Analytical treatment of the dHvA frequency combinations due to chemical potential oscillations in an idealized two-band Fermi liquid

TL;DR

This paper analytically investigates the de Haas-van Alphen oscillation spectrum in a two-band Fermi liquid, revealing how chemical potential oscillations produce forbidden frequency combinations, with results validated by numerical simulations.

Contribution

It provides exact analytical expressions for Fourier components of oscillations in a two-band Fermi liquid, including effects of chemical potential oscillations, at zero and finite temperatures.

Findings

Analytical formulas match numerical results well.

Chemical potential oscillations produce forbidden frequency combinations.

High-temperature asymptotic expansion derived.

Abstract

de Haas-van Alphen oscillation spectrum is studied for an idealized two-dimensional Fermi liquid with two parabolic bands in the case of canonical (fixed number of quasiparticles) and grand canonical (fixed chemical potential) ensembles. As already reported in the literature, oscillations of the chemical potential in magnetic field yield frequency combinations that are forbidden in the framework of the semiclassical theory. Exact analytical calculation of the Fourier components is derived at zero temperature and an asymptotic expansion is given for the high temperature and low magnetic field range. A good agreement is obtained between analytical formulae and numerical computations.