The concept of metals and insulators

Abstract

According to the quantum mechanical concept of metals and insulators introduced by Wilson [96, 97], metallic conductivity is expected for systems in which the density of states at the Fermi level remains finite at zero temperature. In contrast, an insulator exhibits a gap in the density of states at the Fermi level. This situation is schematically depicted in Fig. 3.1. It was realized later that this condition is not sufficient in disordered conductors, where the nature of the wave function at the Fermi level is decisive [98]. Extended wave functions are typical for a metal, while localized wave functions lead to insulating behavior [99] (see Fig. 3.1). These concepts, however, rely on a single-particle description and it will be discussed in later sections how interactions change this notion of metals and insulators.