  Floquet engineering is an important tool for realizing topologically
nontrivial band structures for charge-neutral atoms in optical lattices.
However, the preparation of a topological-band-insulator-type state of
fermions, with one nontrivial quasi-energy band filled completely and the
others empty, is challenging as a result of both driving induced heating as
well as imperfect adiabatic state preparation (with the latter induced by the
unavoidable gap closing when passing the topological transition). An
alternative procedure that has been proposed is to prepare such states
dissipatively, i.e. as a steady state that emerges when coupling the system to
reservoirs. Here we discuss a concrete scheme that couples the system to a
weakly interacting Bose condensate given by second atomic species acting as a
heat bath. Our strategy relies on the engineering of the potential for the bath
particles, so that they occupy weakly coupled tubes perpendicular to the
two-dimensional system. Using Floquet-Born-Markov theory, we show that the
resulting nonequilibrium steady state of the driven-dissipative system
approximates a topological insulator. We even find indications for the
approximate stabilization of an anomalous Floquet topological insulator, a
state that is impossible to realize in equilibrium.
