Disordered and Other Nonperiodic Solids

Summary

Various types of disordered materials are mentioned and their main structural and other properties are briefly reviewed. The multiple scattering (in the presence of strong disorder) and the wave interference reduce the diffusion coefficient and tend to localize the electrons. The dimensionality is an important factor, in the sense that for D < 2 any amount of disorder is enough to localize all the states, while for D > 2 a critical amount of disorder (depending on the energy) is needed for localization. The critical dimensionality, D = 2, in the absence of magnetic field belongs to the D < 2 category, while in the presence of magnetic field belongs to the D > 2 category, including the possibility of frictionless flow (the Quantum Hall phase). In general, the magnetic field tends to undo the effects of interference. In quasi-one-dimensional systems, the conductance, G, between contacts p and q is related to the transmission coefficient, $\overline T$ _pq, through the relation, $G_{pq} \, = \,2(e^2 /h)\overline T _{pq}$. The coherent potential approximation is a powerful method for obtaining averages by introducing a periodic effective medium determined self-consistently.