LAUSR

We investigate the higher-order topological insulators on the breathing kagome lattices with $p$-orbital freedom. The bulk topological phase diagram is obtained by calculating the ${Z}_{3}$ Berry phase of the $p$-band model. The existence of a different class of orbital corner states is demonstrated on the (zero-dimensional) finite-size triangular structure. We find that the transverse hopping of the $p$ orbital is essential for the corner states to appear on the finite-size structure. The orbital configurations of the corner states are also explored and rich orbital orders are identified. Moreover, we show that the orbital corner states can be realized in a realistic photonic system, which are in good agreement with the predictions of the tight-binding model and then offer a versatile platform for the orbital physics.