  Recently it was predicted, on the basis of a lattice gas model, that scalar
active matter in a gravitational field would rise against gravity up a
confining wall or inside a thin capillary - in spite of repulsive particle-wall
interactions [Phys. Rev. Lett. 124, 048001 (2020)]. In this paper we confirm
this prediction with sedimenting active Brownian particles (ABPs) in a box
numerically and elucidate the mechanism leading to the formation of a meniscus
rising above the bulk of the sedimentation region. The height of the meniscus
increases with the activity of the system, algebraically with the P\'eclet
number. The formation of the meniscus is determined by a stationary circular
particle current, a vortex, centered at the base of the meniscus, whose size
and strength increase with the ABP activity. The origin of these vortices can
be traced back to the confinement of the ABPs in a box: already the stationary
state of ideal (non-interacting) ABPs without gravitation displays circular
currents that arrange in a highly symmetric way in the eight octants of the
box. Gravitation distorts this vortex configuration downward, leaving two major
vortices at the two side walls, with a strong downward flow along the walls.
Repulsive interactions between the ABPs change this situation only as soon as
motility induced phase separation (MIPS) sets in and forms a dense, sedimented
liquid region at the bottom, which pushes the center of the vortex upwards
towards the liquid-gas interface. Self-propelled particles therefore represent
an impressive realization of scalar active matter that forms stationary
particle currents being able to perform visible work against gravity or any
other external field, which we predict to be observable experimentally in
active colloids under gravitation.
