Delocalization in one-dimensional tight-binding models with fractal disorder II: existence of mobility edge

摘要

In the previous work, we investigated the correlation-induced localization-delocalization transition (LDT) of the wavefunction at the band center (E = 0) in the one-dimensional tight-binding model with fractal disorder [H.S. Yamada, Eur. Phys. J. B 88, 264 (2015)]. In the present work, we study the energy (E not equal 0) dependence of the normalized localization length (NLL) and the delocalization of the wavefunction at different energy in the same system. The mobility edges in the LDT arise when the fractal dimension of the potential landscape is larger than the critical value depending on the disorder strength, which is consistent with the previous result. In addition, we present the distribution of individual NLL and Lyapunov exponents in the system with LDT.