Excitation Spectrum and Collective Modes of Composite Fermions

TL;DR

This paper investigates the excitation spectrum and collective modes of composite fermions in the fractional quantum Hall effect, showing how certain eigenstates are eliminated and how collective modes can be described within the composite fermion framework.

Contribution

It demonstrates that many eigenstates of non-interacting electrons are eliminated upon composite fermion transformation, providing a better understanding of the spectrum and collective modes at fractional fillings.

Findings

Collective mode branches are well described as composite fermion modes.

At small wave vectors, a single collective mode exists for all fractional quantum Hall states.

Certain eigenstates of non-interacting electrons are eliminated after the composite fermion transformation.

Abstract

According to the composite fermion theory, the interacting electron system at filling factor $\nu$ is equivalent to the non-interacting composite fermion system at $\nu^*=\nu/(1-2m\nu)$, which in turn is related to the non-interacting electron system at $\nu^*$. We show that several eigenstates of non-interacting electrons at $\nu^*$ do not have any partners for interacting electrons at $\nu$, but, upon composite fermion transformation, these states are eliminated, and the remaining states provide a good description of the spectrum at $\nu$. We also show that the collective mode branches of incompressible states are well described as the collective modes of composite fermions. Our results suggest that, at small wave vectors, there is a single well defined collective mode for all fractional quantum Hall states. Implications for the Chern-Simons treatment of composite fermions will be discussed.