Disorder perturbed Flat Bands I: Level density and Inverse Participation Ratio
arXiv:1712.03523 · doi:10.1103/PhysRevB.98.054206
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.
34 Pages, 4 figures, Previous version divided in two parts to include new sections and details, title and abstract changed too
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