Fractional quantum Hall states of clustered composite fermions

Abstract

The energy spectra and wavefunctions of up to 14 interacting quasielectrons (QE's) in the Laughlin ν = 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 νQE = 1 2 , 1 3 , 2 3 , corresponding to the electron fillings ν = 3 8 , 4 11 , 5 13 . The equivalent quasihole (QH) states occur at νQH = 1 4 , 1 5 , 2 7 , corresponding to ν = 3 10 , 4 13 , 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.

Transition from Free to Interacting Composite Fermions away fromν=1/3

“…The experimental evidence for such higher order states bring into question the validity of the weakly interacting CF framework [4]. While these higher order fractions were actually predicted in the earlier hierarchical model [5,6], it was argued that the CF model may account for these new fractions when CF residual interactions are incorporated beyond the mean-field level [7,8,9,10,11,12,13,14].…”

“…This ordering assumes full spin polarization in the full range 1/3 < ν < 2/5. While this assumption has been debated [7,8,13,14], transport experiments with tilted magnetic fields indicate that at least the state at ν = 4/11 is fully spin polarized for B T > 10 T . In the following we show that the filling factor dependence of the SF peak energy clarifies this issue.…”

Fractional quantum Hall effect at Landau level fillingν=4/11

“…In fact, almost all the existing finite-size numerical calculations [13][14][15][16][17][18] seem to favor a partially spin polarized ground state for the experimentally observed 4/11 state. However, the numerical simulations were carried out in 2DES of zero thickness.…”

“…Yet, its origin remains elusive. Several proposals [13][14][15][16][17][18] have been made. Among them, the numerical simulations by Wójs, Yi, and Quinn (WYQ) [15] showed that a spin-polarized 4/11 FQHE state is an unconventional FQHE state of CFs and, possibly, a new nonAbelian state.…”

“…Several proposals [13][14][15][16][17][18] have been made. Among them, the numerical simulations by Wójs, Yi, and Quinn (WYQ) [15] showed that a spin-polarized 4/11 FQHE state is an unconventional FQHE state of CFs and, possibly, a new nonAbelian state. Recently, using the CF diagonalization technique, Mukherjee et al [17] predicted a spin transition from a partially spin polarized state (which was believed to be the case for the experimentally observed 4/11 state [14]) to a fully spin-polarized state (or the WYQ state).…”