Observation of Anderson Localization in an Electron Gas

Anderson has shown that there is no diffusion of an electron in certain random lattices, and Mott has pointed out that, for electrons in materials in which there is a potential energy varying in a random way from atom to atom, Anderson's work predicts that there should be a range of energies at the bottom of the conduction band for which an electron can move only by thermally activated hopping from one localized state to another. An energy $E_c$ will separate the energies where this happens from the nonlocalized range of energies where there is no thermal activation. Cerium sulfide, investigated some years ago by Cutler and Leavy, is a particularly suitable material testing whether this is so because, in the neighborhood of the composition ${\mathrm{Ce}}_2$${\mathrm{S}}_3$, $\frac{1}{9}$ of the cerium sites are vacancies distributed at random, and the number of free electrons can be varied with only very small changes in the number of vacancies. It is shown that the experimental results find a natural explanation in terms of this model: Conduction is by hopping when the concentration of electrons is low and the Fermi energy $E_F$ lies below $E_c$; but when the concentration is higher and $E_F>E_c$, conduction is by the usual band mechanism with a short mean free path. The thermoelectric power is examined in both ranges, and the Hall mobility in the hopping region ($E_F<E_c$) seems in fair agreement with the theory of Holstein and Friedman.