur for pairing in nonnodal s-wave channels, whereas topological quantum phase transitions, in which the order parameter symmetry does not change, arise for pairing in any nodal higher angular momentum channels, such as d-wave. We conclude by discussing a few open questions regarding the BCS-to-BEC evolution in 2D, including modulus fluctuations of the order parameter, tighter upper bounds on critical temperatures, and the exploration of lattice effects in two-band superconductors and superfluids.

The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter θ. θ = 0, π correspond to bosons and fermions, respectively; at intermediate values, we say that we have fractional statistics. In two dimensions, θ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve nonabelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of nonabelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern–Simons terms. The crossings of one-dimensional anyons on a ring are unidirectional, such that a fractional phase θ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently, the anyon behavior predicted for quasiparticles in the ν = 1/3 fractional quantum Hall state has been observed in both scattering and interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.

The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is subballistic at any nonzero temperature: An initially localized spin fluctuation spreads in time t to a width t^2/3. This exponent as well as the functional form of the dynamical spin correlation function suggest that spin transport is in the Kardar–Parisi–Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.

Rich out-of-equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular, or colloidal systems; flocking in natural or artificial active matter; and the organization and subsistence of ecosystems. The learning process, and ensuing amazing performance, of deep neural networks bears resemblance with some of the before-mentioned examples. Quantum mechanical extensions are also of interest. In exact or approximate manner, the evolution of these systems can be expressed in terms of a dynamical mean-field theory that not only captures many of their peculiar effects but also has predictive power. This short review presents a summary of recent developments of this approach with emphasis on applications on the examples mentioned above.

High-temperature superconductivity, with transition temperatures up to ≈134 K at ambient pressure, occurs in layered cuprate compounds. The conducting CuO2 planes, which are universally present, are responsible for the superconductivity but also show a disposition to other competing states including spin and charge order. Charge-density-wave (CDW) order appears to be a universal property of cuprate superconductors. It has been studied via a multitude of probes including X-ray and neutron scattering, nuclear magnetic resonance, scanning probe techniques, electronic transport, and quantum oscillations. Here, we review the microscopic properties of the CDW order. We discuss the nature of the ordered state, that is, its symmetry and microscopic structure. Furthermore, we show how the CDW order is related to quenched disorder, host structure, symmetry breaking perturbations, and magnetic fields. We also describe measurements of dynamic collective charge excitations that are closely related to the quasi-static CDW order. Finally, we highlight some of the debated issues in the field, including the origin of the CDW order, the relationship to spin order, and the nature of the spatial CDW correlations.

Living cells are spatially organized by compartments that can nucleate, grow, and dissolve. Compartmentalization can emerge by phase separation, leading to the formation of droplets in the cell's nucleo- or cytoplasm, also called biomolecular condensates. Such droplets can organize the biochemistry of the cell by providing specific chemical environments in space and time. These compartments provide transient environments, suggesting the relevance of nonequilibrium physics of droplets as a key to unraveling the underlying physicochemical principles of biological functions in living cells. In this review, we highlight coarse-grained approaches that capture the physics of chemically active emulsions as a model for condensates orchestrating chemical processes. We also discuss the dynamics of single molecules in condensates and the material properties of biological condensates and their relevance for the cell. Finally, we propose wetting, prewetting, and surface phase transitions as a possibility for intracellular surfaces to control biological condensates, spatially organize membranes, and exert mechanical forces.

Life evolved organisms to adapt dynamically to their environment and autonomously exhibit behaviors. Although complex behaviors in organisms are typically associated with the capability of neurons to process information, the unicellular organism Physarum polycephalum disabuses us by solving complex tasks despite being just a single although gigantic cell shaped into a mesmerizing tubular network. In Physarum, smart behaviors arise as network tubes grow or shrink due to the mechanochemical coupling of contractile tubes, fluid flows, and transport across the network. Here, from a physicist's perspective, we introduce the biology and active chemomechanics of this living matter network. We review Physarum's global response in migration and dynamic state to its environment before revisiting its network architecture and flow and transport patterns. Finally, we summarize recent studies on storing and processing information to mount well-informed behaviors.

At the scale of drops, water either sticks to inclined solids or moves, yet slowly—without the mobility we expect of a liquid of low viscosity. We first recall that the contact line that bounds a drop is responsible for these special adhesion and enhanced friction properties. Then, we discuss how inducing nonwetting states (pearls and marbles) minimizes the role of this line, restores mobility, and even boosts the liquid when it is viscous.

The superconducting nickelates were first proposed as potential analogs to the cuprate unconventional superconductors in 1999, but it took twenty years before superconductivity was successfully stabilized in epitaxial thin films. Since then, a flurry of both experimental and theoretical efforts have sought to understand the similarities and differences between the two systems and how they manifest in the macroscopic superconducting and normal state properties. Although the nickelates and cuprates indeed share many commonalities within their respective phase diagrams, several notable differences have also emerged, especially regarding their parent compounds, electronic hybridization, and fermiology. Here, we provide a survey of the rapidly developing landscape of layered nickelate superconductors, including recent experimental progress to probe not just the superconducting but also normal state and other ordered phases stabilized in these compounds.

Understanding the physics of behavior in animals is a challenging and fascinating area of research that has gained increasing attention in recent years. In this review, we delve into the intricate temporal and spatial scales of animal behavior for both individuals and collectives. We explore the experimental and theoretical approaches used to study behavior, highlighting the importance of feedback loops, emergent behavior, and environmental factors in shaping the actions of creatures great and small. The emergence of novel technologies, such as high-speed imaging and tracking, has provided unparalleled insight into the captivating nuances of animal behavior, and we review how these insights have been used to validate physics-based models of animal behavior. We also consider the potential applications of this research in robotics and artificial intelligence, identify new areas for exploration, and envision the possibility of further breakthroughs that will illuminate the complex dynamics of animal behavior.