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

Abstract

Notion of square-root topological insulators have been recently generalized to higher-order topological insulators. In two-dimensional square-root higher-order topological insulators, emergence of in-gap corner states are inherited from the squared Hamiltonian which hosts higher-order topology. In this paper, we propose that the martini lattice model serves as a concrete example of higher-order topological insulators. Furthermore, we also propose a suquare-root higher-order topological insulator based on the martini model. Specifically, we propose that the honeycomb lattice 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 of these two models, that in-gap corner states appear at finite energies and that they are portected by non-trivial bulk ${\mathbb{Z}}_3$ topological invariant.

10 pages, 10 figures

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• Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals
• Unconventional gapless semiconductor in an extended martini lattice in covalent honeycomb materials
• Topological phase diagram of twisted bilayer graphene as a function of the twist angle
• High-root topological edge-state bands
• Exceptional horns in $n$-root graphene and Lieb photonic ring lattices