  We propose a cold-atom setup which allows for a dimensional crossover from a
two-dimensional quantum spin Hall insulating phase to a three-dimensional
strong topological insulator by tuning the hopping between the layers. We
further show that additional Hubbard onsite interactions can give rise to spin
liquid-like phases: weak and strong topological Mott insulators. They represent
the celebrated paradigm of a quantum state of matter which merely exists
because of the interplay of the non-trivial topology of the band structure and
strong interactions. While the theoretical understanding of this phase has
remained elusive, our proposal shall help to shed some light on this exotic
state of matter by paving the way for a controlled experimental investigation
in optical lattices.
