  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 strained induced pseudo magnetic fields are oppositely oriented in
the two valleys [1-3] and can be as large as 60-300 Tesla as reported in recent
experiments [4,5]. For strained graphene at neutrality, a spin or a valley
polarized state is predicted depending on the value of the onsite 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 [5-8], 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.
