  Self-propelled micron-size particles suspended in a fluid, like bacteria or
synthetic microswimmers, are strongly non-equilibrium systems where particle
motility breaks the microscopic detailed balance, often resulting in
large-scale collective motion. Previous theoretical work has identified
long-range hydrodynamic interactions as the main driver of collective motion in
unbounded dilute suspension of rear-actuated ("pusher") microswimmers. In
contrast, most experimental studies of collective motion in microswimmer
suspensions have been carried out in quasi-2-dimensional geometries such as in
thin films or near solid or fluid interfaces, where both the swimmers' motion
and their long-range flow fields become altered due to the proximity of a
boundary. Here, we study numerically a minimal model of microswimmers in such a
restricted geometry, where the particles move in the midplane between two
no-slip walls. For pushers, we demonstrate collective motion with only
short-ranged order, in contrast with the long-ranged flows observed in
unbounded systems. For front-actuated ("puller") microswimmers, we discover a
long-wavelength density instability resulting in the formation of dense
microswimmer clusters. Both types of collective motion are fundamentally
different from their previously studied counterparts in unbounded domains. Our
results illustrate that hydrodynamic screening due to the presence of a wall is
subdominant in determining the collective state of the suspension, which is
instead dictated by the geometrical restriction of the swimmers' motion.
