de Haas–van Alphen Effect in Canonical and Grand Canonical Multiband Fermi Liquid

A qualitatively different character of de Haas–van Alphen 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 $\mu$ 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: $P_f=1\mathrm{}/{2n}_e\phi$ for spin-split Landau levels and $P_f=1\mathrm{}/n_e\phi$ in the case of spin degenerate levels where $\phi$ is the flux quantum.