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, $m^{\ast }$, and quasi--particle Landau interaction function $f(\theta -{\theta }^{\prime })$. Analyzing infra--red divergences of perturbation theory, we get an exact expression for $m^{\ast }$, and conjecture the form of the $f(\theta -{\theta }^{\prime })$. We then conclude that in the limit of infinite cyclotron frequency, and small $\mathbf{q},\omega$, the composite fermion excitation spectrum is continuous for $0<\omega <\gamma \frac{e^2}{\epsilon h}q$, with $\gamma$ 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

References in corpus (5)

• On the low energy properies of fermions with singular interactions
• Non-Fermi Liquid Fixed Point in 2+1 Dimensions
• Gauge-invariant response functions of fermions coupled to a gauge field
• Singularities in the Fermi liquid description of a partially filled Landau level and the energy gaps of fractional quantum Hall states
• Gauge Interactions and Bosonized Fermion Liquids

Cited by in corpus (6)

• Half-filled Landau level as a Fermi liquid of dipolar quasiparticles
• Composite Fermions with Orbital Magnetization
• A Fermi Fluid Description of the Half-Filled Landau Level
• Towards a Fermi Liquid Theory of the $\nu$=1/2 State : Magnetized Composite Fermions
• Orthogonality catastrophe in a composite fermion liquid
• Dynamical properties of a two-dimensional electron gas in a magnetic field within the composite fermion model