# Boundary edge networks induced by bulk topology

## TL;DR

This paper develops an effective edge network theory to analyze boundary topology in topological insulators, accurately predicting bound state properties and clarifying complex edge phenomena in higher-order and fullerene systems.

## Contribution

It introduces a novel edge network approach that captures boundary topology and bound state characteristics in coupled edge states of topological insulators.

## Key findings

- Edge networks predict energy and fractional charge of bound states.
- The theory applies to second-order topological insulators and topological fullerenes.
- It simplifies understanding of complex boundary phenomena.

## Abstract

We introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators. Two examples studied are a two-dimensional second-order topological insulator and three-dimensional topological fullerenes, which involve multi-leg junctions. As a consequence of bulk-edge correspondence, these edge networks can faithfully predict properties such as the energy and fractional charge related to the bound states (edge solitons) in the aforementioned systems, including several aspects that were previously complicated or obscure.