  Collective guidance of out-of-equilibrium systems without using external
fields is a challenge of paramount importance in active matter, ranging from
bacterial colonies to swarms of self-propelled particles. Designing strategies
to guide active matter using microfabricated circuits will provide insights for
applications from sensing, drug delivery to water remediation. However,
achieving directed motion without breaking detailed balance, for example by
asymmetric topographical patterning, is challenging. Here we engineer a
two-dimensional periodic topographical design with detailed balance in its unit
cell where we observe spontaneous particle edge guidance and corner
accumulation of self-propelled particles. This emergent behaviour is guaranteed
by a second-order non-Hermitian skin effect, a so far unobserved topologically
robust non-equilibrium phenomenon, that we use to dynamically break detailed
balance. Our stochastic circuit model predicts, without fitting parameters, how
guidance and accumulation can be controlled and enhanced by design: a device
guides particles more efficiently if the topological invariant characterizing
it is non-zero. Our work establishes a fruitful bridge between active and
topological matter, and our design principles offer a broad blueprint to design
devices that display spontaneous, robust and predictable guided motion and
accumulation, guaranteed by out-of-equilibrium topology.
