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

Article

关键词: METAL-INSULATOR-TRANSITION;    2 DIMENSIONS;    MODEL;    CONDUCTANCE;    PERCOLATION;    ELECTRONS;    BEHAVIOR;    SYSTEMS;   

DOI  :  10.1103/PhysRevB.66.195113

来源: SCIE

【 摘 要 】

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 wave-function amplitudes at arbitrary distances from the origin of L(d-1)xinfinity 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 Lless than or equal to64 sites were used, attempted fits of Gaussian (log-normal) forms to the wave-function 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 0.15less than or similar to-Sless than or similar to0.30 for the range of parameters used in our study.

【 授权许可】

Free