Continuous gravitational waves from rapidly rotating neutron stars are on the new frontiers of gravitational wave astrophysics and have strong connections to electromagnetic astronomy, nuclear astrophysics, and condensed matter physics. In this Colloquium I survey prospects for detection of continuous gravitational waves from various neutron star populations, especially aided by electromagnetic observations. Although there are caveats, current theories and observations suggest that the first detections are likely within a few years, and that many are likely in the era of next generation detectors such as Cosmic Explorer and the Einstein Telescope. I also survey what can be learned from these signals, each one of which will contain more cycles than all the compact binary mergers ever detected. Since continuous gravitational wave emission mechanisms depend on aspects of neutron star physics, such as crustal elasticity, which are not well constrained by current astronomical observations and physical experiments, their detection can tell us a great deal that is new about extreme matter. Even more can be learned by combining gravitational wave observations with data from the Square Kilometre Array, the Next Generation Very Large Array, FAST, and other electromagnetic detectors operating in the next generation era.
Three important driving forces for creating qualitatively new phases in quantum materials are the topology of the materials' electronic band structures, frustration in the electrons' motion or magnetic interactions, and strong correlations between their charge, spin, and orbital degrees of freedom. In very few material systems do all of these aspects come together to contribute on an equal footing to stabilize new electronic states with unprecedented properties; however the search for such systems can be guided by models of configurational motifs or key sublattices that can host such physics. One of the most fascinating structural motifs for realizing this rich interplay of frustration, electronic topology, and electron correlation effects is the kagome lattice. In this review, we provide an overview of the theoretical underpinnings driving the physics of kagome lattices, and we then discuss experimental progress in realizing novel states enabled by kagome networks in crystalline materials. Different material classes are discussed with an emphasis on the phenomenologies of their electronic states and how they map to interactions arising from their kagome lattices.
