Hall Effect Characterization of the Electrical Properties of 2D and Topologically Protected Materials

Abstract

In this chapter we present the classical, quantum, and topological descriptions of electron transport measurements. Hall measurements are introduced using classical physics. The quantization of the electronic levels due to a magnetic field known as the Landau levels is shown. The observation of the quantization of the conductivity in a 2D electron gas at low temperature and high magnetic field due to the pioneering research of von Klitzing is presented. This leads to the introduction of the Berry phase and topological explanation of the quantized conductance. The relationship between the Kubo formula for conductance and topological quantification due to the research of Thouless, Kohmoto, Nightingale, and den Nijs is presented. The Hall characterization of single layer graphene and the observation of the Berry phase confirming the presence of Dirac carriers is used to demonstrate the topological properties of graphene. The family of Hall effects is also presented.