Higher-order topological insulators in two-dimensional Dirac materials

Abstract

As a novel topological state, a higher-order topological insulator has attracted enormous interest, which in d spatial dimensions has gapless boundary states at (d-n) dimensions (integer n is larger than 1). Until now, merely few two-dimensional (2D) materials have been identified as higher-order topological insulators and their experimental confirmations are still absent. Here we propose a universal strategy of antidot engineering to realize second-order topological insulators (SOTIs) in 2D Dirac materials. Based on symmetry analysis, tight-binding model, and first-principles calculations, we demonstrate SOTIs in antidot-decorated Xene (X=C, Si,and Ge) by displaying its finite bulk quadrupole moment, weak topological edge states, and in-gap topological corner states. An inherent connection is established for the existing various mechanisms of the SOTIs, including quadrupole polarization, filling anomaly, and generalized Su-Schrieffer-Heeger model on a Kekulé lattice. The robustness of topological corner states of the SOTIs against edge perturbations and bulk disorders is explicitly demonstrated, rendering our strategy appealing to experimental realization of topological corner states.