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

Abstract

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 $\ensuremath{\mu}$ 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: ${P}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/{2n}_{e}\ensuremath{\varphi}$ for spin-split Landau levels and ${P}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/{n}_{e}\ensuremath{\varphi}$ in the case of spin degenerate levels where $\ensuremath{\varphi}$ is the flux quantum.