Two-dimensional weak-type topological insulators in inversion symmetric crystals

TL;DR

This paper introduces a new class of two-dimensional topological insulators, called 2D Stiefel-Whitney insulators, protected by inversion and time-reversal symmetries, with potential applications in realizing topological flat bands.

Contribution

It proposes a novel 2D topological insulator model based on the 2D SSH chain and develops weak $oldsymbol{ ext{Z}_2}$ topological indices using Stiefel-Whitney numbers, expanding understanding of topological phase transitions.

Findings

Identification of 2DSWI protected by inversion and time-reversal symmetries

Topological phase transitions via Dirac points in the Brillouin zone

Potential for realizing topological flat bands in solid-state systems

Abstract

The Su-Schrieffer-Heeger (SSH) chain is an one-dimensional lattice that comprises two dimerized sublattices. Recently, Zhu, Prodan, and Ahn (ZPA) proposed in [L. Zhu, E. Prodan, and K. H. Ahn, Phys. Rev. B \textbf{99}, 041117 (2019)] that one-dimensional flat bands can occur at topological domain walls of a two-dimensional array of the SSH chains. Here, we newly suggest a two-dimensional topological insulator that is protected by inversion and time-reversal symmetries without spin-orbit coupling. It is shown that the two-dimensional SSH chains realize the proposed topological insulator. Utilizing the first Stiefel-Whitney numbers, a weak type of $\mathbb{Z}_2$ topological indices are developed, which identify the proposed topological insulator, dubbed a two-dimensional Stiefel-Whitney insulator (2DSWI). The ZPA model is employed to study the topological phase diagrams and topological phase transitions. It is found that the phase transition occurs via the formation of the massless Dirac points that wind the entire Brillouin zone. We argue that this unconventional topological phase transition is a characteristic feature of the 2DSWI, manifested as the one-dimensional domain wall states. The new insight from our work could help efforts to realize topological flat bands in solid-state systems.