Skyrmions and Hall Transport

Skyrmions in chiral magnetic materials are stable, particle-like spin textures that are protected by a topological quantum number. Typical Skyrmion motions are complex, and their transport properties are involved with electric and thermal Hall conductivities along with linear and angular momenta. The identification of these quantities is often subtle, due to the Skyrmions’ extended nature and their interactions with conduction electrons and other backgrounds. Is there a guiding principle for possible physical quantities relevant for Skyrmions and relations among them? This talk answers the question in two parts. First, we note that Skyrmions are allowed due to broken parity symmetry (mirror symmetry). We provide a review on the parity breaking hydrodynamics, Hall viscosity, angular momentum and central extension of a commutation relation between the momentum operators. The underly theme of all these phenomena is parity symmetry breaking. Second, we provide a simple geometric picture of field theory Ward identities and its application to Skyrmion Hall transport that involves thermal, electric Hall conductivities and Hall viscosity. The topological charge density of Skyrmions has a distinct signature in the electric Hall conductivity that is identified in existing experimental data. In particular, we provide a simple and clear way to measure Hall viscosity that has been widely studied theoretically.