Polymerized triptycene as a candidate material of higher-order topological insulator

Higher-order topological insulators (HOTIs) have attracted growing attention as a novel class of topological state of matter, where boundary states, protected by topological natures of Bloch wave functions in a bulk, appear at boundaries with co-dimension larger than one. So far, various theoretical models for HOTIs have been proposed, and it is highly desirable to search suitable materials to realize the HOTIs.
In this presentation, we propose that a class of carbon-based materials called polymerized triptycene is a promising platform for a two-dimensional second-order topological insulator. The materials are composed of triptycene molecules and phenyl rings connecting the triptycene molecules. In this class of materials, the C₆ rings form a kagome-type network, which becomes a platform to realize the HOTI when introducing the ``breathing” structure. We show by the analysis of the tight-binding model that the corner states appear under the appropriate choice of the sample edges. We also demonstrate that the corner states are topologically protected by the bulk topological invariant, or the Z₃ Berry phase, that characterizes HOTIs.