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Higher-order topological insulators have attracted considerable interests asa novel topological phase of matter, where topologically non-trivial nature ofbulk protects boundary states whose co-dimension is larger than one. It hasbeen revealed that the alternating pattern of hopping amplitudes intwo-dimensional lattices provides a promising route to realization of thehigher-order topological insulators. In this paper, we propose that ahoneycomb-lattice model with anti-Kekul\'{e} distortion hosts a higher-ordertopological phase. Here, the term anti-Kekul\'{e} distortion means that thepattern of strong and weak hoppings is opposite to that for the conventionalKekul\'{e} distortion. We demonstrate the existence of the higher-ordertopological phase by calculating the $\mathbb{Z}_6$ Berry phase that serves asa bulk topological invariant of the higher-order topological phase, and byshowing the existence of corner states.

Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekul\'{e} Distortion