Topologically non-trivial Hofstadter bands on the kagome lattice

TL;DR

This paper explores the topological properties of Hofstadter bands on the kagome lattice under magnetic fields, revealing non-trivial Chern numbers and boundary-dependent edge state dispersions, with implications for optical lattice realizations.

Contribution

It introduces the study of topologically non-trivial Hofstadter bands on the kagome lattice and discusses boundary effects and potential experimental implementations.

Findings

Finite Chern numbers indicate non-trivial topology.

Edge state dispersions depend on boundary shape.

Potential realization in optical lattices suggested.

Abstract

We investigate how the multiple bands of fermions on a crystal lattice evolve if a magnetic field is added which does not increase the number of bands. The kagome lattice is studied as generic example for a lattice with loops of three bonds. Finite Chern numbers occur as non-trivial topological property in presence of the magnetic field. The symmetries and periodicities as function of the applied field are discussed. Strikingly, the dispersions of the edge states depend crucially on the precise shape of the boundary. This suggests that suitable design of the boundaries helps to tune physical properties which may even differ between upper and lower edge. Moreover, we suggest a promising gauge to realize this model in optical lattices.