Conductance of 1D quantum wires with anomalous electron-wavefunction localization

Abstract

We study the statistics of the conductance $g$ through one-dimensional disordered systems where electron wavefunctions decay spatially as $|\psi |\sim \exp (-\lambda r^{\alpha })$ for $0<\alpha <1$, $\lambda$ being a constant. In contrast to the conventional Anderson localization where $|\psi |\sim \exp (-\lambda r)$ and the conductance statistics is determined by a single parameter: the mean free path, here we show that when the wave function is anomalously localized ($\alpha <1$) the full statistics of the conductance is determined by the average $<\ln g>$ and the power $\alpha$. Our theoretical predictions are verified numerically by using a random hopping tight-binding model at zero energy, where due to the presence of chiral symmetry in the lattice there exists anomalous localization; this case corresponds to the particular value $\alpha =1/2$. To test our theory for other values of $\alpha$, we introduce a statistical model for the random hopping in the tight binding Hamiltonian.

6 pages, 8 figures. Few changes in the presentation and references updated. Published in PRB, Phys. Rev. B 85, 235450 (2012)

References in corpus (5)

• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Nonalgebraic length dependence of transmission through a chain of barriers with a Levy spacing distribution
• Conductance through quantum wires with Levy-type disorder: universal statistics in anomalous quantum transport
• Photonic heterostructures with Levy-type disorder: statistics of coherent transmission
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