2023/10/05 by A. M. Martínez-Argüello, Martínez-Argüello, A. M., K. B. Hidalgo-Castro +3
Materials Science · Mathematics · Physics and Astronomy · #Bipartite graph #Combinatorics #Complex network #Computer science #Crossover #Degree distribution #Discrete mathematics #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #G.1 #G.1 (Primary) #Geometry #Graph #Graph theory and applications #Graphene research and applications #H.1 #H.1 (Secondary) #Materials science #Mathematics #Matrix (chemical analysis) #Physics #Quantum and electron transport phenomena #Quantum mechanics #Random graph #Random matrix #Scaling #Scattering #Scattering length #Statistical physics
paper · pdf · doi:10.48550/arxiv.2310.03936
openalex publication_date 2023/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.