Fractional Quantum Hall States of Clustered Composite Fermions

TL;DR

This paper investigates the energy spectra of interacting quasielectrons in the fractional quantum Hall state, revealing clustering behavior and identifying new incompressible states at specific filling factors, challenging existing models.

Contribution

It demonstrates that quasielectrons form clusters at high density, invalidating the simple composite fermion picture, and identifies novel fractional quantum Hall states with distinct correlations.

Findings

Quasielectrons form pairs or larger clusters at high density.

Finite-size incompressible ground states are identified at specific filling factors.

QE and QH correlations differ from traditional FQH states, leaving their origin uncertain.

Abstract

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