Fractional Quantum Hall Effect and Electron Correlations in Partially Filled First Excited Landau Level

The possibility of using non-Abelian quasiparticle excitations in quantum computing has led to a revival of interest in the fractional quantum Hall (FQH) states of excited Landau levels.We present a quantitative study of most prominent incompressible quantum Hall states in the partially filled first excited Landau level (LL1) which have been recently studied experimentally by Choi et al.(cond-mat:0707.0236v2). The pseudopotential describing the electron- electron interaction in LL1 is harmonic at short range. It produces a series of incompressible states which is different from its LL0 counterpart. The numerical data indicate that the most prominent states $\nu=\frac{5}{2}$, $\frac{7}{3}$, and $\frac{8} {3}$ are not produced by Laughlin correlated electrons, but result from a tendency of electrons to form pairs or larger clusters which eventually become Laughlin correlated. States with smaller gaps at filling factors $\frac{14}{5}$, $\frac{16} {7}$, $\frac{11}{5}$, $\frac{19}{7}$ are Laughlin correlated electrons or holes and fit Jain's sequence of filled $\rm{CF}^4 $ levels.