  We study two species of (or spin-1/2) fermions with short-range intra-species
repulsion in the presence of opposite (effective) magnetic field, each at
Landau level filling factor 1/3. In the absence of inter-species interaction,
the ground state is simply two copies of the 1/3 Laughlin state, with opposite
chirality, representing the fractional topological insulator (FTI) phase. We
show this phase is stable against moderate inter-species interactions. However
strong enough inter-species repulsion leads to phase separation, while strong
enough inter-species attraction drives the system into a superfluid phase. We
obtain the phase diagram through exact diagonalization calculations. The
FTI-superfluid phase transition is shown to be in the (2+1)D XY universality
class, using an appropriate Chern-Simons-Ginsburg-Landau effective field
theory.
