  An exciting new prospect in condensed matter physics is the possibility of
realizing fractional quantum Hall (FQH) states in simple lattice models without
a large external magnetic field. A fundamental question is whether
qualitatively new states can be realized on the lattice as compared with
ordinary fractional quantum Hall states. Here we propose new symmetry-enriched
topological states, topological nematic states, which are a dramatic
consequence of the interplay between the lattice translation symmetry and
topological properties of these fractional Chern insulators. When a partially
filled flat band has a Chern number N, it can be mapped to an N-layer quantum
Hall system. We find that lattice dislocations can act as wormholes connecting
the different layers and effectively change the topology of the space. Lattice
dislocations become defects with non-trivial quantum dimension, even when the
FQH state being realized is by itself Abelian. Our proposal leads to the
possibility of realizing the physics of topologically ordered states on high
genus surfaces in the lab even though the sample has only the disk geometry.
