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

S. Curnoe·P. C. E. Stamp
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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 $omega_c/μ$. 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.

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S. Curnoe, P. C. E. Stamp. 1997-12-18. Quantum Oscillations of Electrons and of Composite Fermions in Two Dimensions: Beyond the Luttinger Expansion. https://doi.org/10.1103/physrevlett.80.3312

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