Non-linear topolectric circuits: A new frontier in synthetic metamaterial design*

Topolectric circuits have proven themselves as a versatile, easily accessible and flexible platform to study topological states in metamaterials. As of yet, the majority of explored models are linear circuits, consisting only of resistors, capacitors, and inductors, despite the family of electric circuit elements being far larger. Circuit networks incorporating non-linear components, such as diodes, transistors or more complex analog multipliers, promise new intriguing phenomena, such as the interplay of non-linear chaos with topology. In this presentation, we will summarize the field's state of the art, which reaches from Floquet states in periodically driven networks to Soliton solutions of non-linear transmission lines. We will elaborate on the chances and challenges non-linearities pose, and argue that they will be paramount for the next step in metamaterial design.