It is found that all the { \em singlet orbital pairing} instabilities are { \em absent} in a class of spin-polarized multi-orbital systems with quadratic band touching, which opens the way for { \em triplet orbital pairing} order. The ground states are found to be { \em non-Abelian} states with p-wave orbital pairing in checkerboard (away from 1/2 filling) and kagome (above 1/3 filling) lattices with { \em isotropic} attractive interaction which can be realized in ultracold multi-orbital optical lattices. The special property of such systems is generalized to more classes of multi-orbital systems, where the fully-gapped { \em non-Abelian} states are possibly the ground states. Those findings are helpful in achieving topological quantum computation.
Categories: cond-mat.quant-gas cond-mat.supr-con quant-ph