Second Order Topological Insulator State in Hexagonal Lattices and its Abundant Material Candidates

TL;DR

This paper introduces mechanisms to realize second order topological insulators in hexagonal lattices, identifies real material candidates, and demonstrates their nontrivial topology and protected corner states with large band gaps.

Contribution

It proposes two mechanisms for 2D SOTIs in hexagonal lattices, constructs models, and predicts abundant real material candidates with topological properties.

Findings

Demonstrates nontrivial band topology characterized by $w_2$

Identifies real material candidates with large band gaps up to 3.5 eV

Predicts protected corner states with fractional charge

Abstract

We propose two mechanisms to realize the second order topological insulator (SOTI) state in spinless hexagonal lattices, viz., chemical modification and anti-Kekul\'e/Kekul\'e distortion of hexagonal lattice. Correspondingly, we construct two models and demonstrate the nontrivial band topology of the SOTI state characterized by the second Stiefel-Whitney class $w_2$ in the presence of inversion symmetry ($\textit{P}$) and time-reversal symmetry ($\textit{T}$). Based on the two mechanisms and using first-principles calculations and symmetry analysis, we predict three categories of real light element material candidates, i.e., hydrogenated and halogenated 2D hexagonal group IV materials XY (X=C, Si, Ge, Sn, Y=H, F, Cl), 2D hexagonal group V materials (blue phosphorene, blue arsenene, and black phosphorene, black arsenene), and the recent experimentally synthesized anti-Kekul\'e/Kekul\'e order graphenes and the counterparts of silicene/germanene/stanene. We explicitly demonstrate the nontrivial topological invariants and existence of the protected corner states with fractional charge for these candidates with giant bulk band gap (up to 3.5 eV), which could facilitate the experimental verification by STM. Our approaches and proposed abundant real material candidates will greatly enrich 2D SOTIs and promote their intriguing physics research.