Electron correlations in partially filled lowest and excited Landau levels

The electron correlations near the half-filling of the lowest and excited Landau levels (LL's) are studied using numerical diagonalization. It is shown that in the low-lying states electrons avoid pair states with relative angular momenta R corresponding to positive anharmonicity of the interaction pseudopotential V(R). In the lowest LL, the superharmonic behavior of V(R) causes Laughlin correlations (avoiding pairs with R=1) and the Laughlin-Jain series of incompressible ground states. In the first excited LL, V(R) is harmonic at short range and a different series of incompressible states results. Similar correlations occur in the paired Moore-Read ν=5/2 state and in the ν=7/3 and 8/3 states, all having small total parentage from R=1 and 3 and large parentage from R=5. The ν=7/3 and 8/3 states are different from Laughlin ν=1/3 and 2/3 states and, in finite systems, occur at a different LL degeneracy (flux). The series of Laughlin-correlated states of electron pairs at ν=2+2/(q₂+2)=8/3, 5/2, 12/5, and 7/3 is proposed, although only in the ν=5/2 state pairing has been confirmed numerically. In the second excited LL, V(R) is subharmonic at short range and (near the half-filling) the electrons group into spatially separated larger ν=1 droplets to minimize the number of strongly repulsive pair states at R=3 and 5.