Quasiparticle interactions in fractional quantum Hall systems

A partially filled shell (Landau level) of Laughlin quasiparticles (QP's) gives rise to an incompressible daughter state if the QP's themselves are Laughlin correlated. This occurs only if the pseudopotential V-QP(L') describing the interaction energy of a QP pair as a function of the total pair angular momentum L' satisfies special conditions. V-QP(L') can be obtained quite accurately from numerical studies of small systems. It does not always satisfy these conditions (e.g. for quasielectrons of the Laughlin v = 1/3 state at their v(QE) = 1/3 filling). In such cases, formation of pairs or larger clusters may explain the recently observed incompressible states (like v = 4/11).