Chapter 15 - Electron Gas in Magnetic Fields

Abstract

When a magnetic field is applied to an otherwise freely moving electron, the classical cyclotron motion perpendicular to the field is quantized into discrete Landau levels. Magnetic fields strongly influence the magnetic susceptibility and transport properties of ordinary (i.e. three dimensional) metals or semiconductors, and we discuss in particular Landau diamagnetism, magnetic moment oscillations in the de Haas-van Alphen effect, Pauli paramagnetism. Magnetic field effects are of utmost importance in the transport properties of a two-dimensional electron gas, where the integer and fractional quantum Hall effects have been discovered. In the integer quantum Hall effect, the quantization due to the magnetic field manifests itself in well-defined plateaus in the Hall resistance, which allow to measure the fundamental resistance quantum h/e2 with the astonishing accuracy of one part in billions. In the fractional quantum Hall effect, a novel and challenging world of composite particles opens to the experimental and theoretical investigation.