Pseudospin Polarized Dual-Higher-Order Topology in Hydrogen-Substituted Graphdiyne.

Although the topological band theory is applicable to both Fermionic and bosonic systems, the same electronic and phononic topological phases are seldom reported in one natural material. In this work, we show the presence of a dual-higher-order topology in hydrogen-substituted graphdiyne (H-GDY) by first-principles calculations. The intriguing enantiomorphic flat-bands are realized in both electronic and phononic bands of H-GDY, which is confirmed to be an organic 2D second-order topological insulator (SOTI). Most importantly, we found that the topological corner states are pseudospin polarized in H-GDY, exhibiting a clockwise or counterclockwise texture perpendicular to the radial direction. Our results not only identify the existence of the dual-higher-order topology in covalent organic frameworks but also uncover a unique pseudospin polarization-coordinate locking relation, further extending the well-known spin-momentum locking relation in conventional topological insulators.