Failure of single-parameter scaling of wave functions in Anderson localization

Abstract

We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the origin of $L^{d-1}\times \infty$ disordered systems. For $d=1$ our approach is shown to reproduce exact diagonalization results available in the literature. In $d=2$, where strips of width $L\le 64$ sites were used, attempted fits of gaussian (log-normal) forms to the wavefunction amplitude distributions result in effective localization lengths growing with distance, contrary to the prediction from single-parameter scaling theory. We also show that the distributions possess a negative skewness $S$, which is invariant under the usual histogram-collapse rescaling, and whose absolute value increases with distance. We find $0.15\lesssim -S\lesssim 0.30$ for the range of parameters used in our study, .

RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be published)

References in corpus (5)

• Reconciling Conductance Fluctuations and the Scaling Theory of Localization
• Anomalous Conductance Distribution in Quasi-One Dimension: Possible Violation of One-Parameter Scaling Hypothesis
• Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model
• No indications of metal-insulator transition for systems of interacting electrons in two dimensions
• Reentrant behaviour and universality in the Anderson transition

Cited by in corpus (6)

• Fluctuations of the Lyapunov exponent in 2D disordered systems
• The phase diagram of the multi-dimensional Anderson localization via analytic determination of Lyapunov exponents
• Non-equilibrium transport through a disordered molecular nanowire
• Reply to Comment on "Exact analytic solution for the generalized Lyapunov exponent of the 2-dimensional Anderson localization"
• Scaling properties of one-dimensional off-diagonal disorder
• Localization and spin transport in honeycomb structures with spin-orbit coupling