Pseudopotentials, correlations, and hierarchy states in quantum hall systems: When the composite Fermion picture works and why

A system of Fermions in a shell of angular momentum l can form a set of multiplets of total angular momentum L . The composite Fermion (CF) picture picks out the lowest lying energy multiplets by selecting from this set a subset that is “Laughlin correlated”, i.e. which maximally avoids pair orbits with the largest pair angular momentum L ′ (or smallest relative angular momentum R = 2 l − L ′ ). We demonstrate that Laughlin correlations occur only when the pseudopotential V ( L ′ ) (the interaction energy of a pair as a function of L ′ ) increases with L ′ more rapidly, than the eigenvalue of L ′ 2 at the value of L ′ (or R ) avoided in the Laughlin correlated state. This requirement is not satisfied for QEs and QHs of the Laughlin ν = 1 / 3 and ν = 1 / 5 states at R = 1 and R = 3 respectively. At ν QE = 1 / 3 and ν QH = 1 / 5 , clustering of QPs gives lower energy than Laughlin correlations. Novel spin polarized incompressible states at ν = 4 / 11 and ν = 4 / 13 cannot be explained as a second generation in the CF hierarchy.