  A salient feature of topological phases are surface states and many of the
widely studied physical properties are directly tied to their existence.
Although less explored, a variety of topological phases can however similarly
be distinguished by their response to localized flux defects, resulting in the
binding of modes whose stability can be traced back to that of convectional
edge states. The reduced dimensionality of these objects renders the
possibility of arranging them in distinct geometries, such as arrays that
branch or terminate in the bulk. We show that the prospect of hybridizing the
modes in such new kinds of channels poses profound opportunities in a dynamical
context. In particular, we find that creating junctions of $\pi$-flux chains or
extending them as function of time can induce transistor and stop-and-go
effects. Pending controllable initial conditions certain branches of the
extended defect array can be actively biased. Discussing these physical effects
within a generally applicable framework that relates to a variety of
established artificial topological materials, such as mass-spring setups and LC
circuits, our results offer an avenue to explore and manipulate new transport
effects that are rooted in the topological characterization of the underlying
system.
