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

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.