Second-order topological insulator state in hexagonal lattices and its abundant material candidates

We propose two mechanisms to realize the second-order topological insulator (SOTI) state in spinless hexagonal lattices, viz., chemical modification and anti-Kekulé/Kekulé distortion of hexagonal lattices. Correspondingly, we construct two models and demonstrate the nontrivial band topology of the SOTI state characterized by the second Stiefel-Whitney class w2 in the presence of inversion symmetry (P) and time-reversal symmetry (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 two-dimensional (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-Kekulé/Kekulé order graphenes and the counterparts of silicene/germanene/stanene. We explicitly demonstrate the nontrivial topological invariants and the existence of the protected corner states with a fractional charge for these candidates with a giant bulk band gap (up to 3.5 eV), which could facilitate the experimental verification by scanning tunneling microscopy. Our approaches and proposed abundant real material candidates will greatly enrich 2D SOTIs and promote their intriguing physics research.