  We report the observation of a new series of Abelian and non-Abelian
topological states in fractional Chern insulators (FCI). The states appear at
bosonic filling nu= k/(C+1) (k, C integers) in several lattice models, in
fractionally filled bands of Chern numbers C>=1 subject to on-site Hubbard
interactions. We show strong evidence that the k=1 series is Abelian while the
k>1 series is non-Abelian. The energy spectrum at both groundstate filling and
upon the addition of quasiholes shows a low-lying manifold of states whose
total degeneracy and counting matches, at the appropriate size, that of the
Fractional Quantum Hall (FQH) SU(C) (color) singlet k-clustered states
(including Halperin, non-Abelian spin singlet states and their
generalizations). The groundstate momenta are correctly predicted by the FQH to
FCI lattice folding. However, the counting of FCI states also matches that of a
spinless FQH series, preventing a clear identification just from the energy
spectrum. The entanglement spectrum lends support to the identification of our
states as SU(C) color-singlets but offers new anomalies in the counting for
C>1, possibly related to dislocations that call for the development of new
counting rules of these topological states.
