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

Abstract

Starting from the Luttinger-Ward functional [J. M. Luttinger and J. C. Ward, Phys. Rev. 118, 1417 (1960)PHRVAO0031-899X10.1103/PhysRev.118.1417] 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.