# Topological chiral modes in random scattering networks

## TL;DR

This paper demonstrates the existence of topological chiral modes in random scattering networks using graph theory, linking them to Floquet topological insulators and extending their applicability beyond periodic driving systems.

## Contribution

It introduces a topological framework for chiral modes in random networks, generalizing Floquet topological insulator edge states to non-periodic dynamical systems.

## Key findings

- Existence of interface chiral modes in random networks.
- Mapping of regular networks to Floquet topological models.
- Extension of topological chiral states beyond Floquet systems.

## Abstract

Using elementary graph theory, we show the existence of interface chiral modes in random oriented scattering networks and discuss their topological nature. For particular regular networks (e.g. L-lattice, Kagome and triangular networks), an explicit mapping with time-periodically driven (Floquet) tight-binding models is found. In that case, the interface chiral modes are identified as the celebrated anomalous edge states of Floquet topological insulators and their existence is enforced by a symmetry imposed by the associated network. This work thus generalizes these anomalous chiral states beyond Floquet systems, to a class of discrete-time dynamical systems where a periodic driving in time is not required.