The de Haas-van Alphen effect in canonical and grand canonical multiband Fermi liquid

Abstract

A qualitatively different character of dHvA oscillations has been found in a multiband (quasi)two dimensional Fermi liquid with a fixed fermion density $n_{e}$ (canonical ensemble) compared with an open system where the chemical potential $μ$ is kept fixed (grand canonical ensemble). A new fundamental period $P_{f}$ appears when $n_{e}$ is fixed, a damping of the Landau levels is relatively small and a background density of states is negligible. $P_{f}$ is determined by the total density rather than by the partial densities of carriers in different bands: $P_{f}=1/(2n_{e}ϕ)$ for spin-split Landau levels and $P_{f}=1/(n_{e}ϕ)$ in the case of spin degenerate levels where $ϕ$ is the flux quantum.