High-Dimensional Disorder-Driven Phenomena in Weyl Semimetals, Semiconductors, and Related Systems

It is commonly believed that a noninteracting disordered electronic system can undergo only the Anderson metal-insulator transition. It has been suggested, however, that a broad class of systems can display disorder-driven transitions distinct from Anderson localization that have manifestations in the disorder-averaged density of states, conductivity, and other observables. Such transitions have received particular attention in the context of recently discovered 3D Weyl and Dirac materials but have also been predicted in cold-atom systems with long-range interactions, quantum kicked rotors, and all sufficiently high-dimensional systems. Moreover, such systems exhibit unconventional behavior of Lifshitz tails, energy-level statistics, and ballistic-transport properties. Here, we review recent progress and the status of results on non-Anderson disorder-driven transitions and related phenomena.