Orbital degree of freedom induced multiple sets of second-order topological states in two-dimensional breathing Kagome crystals

The lattice geometry induced second-order topological corner states in breathing Kagome lattice have attracted enormous research interests, while the realistic breathing Kagome materials identified as second-order topological insulators are still lacking. Here, we report by first-principles calculations the second-order topological states emerging in two-dimensional d-orbital breathing Kagome crystals, i.e., monolayer niobium/tantalum chalcogenide halides M₃QX₇ (M = Nb, Ta; Q = S, Se, Te; X = Cl, Br, I). We find that the orbital degree of freedom of d orbitals can give rise to multiple sets of corner states. Combining fraction corner anomaly, orbital components and real space distribution of the corner states, we can also identify the topology of these corner states. Our work not only extends the lattice geometry induced second-order topological states to realistic materials, but also builds a clear and complete picture on their multiple sets of second-order topological states.