Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems
JA Méndez-Bermúdez, AJ Martínez-Mendoza… - Physical Review E, 2016 - APS
Physical Review E, 2016•APS
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− ln G is proportional to
the length of the wire L for all values of α, providing the localization length ξ from− ln G= 2 …
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− ln G is proportional to
the length of the wire L for all values of α, providing the localization length ξ from− ln G= 2 …
We perform a detailed numerical study of the conductance through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large , with . Our model serves as a generalization of the 1D Lloyd model, which corresponds to . First, we verify that the ensemble average −lnG is proportional to the length of the wire for all values of , providing the localization length from −lnG=2L/ξ. Then, we show that the probability distribution function is fully determined by the exponent and −lnG. In contrast to 1D wires with standard white-noise disorder, our wire model exhibits bimodal distributions of the conductance with peaks at and 1. In addition, we show that is proportional to , for , with , in agreement with previous studies.
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