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

• Received 1 October 2015

DOI:https://doi.org/10.1103/PhysRevE.93.012135