Corner modes of the breathing kagome lattice: Origin and robustness

We study the non-trivial phase of two-dimensional breathing kagome lattice, displaying both edge and corner modes. The localized modes a flake were initially identified as signature higher-order topological but later shown to be trivial for perturbations that thought protect them. Using various theoretical simulation techniques, we confirm it does not display topology are nature. Nevertheless, they might protected. First, show set within tight-binding model can move away from zero energy, also repeat some used trivial. In addition, analyze protection in more detail find only respecting sublattice or generalized chiral crystalline symmetries, lattice connectivity, pin energy robustly. A destructive interference corroborates results. Finally, muffin-tin bulk lattice. symmetry markers, such Wilson loops Topological Quantum Chemistry, identify two phases adiabatically disconnected different obstructed atomic limits.