Flat band, spin-1 Dirac cone, and Hofstadter diagram in the fermionic square kagome model

TL;DR

This paper explores the unique band structures of fermions on a square kagome lattice, revealing flat bands, spin-1 Dirac cones, and Hofstadter spectra, highlighting complex topological and localized states in this frustrated lattice system.

Contribution

It uncovers the coexistence of flat bands, spin-1 Dirac cones, and their topological properties in the square kagome lattice, providing new insights into its electronic structure.

Findings

Identification of a flat band with localized states

Discovery of two spin-1 Dirac cones with asymmetric spectra

Analysis of Hofstadter spectrum and Chern numbers near Dirac cones

Abstract

We study characteristic band structures of the fermions on a square kagome lattice, one of the two-dimensional lattices hosting a corner-sharing network of triangles. We show that the band structures of the nearest-neighbor tight-binding model exhibit many characteristic features, including a flat band which is ubiquitous among frustrated lattices. On the flat band, we elucidate its origin by using the molecular-orbital representation and also find localized exact eigenstates called compact localized states. In addition to the flat band, we also find two spin-1 Dirac cones with different energies. These spin-1 Dirac cones are not described by the simplest effective Dirac Hamiltonian because the middle band is bended and the energy spectrum is particle-hole asymmetric. We also investigated the Hofstadter problem on a square kagome lattice in the presence of an external field and find that the profile of the Chern numbers around the modified spin-1 Dirac cones coincides with the conventional one.