Second-order topological insulators in Kekule-patterned hexagonal biphenylene networks

Biphenylene network, a two-dimensional material, has recently been extensively studied, owing to its potential applications. Here, we introduce an experimentally synthesized configuration of hexagonal biphenylene network (h-BPN) as a second-order topological insulator (SOTI). We begin by discussing the higher-order topological origin of h-BPN, which is an extended model of the Kekule lattice characterized by a multi-node pi-conjugation. Through first-principles calculations and tight-binding model, we reveal SOTI in h-BPN, characterized by non-zero fractional corner charges. Furthermore, we show that by varying the number of biphenylene units, h-BPN exhibits adjustable second-order topological phases with alternating parity. Specifically, odd biphenylene indices in the h-BPN system correspond to a SOTI, while even indices result in a trivial insulator. We propose that the h-BPN evolves from the Kekule lattice. These materials will have important applications in two-dimension devices as higher-order topological materials.