  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.
