Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant

The notion of square-root topological insulators has been recently generalized to higher-order topological insulators. In two-dimensional square-root higher-order topological insulators, the emergence of in-gap corner states is inherited from the squared Hamiltonian, which hosts higher-order topology. In this paper, we first propose that the martini lattice model serves as a concrete example of a higher-order topological insulator. We further propose a square-root higher -order topological insulator based on the martini lattice model. Specifically, we propose that the honeycomb model with two-site decoration, whose squared Hamiltonian consists of two martini lattice models, realizes square-root higher-order topological insulators. We show, for both the martini lattice and the decorated honeycomb model, that in-gap corner states appear at finite energies and that non-trivial bulk Z3 topological invariant protects them.