Topological states on the breathing kagome lattice

We theoretically study the topological properties of the tight-binding model on the breathing kagome lattice with antisymmetric spin-orbit coupling (SOC) between nearest neighbors. We show that the system hosts nontrivial topological phases even without second-nearest-neighbor hopping, and that the weakly dispersing band of the kagome lattice can become topological. The main results are presented in the form of phase diagrams, where the $\mathbb{Z}_2$ topological index is shown as a function of SOC (intrinsically allowed and Rashba) and lattice trimerization. In addition, exact diagonalization is compared with effective low-energy theories around the high-symmetry points. We find that the weakly dispersing band has a very robust topological property associated with it. Moreover, the Rashba SOC can produce a topological phase rather than hinder it, in contrast to the honeycomb lattice. Finally, we consider the case of a fully spin polarized (ferromagnetic) system, breaking time-reversal symmetry. We find a phase diagram that includes systems with finite Chern numbers. In this case too, the weakly dispersing band is topologically robust to trimerization.