# Synthetic dimensions and topological chiral currents in mesoscopic rings

## TL;DR

This paper explores how synthetic dimensions in mesoscopic rings enable topological states, leading to observable chiral currents influenced by magnetic interactions, thus connecting lower-dimensional systems to higher-dimensional topological phenomena.

## Contribution

It introduces a novel approach linking synthetic dimensions to topological states in mesoscopic devices, demonstrated through a mapping to quantum Hall models and analysis of persistent currents.

## Key findings

- Synthetic dimensions facilitate topological states in mesoscopic rings.
- Magnet-induced synthetic dimensions produce quantized topological effects.
- Persistent currents reveal signatures of topological chiral states.

## Abstract

The recently-introduced concept of "synthetic dimensions" allows for the realization of higher-dimensional topological phenomena in lower-dimensional systems. In this work we study the complementary aspect that synthetic dimensions provide a natural route to topological states in mesoscopic hybrid devices. We demonstrate this for the current induced into a closed one-dimensional Aharonov-Bohm ring by the interaction with a dynamic mesoscopic magnet. The quantization of the magnetic moment provides a synthetic dimension that complements the charge motion around the ring. We present a direct mapping that places the combined ring-magnet system into the class of quantum Hall models, and demonstrate that topological features, combined with the magnet's anisotropy, can lead to clear signatures in the persistent current of the single-particle ground state.