Quantum Oscillations of Electrons and of Composite Fermions in Two Dimensions: Beyond the Luttinger Expansion

Abstract

Quantum oscillation phenomena, in conventional 2-dimensional electron systems and in the fractional quantum Hall effect, are usually treated in the Lifshitz-Kosevich formalism. This is justified in three dimensions by Luttinger's expansion, in the parameter $omeg{a}_c/\mu$. We show that in two dimensions this expansion breaks down, and derive a new expression, exact in the limit where rainbow graphs dominate the self-energy. Application of our results to the fractional quantum Hall effect near half-filling shows very strong deviations from Lifshitz-Kosevich behaviour. We expect that such deviations will be important in any strongly-interacting 2-dimensional electronic system.

4 pages, 3 figures, LaTex

References in corpus (5)

• Singularities in the Fermi liquid description of a partially filled Landau level and the energy gaps of fractional quantum Hall states
• Non-Fermi Liquid Behavior In Quantum Critical Systems
• Pulsed Magnetic Field Measurements of the Composite Fermion Effective Mass
• Spectral Function Analysis of Fermi Liquids and of Composite Fermions in a Finite Magnetic Field: Renormalised Gaps
• Singular Behaviour of Electrons and of Composite Fermions in a Finite Effective Field

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