We discuss how, in appropriately designed configurations, solenoids carrying
a semifluxon can be used as topological energy barriers for charged quantum
systems. We interpret this phenomenon as a consequence of the fact that such
solenoids induce nodal lines in the wave function describing the charge, which
on itself is a consequence of the Aharonov-Bohm effect. Moreover, we present a
thought experiment with a cavity where just two solenoids are sufficient to
create topological bound states.