Absence of Landau's Diamagnetism in Two Dimensions

A quantum statistical theory is developed for the de Haas-van Alphen (dHvA) oscillation in the magnetization for a 2D system of quasifree electrons. The oscillatory density of states associated with the Landau levels gives rise to the dHvA oscillation. Significantly, there is no Landau’s diamagnetic term proportional to B2. This leads to the conclusion that the 2D electron system is always paramagnetic, but shows a magnetic oscillation. The difference between 2D and 3D electron systems is also briefly discussed.