The Composite Fermion Hierarchy: Condensed States of Composite Fermion Excitations?

TL;DR

This paper develops a composite fermion hierarchy theory related to the Haldane picture, clarifies its relation to Jain states, and explains the limitations of the hierarchy approach for certain fractional quantum Hall states.

Contribution

It introduces a new hierarchy theory for composite fermions based on quasiparticles and clarifies its relation to existing Jain and Haldane theories.

Findings

Jain theory coincides with Haldane hierarchy for principal CF fillings

Provides a simple interpretation of many-quasiparticle spectra in Fermi liquid approach

Explains the failure of CF hierarchy for the 4/11 state

Abstract

A composite Fermion hierarchy theory is constructed in a way related to the original Haldane picture by applying the composite Fermion (CF) transformation to quasiparticles of Jain states. It is shown that the Jain theory coincides with the Haldane hierarchy theory for principal CF fillings. Within the Fermi liquid approach for few electron systems on the sphere a simple interpretation of many-quasiparticle spectra is given and provides an explanation of failure of CF hierarchy picture when applied to the hierarchical $4/11$ state.