Absence of Landau's Diamagnetism in Two Dimensions

TL;DR

This paper develops a quantum statistical theory for 2D electron systems, showing the absence of Landau's diamagnetism and revealing that such systems are always paramagnetic with magnetic oscillations.

Contribution

It introduces a theory explaining the de Haas-van Alphen oscillations in 2D systems and demonstrates the absence of Landau's diamagnetic term, highlighting a fundamental difference from 3D systems.

Findings

2D electron systems exhibit no Landau diamagnetism.

Magnetization oscillates due to Landau levels in 2D.

2D systems are inherently paramagnetic.

Abstract

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.