  Using simulation and theory we study the dynamics of a colloidal suspension
in two dimensions subject to a time-delayed repulsive feedback that depends on
the positions of the colloidal particles. The colloidal particles experience an
additional potential that is a superposition of repulsive potential energies
centered around the positions of all the particles a delay time ago. Here we
show that such a feedback leads to self-organization of the particles into
traveling bands. The width of the bands and their propagation speed can be
tuned by the delay time and the range of the imposed repulsive potential. The
emerging traveling band behavior is observed in Brownian dynamics computer
simulations as well as microscopic dynamic density functional theory (DDFT).
Traveling band formation also persists in systems of finite size leading, in
the case of circularly confined systems, to rotating traveling waves.
