LAUSR

We study corner states on a flat band in the square lattice. To this end, we introduce a two-dimensional model including Su-Schrieffer-Heeger type bond alternation responsible for corner states as well as next-nearest-neighbor hoppings yielding flat bands. The key symmetry of the model for corner states is space-time inversion ($\mathcal{PT}$) symmetry, which guarantees quantized Berry phases. This implies that edge states as well as corner states would show up if boundaries are introduced to the system. We also argue that an infinitesimal $\mathcal{PT}$ symmetry-breaking perturbation could drive flat bands into flat Chern bands.