2024/05/25 by Maxine M. McCarthy, McCarthy, Maxine M., D. M. Whittaker +1 · 1 citation
Computer Science · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Image Retrieval and Classification Techniques #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2405.16274
openalex publication_date 2024/05/25 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28
We present the theory and experimental demonstration of a topological classification of finite tight binding Hamiltonians with chiral symmetry. Using the graph-theoretic notion of complete matchings, we show that many chiral tight binding structures can be divided into a number of sections, each of which has independent topological phases. Hence the overall classification is Nℤ2, corresponding to 2N distinct phases, where N is the number of sections with a non-trivial ℤ2 classification. In our classification, distinct topological phases are separated by exact closures in the energy spectrum of the Hamiltonian, with degenerate pairs of zero energy states. We show that that these zero energy states have an unusual localisation across distinct regions of the structure, determined by the manner in which the sections are connected together. We use this localisation to provide an experimental demonstration of the validity of the classification, through radio frequency measurements on a coaxial cable network which maps onto a tight binding system. The structure we investigate is a cable analogue of an ideal graphene ribbon, which divides into four sections and has a 4ℤ2 topological classification.