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

J A Méndez-Bermúdez1, A J Martínez-Mendoza1,2, V A Gopar3

  • 1Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico.

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Summary
This summary is machine-generated.

This study numerically investigates conductance in disordered one-dimensional wires. It reveals that long-tailed energy distributions lead to bimodal conductance, unlike standard models.

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Area of Science:

  • Condensed Matter Physics
  • Disordered Systems
  • Quantum Transport

Background:

  • Understanding electron transport in disordered materials is crucial for electronic devices.
  • One-dimensional (1D) systems exhibit unique quantum phenomena, including Anderson localization.
  • Previous models often assume simple disorder distributions, limiting applicability.

Purpose of the Study:

  • To numerically study conductance (G) in 1D tight-binding wires with on-site disorder.
  • To analyze the impact of long-tailed energy distributions on conductance properties.
  • To generalize and compare findings with the established 1D Lloyd model.

Main Methods:

  • Detailed numerical simulations of 1D tight-binding wires.
  • Characterization of random on-site energies using long-tailed distributions P(ε)∼1/ε^{1+α}.
  • Calculation of ensemble averages of -lnG to determine localization length (ξ).
  • Analysis of the conductance probability distribution function P(G).

Main Results:

  • Confirmed that ensemble average 〈-lnG〉 is proportional to wire length L for all α.
  • Derived localization length ξ using the relation 〈-lnG〉=2L/ξ.
  • Showed that P(G) is determined by α and 〈-lnG〉.
  • Observed bimodal conductance distributions with peaks at G=0 and G=1, differing from white-noise disorder.
  • Found P(lnG) ∝ G^{β} for G→0, with β≤α/2.

Conclusions:

  • Long-tailed disorder distributions in 1D wires lead to distinct bimodal conductance behavior.
  • The exponent α and localization length ξ are key parameters governing conductance distributions.
  • The findings offer a more generalized understanding of quantum transport in disordered systems.