Non-Abelian Anyon Superconductivity

Non-Abelian anyons exist in certain spin models and may exist in quantum 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 $d+id$ 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 $\kappa$.