Diffusion and localization in quantum random resistor networks

TL;DR

This paper investigates quantum percolation models using advanced numerical methods to distinguish between localized and extended electronic states, providing insights into transport properties in novel two-dimensional materials.

Contribution

It introduces a comprehensive analysis of localization in quantum resistor networks with new computational approaches and applies them to graphene-like systems.

Findings

Identification of localized versus extended states across parameter ranges

Analysis of local density of states distributions

Discussion of leakage effects in graphene RRN models

Abstract

The theoretical description of transport in a wide class of novel materials is based upon quantum percolation and related random resistor network (RRN) models. We examine the localization properties of electronic states of diverse two-dimensional quantum percolation models using exact diagonalization in combination with kernel polynomial expansion techniques. Employing the local distribution approach we determine the arithmetically and geometrically averaged densities of states in order to distinguish extended, current carrying states from localized ones. To get further insight into the nature of eigenstates of RRN models we analyze the probability distribution of the local density of states in the whole parameter and energy range. For a recently proposed RRN representation of graphene sheets we discuss leakage effects.