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 ε of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large ε, P(ε)∼1/ε^{1+α} with α∈(0,2). Our model serves as a generalization of the 1D Lloyd model, which corresponds to α=1. First, we verify that the ensemble average 〈-lnG〉 is proportional to the length of the wire L for all values of α, providing the localization length ξ from 〈-lnG〉=2L/ξ. Then, we show that the probability distribution function P(G) is fully determined by the exponent α 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 G^{β}, for G→0, with β≤α/2, in agreement with previous studies.