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=2l−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 νQE=1/3 and νQH=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.