Topological metals

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Quantum materials are solids in which quantum mechanics, normally associated with the atomic and subatomic scales, directly manifests in their macroscopic scale observable properties. Such "macroscopic quantum phenomena" are not just interesting fundamentally but are also of great practical importance. It is certain we will be using quantum mechanics in much more creative ways than we are now in future technologies, and the ongoing fundamental study of quantum materials is currently laying the foundation for this. *** Macroscopic quantum phenomena arise when electrons in solids act coherently. Such coherent behavior may result from electron-electron interactions, superconductivity being perhaps the most well-known macroscopic quantum effect that arises from this source. Another, more subtle, and uncovered only recently, source of quantum coherence, is the electronic structure topology, whose growing importance in physics was recognized by the 2016 Physics Nobel Prize. While it was initially thought that the notions of nontrivial electronic structure topology and the associated observable phenomena may only exist in insulators, it has very recently been established that metals may also be "topological". The focus of the field has thus shifted from Topological Insulators to Topological Metals and Semimetals.*** The goal of the proposed research is to develop a complete theory of Topological Metals. The standard paradigm for understanding the physical properties of a metallic solid is the Landau Fermi liquid theory. This needs to be modified to describe new phenomena that arise in Topological Metals. The understanding that is currently emerging is that these new phenomena may be understood as Quantum Anomalies. Quantum anomaly is a concept, which originated in high energy physics, and describes violation of a classical symmetry by quantum effects. This concept is of crucial importance within the Standard Model of particle physics. Amazingly, it has now found its way into non-relativistic condensed matter physics: just one example of a remarkable convergence between condensed matter and particle physics, which is starting to materialize. The proposed research will seek to develop a complete understanding of the observable manifestations of quantum anomalies in topological metals, which represent an entirely new class of macroscopic quantum phenomena, and which are likely to significantly impact future quantum technology.***