Universal insulating-to-metallic crossover in tight-binding random geometric graphs

TL;DR

This paper investigates how the electronic transport properties of tight-binding random geometric graphs transition from insulating to metallic states as their average degree increases, using scattering matrix analysis.

Contribution

It introduces a detailed analysis of scattering and transport in random geometric graphs, revealing a universal crossover and invariance under certain scaling parameters.

Findings

Insulating to metallic crossover observed with increasing average degree.

Transport properties are invariant under a specific scaling parameter.

Large connectivity graphs align with random matrix theory predictions.

Abstract

Within the scattering matrix approach to electronic transport, the scattering and transport properties of tight-binding random graphs are analyzed. In particular, we compute the scattering matrix elements, the transmission, the channel-to-channel transmission distributions (including the total transmission distribution), the shot noise power, and the elastic enhancement factor. Two graph models are considered: random geometric graphs and bipartite random geometric graphs. The results show an insulating to a metallic crossover in the scattering and transport properties by increasing the average degree of the graphs from small to large values. Also, the scattering and transport properties are shown to be invariant under a scaling parameter depending on the average degree and the graph size. Furthermore, for large connectivity and in the perfect coupling regime, the scattering and transport properties of both graph models are well described by the random matrix theory predictions of electronic transport, except for bipartite graphs in particular scattering setups.