Doping lattice non-Abelian quantum Hall states

We study quantum phases of a fluid of mobile charged non-Abelian anyons, which arise upon doping the lattice Moore-Read quantum Hall state at lattice filling \nu = 1/2 ν = 1 / 2 and its generalizations to the Read-Rezayi ( RR_k R R k ) sequence at \nu = k/(k+2) ν = k / ( k + 2 ) . In contrast to their Abelian counterparts, non-Abelian anyons present unique challenges due to their non-invertible fusion rules and non-Abelian braiding structures. We address these challenges using a Chern-Simons-Ginzburg-Landau (CSGL) framework that incorporates the crucial effect of energy splitting between different anyon fusion channels at nonzero dopant density. For the Moore-Read state, we show that doping the charge e/4 e / 4 non-abelion naturally leads to a fully gapped charge- 2 2 superconductor without any coexisting topological order. The chiral central charge of the superconductor depends on details of the interactions determining the splitting of anyon fusion channels. For general RR_k R R k states, our analysis of states obtained by doping the basic non-abelion a_0 a 0 with charge e/(k+2) e / ( k + 2 ) reveals a striking even/odd pattern in the Read-Rezayi index k k . We develop a general physical picture for anyon-driven superconductivity based on charge-flux unbinding, and show how it relates to the CSGL description of doped Abelian quantum Hall states. Finally, as a bonus, we use the CSGL formalism to describe transitions between the RR_k R R k state and a trivial period- (k+2) ( k + 2 ) CDW insulator at fixed filling, driven by the gap closure of the fundamental non-Abelian anyon a_0 a 0 . Notably, for k=2 k = 2 , this predicts a per