  We investigate the interplay between topological effects and Mott physics in
two dimensions on a graphene-like lattice, via a tight-binding model containing
an anisotropic spin-orbit coupling on the next-nearest-neighbour links and the
Hubbard interaction. We thoroughly analyze the resulting phases, namely a
topological band insulator phase or anisotropic quantum Spin Hall phase until
moderate interactions, a N\'eel and Spiral phase at large interactions in the
Mott regime, as well as the formation of a spin-orbital texture in the bulk at
the Mott transition. The emergent magnetic orders at large interactions are
analyzed through a spin wave analysis and mathematical arguments. At weak
interactions, by analogy with the Kane-Mele model, the system is described
through a Z_2 topological invariant. In addition, we describe how the
anisotropic spin-orbit coupling already produces an exotic spin texture at the
edges. The physics at the Mott transition is described in terms of a U(1) slave
rotor theory. Taking into account gauge fluctuations around the mean-field
saddle point solution, we show how the spin texture now proliferates into the
bulk above the Mott critical point. The latter emerges from the response of the
spinons under the insertion of monopoles and this becomes more pronounced as
the spin-orbit coupling becomes prevalent. We discuss implications of our
predictions for thin films of the iridate compound Na2IrO3 and also
graphene-like systems.
