Metal-organic framework as high-order topological insulator with protected corner modes

Abstract

The capacity to design and manipulate the chemical characteristics of metal-organic frameworks (MOFs) presents a promising approach for developing functional materials, particularly with regard to their topological properties. Here, based on first-principles calculations, we predict Ni3(C6S6)2 as a two-dimensional (2D) higher-order topological insulator (HOTI) with protected corner modes, which is the first material example of such topological phase in MOFs reported so far. The non-trivial topology of the material is identified by two different classes of bulk topological invariants: the real Chen number induced by spacetime inversion symmetry, and the fractional corner charge induced by rotational symmetry. The presence of corner states can serve as a diagnostic of its nontrivial topology. Moreover, the HOTI natural is demonstrated to be robust against symmetry perturbations and spin-orbit coupling. Inspired by the topological properties of Ni3(C6S6)2, we can explore regulating organic ligands or metal atoms in metal-organic frameworks to realize other 2D HOTIs, thereby expanding the family of 2D HOTIs. Our findings not only broaden the understanding of physical properties of metal-organic materials, but also extend the study of high-order topological insulators to organic platforms.