Topological States in Generalized Electric Quadrupole Insulators

TL;DR

This paper explores how symmetry breaking affects topological quadrupole insulators, revealing conditions under which their topological properties are preserved or destroyed, and demonstrating robustness against certain disorders.

Contribution

It generalizes the existing model of electric quadrupole insulators to include symmetry-breaking terms, analyzing their impact on topological phases and corner modes.

Findings

Chiral symmetry breaking induces an indirect gap that hides corner modes.

Quadrupole moments can remain quantized without mirror symmetries.

Topological quadrupole phase is robust against specific disorder types.

Abstract

The modern theory of electric polarization has recently been extended to higher multipole moments, such as quadrupole and octupole moments. The higher electric multipole insulators are essentially topological crystalline phases protected by underlying crystalline symmetries. Henceforth, it is natural to ask what are the consequences of symmetry breaking in these higher multipole insulators. In this work, we investigate topological phases and the consequences of symmetry breaking in generalized electric quadrupole insulators. Explicitly, we generalize the Benalcazar-Bernevig-Hughes model by adding specific terms in order to break the crystalline and non-spatial symmetries. Our results show that chiral symmetry breaking induces an indirect gap phase which hides corner modes in bulk bands, ruining the topological quadrupole phase. We also demonstrate that quadrupole moments can remain quantized even when mirror symmetries are absent in a generalized model. Furthermore, it is shown that topological quadrupole phase is robust against a unique type of disorder presented in the system.