Designing multi-directional energy-splitters and topological valley supernetworks

Abstract

Using group theoretic and topological concepts, together with tunneling phenomena, we geometrically design interfacial wave networks that contain splitters which partition energy in 2, 3, 4 or 5 directions. This enriches the valleytronics literature that has, so far, been limited to 2-directional splitters. Additionally, we describe a design paradigm that gives greater detail, about the relative transmission along outgoing leads, away from a junction; previously only the negligible transmission leads were predictable. We utilise semi-analytic numerical simulations, as opposed to finite element methods, to clearly illustrate all of these features with highly resolved edge states. As a consequence of this theory, novel networks, with directionality tunable by geometry, ideal for applications such as beam-splitters, switches and filters are created. Coupling these novel networks, that contain multi-directional energy-splitters, culminates in the first realization of a topological supernetwork.