Synthetic dimensions and topological chiral currents in mesoscopic rings

In condensed matter systems, the topological effect of chiral currents is intimately related to two-dimensional systems. Recently emerging concept of "synthetic dimensions" provides a way to explore two-dimensional physics using one dimensional setups by using internal degrees of freedom as an additional dimension. Synthetic dimensions have so far been predominantly developed in atomic and optical physics. In this work, we extend this concept to condensed matter systems of a mesoscopic ring coupled to a nanomagnet. Regarding the spin degrees of freedom of a nanomagnet as a dimension, we interpret a current in the ring, which is locked to the nanomagnet's spin, as chiral edge currents of a two-dimensional quantum Hall system. We thus provide a broader conceptual setting for synthetic dimensions, extending it to a rich domain of potential practical applications in condensed matter systems.