Fractional topological phases and broken time-reversal symmetry in strained graphene.

We show that strained or deformed honeycomb lattices are promising platforms to realize fractional topological quantum states in the absence of any magnetic field. The strain-induced pseudomagnetic fields are oppositely oriented in the two valleys and can be as large as 60-300 T as reported in recent experiments. For strained graphene at neutrality, a spin- or a valley-polarized state is predicted depending on the value of the on-site Coulomb interaction. At fractional filling, the unscreened Coulomb interaction leads to a valley-polarized fractional quantum Hall liquid which spontaneously breaks time-reversal symmetry. Motivated by artificial graphene systems, we consider tuning the short-range part of interactions and demonstrate that exotic valley symmetric states, including a valley fractional topological insulator and a spin triplet superconductor, can be stabilized by such interaction engineering.