Itinerant and Localized Characters of Electrons

Crystalline solids are composed of a huge number (∼1023) of electrons and nuclei, which make up quantum many-body systems with rich properties. For intuitive understanding of the electronic property of actual solids, it is necessary to extract only essential ingredients out of a large number of degrees of freedom. In this chapter we take a simplified model where positively charged ions form a simple lattice. We discuss basic effects of kinetic energy of electrons, potential energy from ions, and mutual Coulomb interaction energy among electrons. Special attention is paid how the attractive and repulsive Coulomb interactions from ions and other electrons combine to work on each electron. Depending on relative importance of kinetic and mutual interaction energies, electrons take either itinerant states forming energy bands, or localized states around each ion. The discussion in this chapter is restricted to absolute zero of temperature.