Higher-order topological insulators protected by inversion and rotoinversion symmetries

TL;DR

This paper proves the existence of higher-order topological insulators protected by inversion and rotoinversion symmetries, characterized by a $Z_2 invariant, which predicts protected hinge states in certain crystalline materials.

Contribution

It introduces a topological invariant based on symmetric hybrid Wannier functions to identify higher-order topological insulators with specific crystalline symmetries.

Findings

Higher-order topological insulators exist in fourfold rotoinversion invariant crystals.

Inversion-symmetric systems can host these states with or without additional symmetries.

Protected chiral hinge modes are predicted based on the topological invariant.

Abstract

We prove the existence of higher-order topological insulators in: {\it i}) fourfold rotoinversion invariant bulk crystals, and {\it ii}) inversion-symmetric systems with or without an additional three-fold rotation symmetry. These states of matter are characterized by a non-trivial $\mathbb{Z}_2$ topological invariant, which we define in terms of symmetric hybrid Wannier functions of the filled bands, and can be readily calculated from the knowledge of the crystalline symmetry labels of the bulk band structure. The topological invariant determines the generic presence or absence of protected chiral gapless one-dimensional modes localized at the hinges between conventional gapped surfaces.