Second Generation of Composite Fermions in the Hamiltonian Theory

TL;DR

This paper models a second generation of composite fermions in the fractional quantum Hall effect, calculating activation gaps and explaining the emergence of new fractional states at unusual filling factors.

Contribution

It introduces a model for second-generation composite fermions and calculates their activation gaps, explaining new fractional quantum Hall states at unconventional filling factors.

Findings

Second-generation composite fermions have significantly smaller gaps than first-generation.

These states may account for observed fractional quantum Hall states at unusual filling factors.

Stability analyzed via pseudopotential expansion of interaction potential.

Abstract

In the framework of a recently developed model of interacting composite fermions restricted to a single level, we calculate the activation gaps of a second generation of spin-polarized composite fermions. These composite particles consist each of a composite fermion of the first generation and a vortex-like excitation and may be responsible for the recently observed fractional quantum Hall states at unusual filling factors such as nu=4/11,5/13,5/17, and 6/17. Because the gaps of composite fermions of the second generation are found to be more than one order of magnitude smaller than those of the first generation, these states are less visible than the usual states observed at filling factors nu=p/(2ps+1). Their stability is discussed in the context of a pseudopotential expansion of the composite-fermion interaction potential.