  We numerically and experimentally study the segregation dynamics in a binary
mixture of microswimmers which move on a two-dimensional substrate in a static
periodic triangular-like light intensity field. The motility of the active
particles is proportional to the imposed light intensity and they possess a
motility contrast, i.e., the prefactor depends on the species. In addition, the
active particles also experience a torque aligning their motion towards the
direction of the negative intensity gradient. We find a segregation of active
particles near the intensity minima where typically one species is localized
close to the minimum and the other one is centered around in an outer shell.
For a very strong aligning torque, there is an exact mapping onto an
equilibrium system in an effective external potential that is minimal at the
intensity minima. This external potential is similar to (height-dependent)
gravity, such that one can define effective `heaviness' of the self-propelled
particles. In analogy to shaken granular matter in gravity, we define a
`colloidal Brazil nut effect' if the heavier particles are floating on top of
the lighter ones. Using extensive Brownian dynamics simulations, we identify
system parameters for the active colloidal Brazil nut effect to occur and
explain it based on a generalized Archimedes' principle within the effective
equilibrium model: heavy particles are levitated in a dense fluid of lighter
particles if their effective mass density is lower than that of the surrounding
fluid. We also perform real-space experiments on light-activated self-propelled
colloidal mixtures which confirm the theoretical predictions.
