Delocalization in One-Dimensional Tight-Binding Models with Fractal Disorder II: Existence of Mobility Edge

TL;DR

This paper explores how fractal disorder in one-dimensional tight-binding models causes mobility edges, indicating energy-dependent localization-delocalization transitions, with detailed analysis of localization lengths and wavefunction distributions.

Contribution

It extends previous work by analyzing energy dependence of localization in fractal disordered systems and confirms the existence of mobility edges related to fractal dimension and disorder strength.

Findings

Mobility edges occur when fractal dimension exceeds a critical value.

Localization-delocalization transition depends on energy and fractal properties.

Distribution of NLL and Lyapunov exponent analyzed in the transition regime.

Abstract

In the previous work, we investigated the correlation-induced localization-delocalization transition (LDT) of the wavefunction at band center ($E=0$) in the one-dimensional tight-binding model with fractal disorder [Yamada, EPJB (2015) 88, 264]. In the present work, we study the energy ($E \neq 0$) dependence of the normalized localization length and the delocalization of the wavefunction at the 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 exponent in the system with LDT.