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

TL;DR

This paper demonstrates that the traditional Lifshitz-Kosevich formalism fails in two-dimensional electron systems, especially near fractional quantum Hall states, and introduces a new exact expression accounting for strong interactions.

Contribution

It derives a new exact formula for quantum oscillations in 2D systems, surpassing the limitations of the Luttinger expansion and revealing significant deviations in strongly-interacting regimes.

Findings

Lifshitz-Kosevich formalism breaks down in 2D systems

Derived a new expression valid when rainbow graphs dominate

Shows strong deviations near fractional quantum Hall states

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 $omega_c/\mu$. 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.