Disorder perturbed Flat Bands I: Level density and Inverse Participation Ratio

TL;DR

This paper develops a unified mathematical framework to analyze how disorder affects flat band systems, focusing on density of states and localization measures, and confirms that weak disorder has minimal impact on these properties.

Contribution

It introduces a general formulation for density of states and inverse participation ratio in disordered flat band systems, highlighting the role of a single system parameter.

Findings

Weak disorder has negligible effect on statistical measures

Formulation applies broadly to various flat band models

System parameter critical for disorder-driven transitions

Abstract

We consider the effect of disorder on the tight-binding Hamiltonians with a flat band and derive a common mathematical formulation of the average density of states and inverse participation ratio applicable for a wide range of them. The system information in the formulation appears through a single parameter which plays an important role in search of the critical points for disorder driven transitions in flat bands [1]. In weak disorder regime, the formulation indicates an insensitivity of the statistical measures to disorder strength, thus confirming the numerical results obtained by our as well as previous studies.