Annual Review of Condensed Matter Physics - Volume 8, 2017

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.

Weyl semimetals are conductors whose low-energy bulk excitations are Weyl fermions, whereas their surfaces possess metallic Fermi arc surface states. These Fermi arc surface states are protected by a topological invariant associated with the bulk electronic wave functions of the material. Recently, it has been shown that the TaAs and NbAs classes of materials harbor such a state of topological matter. We review the basic phenomena and experimental history of the discovery of the first Weyl semimetals, starting with the observation of topological Fermi arcs and Weyl nodes in TaAs and NbAs by angle and spin-resolved surface and bulk sensitive photoemission spectroscopy and continuing through magnetotransport measurements reporting the Adler–Bell–Jackiw chiral anomaly. We hope that this article provides a useful introduction to the theory of Weyl semimetals, a summary of recent experimental discoveries, and a guideline to future directions.

Epitaxial engineering of solid state heterointerfaces is a leading avenue to realizing enhanced or novel electronic states of matter. As a recent example, bulk FeSe is an unconventional superconductor with a modest transition temperature (Tc) of 9 K. However, when a single atomic layer of FeSe is grown on SrTiO3, its Tc can skyrocket by an order of magnitude to 65 K or 109 K. Since this discovery in 2012, efforts to reproduce, understand, and extend these findings continue to draw both excitement and scrutiny. In this review, we first present a critical survey of experimental measurements performed using a wide range of techniques. We then turn to the open question of microscopic mechanisms of superconductivity. We examine contrasting indications for both phononic (conventional) and magnetic/orbital (unconventional) means of electron pairing, as well as speculations about whether they could work cooperatively to boost Tc in a monolayer of FeSe.

Topological insulators and topological semimetals are both new classes of quantum materials, which are characterized by surface states induced by the topology of the bulk band structure. Topological Dirac or Weyl semimetals show linear dispersion around nodes, termed the Dirac or Weyl points, as the three-dimensional analog of graphene. We review the basic concepts and compare these topological states of matter from the materials perspective with a special focus on Weyl semimetals. The TaAs family is the ideal materials class to introduce the signatures of Weyl points in a pedagogical way, from Fermi arcs to the chiral magnetotransport properties, followed by hunting for the type-II Weyl semimetals in WTe2, MoTe2, and related compounds. Many materials are members of big families, and topological properties can be tuned. As one example, we introduce the multifunctional topological materials, Heusler compounds, in which both topological insulators and magnetic Weyl semimetals can be found. Instead of a comprehensive review, this article is expected to serve as a helpful introduction and summary by taking a snapshot of the quickly expanding field.

Transfer matrices and matrix product operators play a ubiquitous role in the field of many-body physics. This review gives an idiosyncratic overview of applications, exact results, and computational aspects of diagonalizing transfer matrices and matrix product operators. The results in this paper are a mixture of classic results, presented from the point of view of tensor networks, and new results. Topics discussed are exact solutions of transfer matrices in equilibrium and nonequilibrium statistical physics, tensor network states, matrix product operator algebras, and numerical matrix product state methods for finding extremal eigenvectors of matrix product operators.

Andreev reflection, familiar in superconducting systems, shows a much more extensive set of behaviors in the p-wave condensate of superfluid ³He. We discuss the basic ideas of Andreev reflection in the superfluid and its various manifestations. The fact that the process displays almost perfect retroreflection allows us to exploit the remarkable properties of the phenomenon for characterizing the pure quantum turbulence that can exist in these condensates. Finally, we discuss Andreev-reflection “optics” as a means of visualizing this turbulence in real time through the vortex video camera.