Workshop on Topology: Identifying Order in Complex Systems

The recent advances in our understanding of topological states of free-fermion insulators give some valuable concepts and tools for the analysis of metals. The first part of this talk focuses on low-energy electrodynamic responses of simple metals, including the question of when recently discovered Weyl semimetals show a "chiral magnetic effect" related to the chiral anomaly. It turns out that the natural intrinsic version of this effect from a solid-state perspective is related to optical gyrotropy and to the orbital moment of Bloch electrons, which has some interesting similarities and differences compared to the better-known Berry curvature. The second part of the talk asks how the dynamics of metals after a sudden change (e.g., an optical absorption process) is modified by the existence of topological edge states or zero modes, a.k.a. Majorana fermions. A simple model system is shown to have power-law Loschmidt echo in quench dynamics, observable in principle by optical absorption.