Excitation spectrum and collective modes of composite fermions.

Abstract

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