Non-Abelian Anyon Superconductivity

Non-Abelian Anyons are proposed to exist in certain spin models and in Quantuam Hall systems at certain filling fractions. In this work we studied the ground state of dynamical $SU(2)$ level $\kappa$ Chern Simons non-abelian anyons at finite density and no external magnetic field. We find that in the large $\kappa$ limit the topological interaction induces a pairing instability and the ground state is a superconductor with $\it{d+id}$ gap symmetry. We also develop a picture of pairing for the special value $\kappa=2$ and argue that the ground state is a superfluid of pairs for all values of $\kappa$.