de Haas-van Alphen Effect and the Specific Heat of an Electron Gas

Abstract

A model electron gas is studied in order to provide a microscopic justification of the Shoenberg conjecture that the harmonic content of the de Haas-van Alpen oscillations of the magnetization $\overrightarrow{M}$ can properly be explained by replacing the applied field $\overrightarrow{H}$ in the elementary expression for $\overrightarrow{M}\left(\overrightarrow{H}\right)$ by the total induction $\overrightarrow{B}=\overrightarrow{H}+\overrightarrow{M}$. The model contains a current-current interaction between the electrons; and it is shown that the unscreened long-range nature of this interaction leads to a term in the low-temperature specific heat proportional to $T \ln T$. For a gas with terrestrial densities the coefficient of this anomalous term is very small and probably beyond detection.