  Here, we investigate the Cherenkov emission by an array of moving electric
charges in the vicinity of a topologically nontrivial gyrotropic material. It
is shown that the nonreciprocal material response may result in a robustly
asymmetric Cherenkov emission, such that the spectrum of the emitted radiation
and the stopping power depend strongly on the sign of the particle velocity. It
is demonstrated that the main emission channels are determined by the
unidirectional edge states supported by the topological material. We consider
as examples both magnetized plasmas and Weyl semi-metals. The latter may
exhibit a spontaneous nonreciprocal response without a biasing magnetic field.
