Disordered Electronic Systems

The electrical conductivity of an ordinary metal such as gold is usually thought to be well understood. The electrons form a Fermi sea made up of plane waves modulated by the periodic crystal lattice. Because electrons obey Fermi statistics, only a narrow band of them, with an energy within $k_{\mathrm{B}}T$ of the Fermi energy, contributes to the conductivity. At room temperature these electrons are scattered by lattice vibrations, resulting in a loss of momentum and a nonzero resistivity $\mathrm{\rho (T).}$ At low temperatures electron‐electron scattering is the dominant scattering mechanism. In the limiting case of zero temperature there is a residual resistivity ${\rho }_0$ caused by the scattering of the electrons at the Fermi energy by lattice imperfections such as impurities and vacancies. The static defects that disrupt the translational symmetry of the crystalline lattice are the source of the disorder considered in this article.