The Landauer resistance of a one-dimensional metal with periodically spaced random impurities

Abstract

We find the dependence of the ensemble-averaged resistance, 〈ρL〉, of a one-dimensional chain consisting of periodically spaced random delta-function potentials of the chain length L, the incident-electron energy, and the chain disorder parameter w. We show that generally the 〈ρL〉 vs L dependence can be written as a sum of three exponential functions, two of which tend to zero as L℩∞. Hence the asymptotic expression for 〈ρL〉 is always an exponential function of L. Such an expression for 〈ρL〉 means that the electronic states are indeed localized and makes it possible (which is important) to find the dependence of the localization radius on the incident-electron energy and the force with which an electron interacts with the sites of the chain. We also derive a recurrence representation for 〈ρL〉, which proves convenient in numerical calculations.