Annual Review of Condensed Matter Physics - Volume 9, 2018

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.