Fractional quantum Hall states of clustered composite fermions

The energy spectra and wave functions of up to 14 interacting quasielectrons (QE’s) in the Laughlin $\nu =\frac{1}{3}$ fractional quantum Hall (FQH) state are investigated using exact numerical diagonalization. It is shown that at sufficiently high density the QE’s form pairs or larger clusters. This behavior, opposite to Laughlin correlations, invalidates the (sometimes invoked) reapplication of the composite fermion picture to the individual QE’s. The series of finite-size incompressible ground states are identified at the QE filling factors ${\nu }_{\mathrm{QE}}=\frac{1}{2},$ $\frac{1}{3},$ $\frac{2}{3},$ corresponding to the electron fillings $\nu =\frac{3}{8},$ $\frac{4}{11},$ $\frac{5}{13}.$ The equivalent quasihole (QH) states occur at ${\nu }_{\mathrm{QH}}=\frac{1}{4},$ $\frac{1}{5},$ $\frac{2}{7},$ corresponding to $\nu =\frac{3}{10},$ $\frac{4}{13},$ $\frac{5}{17}.$ All these six novel FQH states were recently discovered experimentally. Detailed analysis indicates that QE or QH correlations in these states are different from those of well-known FQH electron states (e.g., Laughlin or Moore–Read states), leaving the origin of their incompressibility uncertain. Halperin’s idea of Laughlin states of QP pairs is also explored, but is does not seem adequate.