Localization and the Mobility Edge in One-Dimensional Potentials with Correlated Disorder

We show that a mobility edge exists in 1D random potentials in the presence of specific long-range correlations. Our approach is based on the relation between the binary correlator of a site potential and the localization length. We present an algorithm to numerically construct potentials with mobility edges at any given energy inside the allowed zone. Another way to generate such potentials is to use chaotic trajectories of nonlinear maps. Our numerical calculations for a few specific potentials demonstrate the presence of mobility edges in a 1D geometry.