Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems

We perform a detailed numerical study of the conductance G through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies e of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large e, P(e)~1/e1+a with a(0, 2). Our model serves as a generalization of the 1D Lloyd model, which corresponds to a=1. First, we verify that the ensemble average -lnG is proportional to the length of the wire L for all values of a, providing the localization length ¿ from -lnG=2L/¿. Then, we show that the probability distribution function P(G) is fully determined by the exponent a and -lnG. In contrast to 1D wires with standard white-noise disorder, our wire model exhibits bimodal distributions of the conductance with peaks at G=0 and 1. In addition, we show that P(lnG) is proportional to Gß, for G¿0, with ß=a/2, in agreement with previous studies