  We consider extended Hubbard models with repulsive interactions on a
Honeycomb lattice and the transitions from the semi-metal phase at half-filling
to Mott insulating phases. In particular, due to the frustrating nature of the
second-neighbor repulsive interactions, topological Mott phases displaying the
quantum Hall and the quantum spin Hall effects are found for spinless and
spinful fermion models, respectively. We present the mean-field phase diagram
and consider the effects of fluctuations within the random phase approximation
(RPA). Functional renormalization group analysis also show that these states
can be favored over the topologically trivial Mott insulating states.
