Incompressible composite fermion liquids

The “second generation” fractional quantum Hall states containing a partially filled composite fermion (CF) Landau level (LL) are studied theoretically. The role of the unique form of the CF–CF interaction in the incompressibility of the underlying quantum electron liquid is explained. In particular, the two- and three-body CF correlation functions for these liquids are determined from exact diagonalization on a Haldane sphere. They are used to show that the CFs form a paired state (rather than a Laughlin liquid) when filling ν=13 of their second LL. Similarly, at ν=12 the CFs do not appear to form a Moore–Read paired state but tend to group into larger clusters instead. The spin polarization of the interacting CFs is also investigated, and a transition to the partially unpolarized ground state is predicted in realistic conditions.