Homogeneous Metallic Systems

Abstract

The traditional theories of electrons in metals, such as the Sommerfeld theory, pay little attention to electron-electron interactions. Instead, the electrons are treated as an ideal gas of fermions. The electrons move in an external potential, which is set up by the nuclei and the core electrons. The interactions between the conduction electrons are not considered, a somewhat astonishing fact given that the latter are not weak at all. Despite this, the Sommerfeld theory has been very successful in describing qualitatively and — in its more sophisticated forms — even quantitatively the physical properties of systems like the alkali or earth-alkali metals. These findings were set in the appropriate theoretical framework by Landau, who introduced the concept of quasiparticle and quasihole excitations of a Fermi liquid [10.1]. These excitations are restricted to a regime in momentum space close to the Fermi surface and are indeed weakly interacting. Instead of trying to calculate their residual interactions microscopically, which would be a very difficult task, the interactions are parametrized. These parameters enter the expressions for different physical quantities and therefore can be determined — at least in principle — when those quantities are measured. Landau’s Fermi-liquid theory was originally devised for isotropic systems like ³He, rather than realistic metals; if extended to anisotropic systems, it loses some of its simplicity and it becomes difficult to make predictions from it. Nevertheless, it remains an important concept for the understanding of real metals.