Intrinsic higher-order topological states in two-dimensional honeycomb quantum spin Hall insulators

The exploration of topological phases remains a cutting-edge research frontier, driven by their promising potential for next-generation electronic and quantum technologies. In this work, we employ first-principles calculations and tight-binding modeling to systematically investigate the topological properties of freestanding two-dimensional (2D) honeycomb Bi, HgTe, and Al₂O₃(0001)-supported HgTe. Remarkably, all three systems exhibit coexistence of intrinsic first- and higher-order topological insulator states, induced by spin–orbit coupling (SOC). These states manifest as topologically protected gapless edge states in one-dimensional (1D) nanoribbons and symmetry-related corner states in zero-dimensional (0D) nanoflakes. Furthermore, fractional electron charges may accumulate at the corners of armchair-edged nanoflakes. Among these materials, HgTe/Al₂O₃(0001) is particularly promising due to its experimentally feasible atomic configuration and low-energy corner states. Our findings highlight the importance of exploring higher-order topological phases in quantum spin Hall insulators and pave the way for new possibilities in device applications.