Scaling behavior of a one-dimensional correlated disordered electronic System

TL;DR

This paper investigates the scaling behavior of a one-dimensional correlated disordered electronic system, analyzing localization length and density of states, and compares numerical results with theoretical approximations.

Contribution

It introduces a model with exponentially correlated disorder and explores its scaling properties, including the effects of correlation length divergence.

Findings

Scaling functions show a crossover near the band edge.

Correlation length diverges as concentration approaches 0 or 1.

Scaling behavior is limited for high correlation lengths and extreme concentrations.

Abstract

A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of "wrong sign" approaches to 1 or 0. The correlated random number sequence can be generated easily with a binary sequence similar to that of a one-dimensional spin glass system. The localization length (LL) and the integrated density of states (IDOS) for long chains are computed. A comparison with numerical results is made with the recently developed scaling technique results. The Coherent Potential Approximation (CPA) is also adopted to obtain scaling functions for both the LL and the IDOS. We confirmed that the scaling functions show a crossover near the band edge and establish their relation to the concentration. For concentrations near to 0 or 1 (longer correlation length case), the scaling behavior is followed only for a very limited range of the potential strengths.