Emergence of a Two-Dimensional Topological Dirac Semimetal Phase in a Phthalocyanine-Based Covalent Organic Framework

Two-dimensional covalent organic frameworks (COFs) offer a great range of structural flexibility via the integration of various molecular building units into periodic frameworks, which makes them of interest for both their fundamental properties and practical applications. Here, via density functional theory calculations, we propose the realization of a two-dimensional topological Dirac semimetal phase in a phthalocyanine-based COF consisting of only light elements (H, C, N, and F). We show that an Au-Bg band inversion can be induced by applying external strains to this tetragonal COF, leading to a topological phase transition from a normal insulator to a topological Dirac semimetal phase. The gapless points emerging upon band inversion survive even when spin-orbit coupling is explicitly considered given the intrinsically negligible spin-orbit coupling strength in this COF. The Dirac semimetal phase of the strained phthalocyanine-based COF is confirmed by the presence of inverted-band characteristics, topological surface states, and a Berry phase of πon a closed k loop surrounding the Dirac point. We also develop a tight-binding model that further demonstrates the Au-Bg band-inverted feature around the two gapless points in three dimensions.