Chiral properties of topological-state loops

The angular momentum quantization of chiral gapless modes confined to a circularly shaped interface between two different topological phases is investigated. By examining several different setups, we show analytically that the angular momentum of the topological modes exhibits a highly chiral behavior, and can be coupled to spin and/or valley degrees of freedom, reflecting the nature of the interface states. The energies and the magnetic moments corresponding to these states can be understood from a semiclassical picture. These loops can be viewed as building blocks for artificial magnets with tunable and highly diverse properties.