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

Materials with properties designed on-demand arise in a synergy between theoretical and experimental approaches. Here, we explore a set of Archimedean lattices, providing a guide to their electronic properties and topological phases. Within these lattices, a rich electronic structure emerges 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 quantum spin Hall (QSH) phases in all Archimedean lattices. Our discussions are validated within density functional theory calculations, where we show the characteristic bands of the studied lattices arising in 2D carbon allotropes.