Two-dimensional weak topological insulators in inversion-symmetric crystals

The Su-Schrieffer-Heeger . (SSH) chain is a one-dimensional lattice that comprises two dimerized sublattices. Recently, Zhu, Prodan, and Ahn (ZPA) [Phys. Rev. B 99, 041117(R) (2019)] proposed flat bands can occur at the topological domain walls of two-dimensional array SSH chains. Here, we suggest insulator protected by inversion time-reversal symmetries without spin-orbit coupling. It shown chains realize insulator. Utilizing first Stiefel-Whitney numbers, weak type ${\mathbb{Z}}_{2}$ indices are developed, which identify insulator, dubbed (2DSWI). ZPA model employed to study phase diagrams transitions. found transition occurs via formation massless Dirac points wind entire Brillouin zone. We argue this unconventional characteristic feature 2DSWI, manifesting as wall states. Using first-principles calculations, find suggested 2DSWI should be realized in 11 known materials, such ${\mathrm{Zn}}_{2}{(\mathrm{P}{\mathrm{S}}_{3})}_{3}$. This insight from our work could help efforts solid-state systems.