# Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks

## TL;DR

This paper introduces a new mechanism for creating robust flatbands in materials using a network superstructure, explaining enhanced superconductivity and revealing higher-order topological corner states.

## Contribution

It proposes a novel principle for flatband realization in real materials through network superstructures, linking it to superconductivity and topological corner states.

## Key findings

- Flatbands are achievable via network superstructures in materials.
- Enhanced superconductivity is explained by the flatband mechanism.
- Higher-order topological corner states are demonstrated in the network.

## Abstract

We propose a new principle to realize flatbands which are robust in real materials, based on a network superstructure of one-dimensional segments. This mechanism is naturally realized in the nearly commensurate charge-density wave of 1T-TaS${}_2$ with the honeycomb network of conducting domain walls, and the resulting flatband can naturally explain the enhanced superconductivity. We also show that corner states, which are a hallmark of the higher-order topological insulators, appear in the network superstructure.