Higher-order topological insulators in two-dimensional Dirac materials

Yang Xue,Bao Zhao,Zhongqin Yang,Youhua Luo,Hao Huan,Zhenyu Zhang

doi:10.1103/physrevresearch.3.l042044

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.Received 5 September 2021Accepted 30 November 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.L042044Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEdge statesFirst-principles calculationsTopological materialsPhysical SystemsGermaneneGrapheneHoneycomb latticeTechniquesDensity functional theorySymmetriesTight-binding modelWannier function methodsCondensed Matter, Materials & Applied Physics

Highlights

A new type of topological insulator, the two-dimensional second-order topological insulator (2D second-order topological insulators (SOTIs)), has been proposed and has attracted considerable attention [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]
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
Using first-principles and tight-binding (TB) model calculations along with symmetry analysis, we show a spinless charge fractionalization of e/2 at the corner states, protected by the C6 or 3 ̄ [C3 + inversion(I )] symmetry, as well as weak topological edge states emerging in the XAL band gap

Summary

Introduction

A new type of topological insulator, the two-dimensional second-order topological insulator (2D SOTI), has been proposed and has attracted considerable attention [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. In the most typical case, the linear Dirac dispersion can be interpreted coming from a pair of spinless pz-like orbitals that reside separately on honeycomblike lattices (planar or buckled). The symmetry-preserving perturbation may split the connected CBR into some separated EBRs. If the Fermi level (EF) resides in the band gap between these EBRs, the introduced perturbation will shift the Wannier function centers ( charge centers) of the pristine honeycomblike system and result in an obstructed atomic limit (OAL) [29,30,33] [Fig. 1(a)], which may give rise to symmetry-protected topological corner states [1,2,13,14].

Published by the American Physical Society

Results and Discussion

The bulk quadrupole moment can be calculated as qi j