# Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices

## TL;DR

This paper investigates the electronic and topological properties of 2D Archimedean lattices, revealing Dirac fermions, flat bands, and quantum spin Hall phases through theoretical models and DFT calculations.

## Contribution

It introduces a comprehensive analysis of topological phases in all Archimedean lattices, combining tight-binding and density functional theory methods.

## Key findings

- Presence of Dirac fermions and flat bands in Archimedean lattices
- Identification of quantum spin Hall phases across lattices
- Validation with 2D carbon allotropes showing characteristic band structures

## Abstract

Materials with designed properties arises in a synergy between theoretical and experimental approaches. In this study we explore the set of Archimedean lattices forming a guidance to its electronic properties and topological phases. Within these lattices, rich electronic structure emerge forming type-I and II Dirac fermions, topological flat bands and high-degeneracy points with linear and flat dispersions. Employing a tight-binding model, with spin-orbit coupling, we characterize a quantum spin Hall (QSH) phase in all Archimedean lattices. Our discussion is validated within density functional theory calculations, where we show the characteristic bands of the studied lattices arising in 2D carbon allotropes.