Two-Dimensional Electrons in a Magnetic Field

Abstract

To understand the quantum Hall effect we first need to understand the motion of electrons in a magnetic field. In this chapter we summarize what is known about single-electron states in a magnetic field, which provides the foundation for the theoretical understanding described in the following chapters. First, we consider the classical motion of an electron in order to obtain an intuitive picture of the motion in a magnetic field. Next, we consider the motion quantum mechanically. We obtain the eigenstates in the absence of an external potential, and then proceed to those in the presence of an external potential. As external potentials, we consider that produced by a uniform electric field, and the confining potential at the sample boundary. Finally, we discuss electronic states in a random potential. Namely, we discuss whether the wave function is extended all over the sample or localized.