Landau diamagnetism of the free electron gas as a Fermi surface effect

TL;DR

This paper provides a clear semi-classical explanation of Landau diamagnetism, showing it originates from electron states near the Fermi surface and explaining associated magnetic oscillations.

Contribution

It introduces a semi-classical approach using magnetic tubes to explain Landau diamagnetism and de Haas-van Alphen oscillations, simplifying previous complex computations.

Findings

Diamagnetic response is due to electron states near the Fermi surface.

Small Fermi energy oscillations result from electron redistribution.

The approach describes both Landau diamagnetism and de Haas-van Alphen oscillations.

Abstract

The diamagnetic response of the free electron gas called the Landau diamagnetism is a complex and elusive effect requiring laborious computations. Here based on the semi-classical treatment of the problem I present a clear picture of the Landau diamagnetism at zero temperature, which offers a simple derivation of this effect and leads to important consequences: 1) the diamagnetic response is due to electron states in a very narrow Fermi surface region in the k-space, 2) small Fermi energy oscillations in an applied magnetic field are caused by redistribution (inflow or outflow) of electrons from the equatorial region of the Fermi surface. The consideration is based on a structure called magnetic tube whose electron states surround a certain Landau level in k-space. A completely filled magnetic tube does not change its energy in an applied magnetic field as if it complied with the Bohr -- van Leeuwen theorem. The intersection of tubes with the Fermi surface leads to the appearance of partially occupied tubes in the region of intersection. The reconstruction of electron states in a magnetic field in this very small narrow region gives rise to the Landau diamagnetic response. In addition to the Landau diamagnetism this approach fully describes the oscillatory de Haas - van Alphen contribution to the magnetic susceptibility from the equatorial region of the Fermi sphere.