Dynamics of anyon clusters in fractional quantum Hall fluids and their possible experimental implications

In a fractional quantum Hall fluid, the quasiparticle excitations are anyons with fractional charge and statistics. Effective interactions among the anyons can be induced by either model or realistic electron-electron (e-e) interactions. Without losing the generality, we investigate such phenomena in the Laughlin 1/3 and Moore-Read (MR) non-Abelian phases, where the emergent anyons display rich internal dynamics with interesting experimental consequences. In particular, bound states of two Laughlin anyons are preferred under short-range e-e interactions, leading to 2e/3 effective charge carriers at low temperatures, which have been seen in experiments. MR phases host two topologically distinct fusion channels: "1" and "ψ". The different effective interactions of e/4 anyons in the two sectors suggest the vanishing of the degeneracy of fusion channels when the e-e interaction is no longer its model Hamiltonian, in which case different bound states could also appear. This indicates the possibility of energetically manipulating the two types of anyons by tuning the bare e-e interactions. We point out that the results of recently developed high-resolution STM measurements will be affected by the effective anyon interactions when anyons are clustered together after the tunneling of electrons. Other possible experiments to detect the formation of anyon clusters and their properties will also be discussed shortly.