Excitation Spectrum and Collective Modes of Composite Fermions

Abstract

According to the composite fermion theory, the interacting electron system at filling factor $ν$ is equivalent to the non-interacting composite fermion system at $ν^*=ν/(1-2mν)$, which in turn is related to the non-interacting electron system at $ν^*$. We show that several eigenstates of non-interacting electrons at $ν^*$ do not have any partners for interacting electrons at $ν$, but, upon composite fermion transformation, these states are eliminated, and the remaining states provide a good description of the spectrum at $ν$. 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.