EIGENSTATES FOR AN ANDERSON MODEL OF AN ORDERED-LATTICE DISORDERED-LATTICE JUNCTION

We analyze the eigenstates in one dimension of a semi-infinite ordered lattice in contact with a semi-infinite disordered lattice described by an Anderson model. Specifically, we study the site wave functions i n the disordered region at distances N from the interface which are sm all compared to the localization length zeta0. The wave functions at t hese length scales are relevant for conduction in the metallic regime of a disordered lattice of finite size. From a perturbation expansion for weak disorder we obtain qualitatively different results for the ra ndom (N-dependent) rates of exponential growth of wave functions in di fferent domains corresponding to the energy band of an infinite nondis ordered chain. Their mean values are anomalous near the band center an d near the band edges, while corresponding to a fixed central limit (z eta0(-1)) between these limits, up to oscillatory terms. The study of the relative rms deviations of the above rates shows that they are sel f-averaging in a range of finite N much-greater-than 1, at any energy. At the intermediate energies the weak disorder expansion is valid for any length scale, while near the band center and near the band edges it ceases to converge beyond a characteristic length zeta1. The length zeta1 defines the border between scales N much-less-than zeta1, where the wave functions are weakly perturbed Bloch amplitudes, and scales N much-greater-than zeta1, where the weak disorder acts as a strong pe rturbation, leading to localized states with stationary positive Lyapu nov exponents (zeta0(-1)). We find that zeta1 scales with the disorder in the same way as does zeta0, while being less than an order of magn itude smaller zeta0. Finally, we relate our results for wave-function growth rates at finite length scales to the resistance of a quasimetal lic sample, using a simple Ansatz for the transmission coefficient. Th e resistance is found to be Ohmic, but anomalous, near the band center and strongly non-Ohmic near the band edges.