  We combine experiments, large scale simulations and continuum models to study
the emergence of coherent structures in a suspension of magnetically driven
microrollers sedimented near a floor. Collective hydrodynamic effects are
predominant in this system, leading to strong density-velocity coupling. We
characterize a uniform suspension and show that density waves propagate freely
in all directions in a dispersive fashion. When sharp density gradients are
introduced in the suspension, we observe the formation of a shock. Unlike
Burgers' shock-like structures observed in other active and driven confined
hydrodynamic systems, the shock front in our system has a well-defined finite
width and moves rapidly compared to the mean suspension velocity. We introduce
a continuum model demonstrating that the finite width of the front is due to
far-field nonlocal hydrodynamic interactions and governed by a geometric
parameter: the average particle height above the floor.
