Quantum oscillations of electrons and of composite fermions in two dimensions: Beyond the Luttinger expansion

Quantum oscillation phenomena, in conventional two-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)/mu. We show that in two dimensions this expansion breaks down, and we 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 behavior. We expect that such deviations will be important in any strongly interacting two-dimensional electronic system.