Modifications of the Lifshitz-Kosevich formula in two-dimensional Dirac systems

TL;DR

This paper derives a modified Lifshitz-Kosevich formula for two-dimensional Dirac systems like graphene, accounting for effects of temperature, disorder, and electron-electron interactions on quantum oscillations.

Contribution

It extends the Lifshitz-Kosevich theory to Dirac materials, incorporating interaction and disorder effects on quantum oscillation behavior.

Findings

Finite temperature and impurity scattering affect oscillation frequency in Dirac systems.

Electron-electron interactions induce additional damping in oscillation amplitude.

Derived a generalized formula applicable to graphene and similar materials.

Abstract

Starting from the Luttinger-Ward functional we derive an expression for the oscillatory part of the grand potential of a two dimensional Dirac system in a magnetic field. We perform the computation for the clean and the disordered system, and we study the effect of electron-electron interactions on the oscillations. Unlike in the two dimensional electron gas (2DEG), a finite temperature and impurity scattering also affects the oscillation frequency. Furthermore, we find that in graphene, compared to the 2DEG, additional interaction induced damping effects occur: to two-loop order electron-electron interactions do lead to an additional damping factor in the amplitude of the Lifshitz-Kosevich-formula.