The Physical Significance of Singularities in the Chern--Simons Fermi Liquid Description of a Partially Filled Landau Level

Abstract

We analyze the linear response of a half filled Landau level to long wavelength and low frequency driving forces, using Fermi liquid theory for composite fermions. This response is determined by the composite fermions quasi--particle effective mass, $m^*$, and quasi--particle Landau interaction function $f(θ-θ')$. Analyzing infra--red divergences of perturbation theory, we get an exact expression for $m^*$, and conjecture the form of the $f(θ-θ')$. We then conclude that in the limit of infinite cyclotron frequency, and small ${\bf q},ω$, the composite fermion excitation spectrum is continuous for $0<ω<γ\frac{e^2}{εh}q$, with $γ$ an unknown number. For fractional quantum Hall states near a half filled Landau level, we derive an exact expression for the energy gap.

4 pages, RevTeX. This paper, being short and non-technical, could serve as a useful starting point for reading our manuscript cond-mat/9502032. The present paper does, however, include results not published in the former