Topology of nanonetworks grown by aggregation of simplexes with defects

Abstract

Motivated by the relevance of higher-order interactions in quantum physics and materials science at the nanoscale, recently a model has been introduced for new classes of networks that grow by the geometrically constrained aggregation of simplexes (triangles, tetrahedra and higher-order cliques). Their key features are hyperbolic geometry and hierarchical architecture with simplicial complexes, which can be described by the algebraic topology of graphs. Based on the model of chemically tunable self-assembly of simplexes [\v{S}uvakov et al., Sci.Rep 8, 1987 (2018)], here we study the impact of defect simplexes on the course of the process and their organisation in the grown nanonetworks for varied chemical affinity parameter and the size of building simplexes. Furthermore, we demonstrate how the presence of patterned defect bonds can be utilised to alter the structure of the assembly after the growth process is completed. In this regard, we consider the structure left by the removal of defect bonds and quantify the changes in the structure of simplicial complexes as well as in the underlying topological graph, representing 1-skeleton of the simplicial complex. By introducing new types of nanonetworks, these results open a promising application of the network science for the design of complex materials. They also provide a deeper understanding of the mechanisms underlying the higher-order connectivity in many complex systems.