ABSTRACT
This chapter introduces the diagrammatic impurity-averaging technique, which will be our basic tool for studying the physical properties of systems with quenched disorder. A metallic conductor exhibits at low temperatures a temperature-independent resistance, the value of which is called the residual resistance. The residual resistance is due to the deviation of the sample from that of an ideal crystal. A conductor always has imperfections: foreign atoms substituting for atoms of the crystal, vacancies due to missing atoms, dislocations in the crystal, grain boundaries, etc. These defects will scatter an electron in the conductor between the different current-carrying eigenstates of the ideal crystal Hamiltonian, and thus cause current degradation. The effect on the electron motion of such imperfections we can model as giving rise to a potential deviating from that of the ideal crystal.
