Non-Abelian Anyon Superconductivity

Abstract

Non-Abelian Anyons exist in certain spin models and may exist 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 $\kappa$.