Topological Protection by Local Support Symmetry and Destructive Interference

TL;DR

This paper introduces the concept of local support symmetries that can protect topological features in materials, even when global symmetries are broken, expanding the understanding of symmetry protection in topological phases.

Contribution

It establishes a unified framework for topological protection by local support symmetries and demonstrates their role through models and a real material example.

Findings

Local support symmetries can protect topological features.

Destructive interference of Bloch waves is crucial for protection.

Realistic material realization in fluorinated biphenylene network.

Abstract

Conventionally, symmetry-protected topological phases and band crossings are protected by global symmetries acting on the entire system. Here, we show that symmetries preserved only on a partial region of a system, termed local support symmetries, can protect topological features of the full system, even in the presence of symmetry-breaking couplings. We establish a unified framework by deriving explicit conditions for such protection in both insulating and metallic phases and show that destructive interference of Bloch wave functions plays a key role. Using representative tight-binding models, we demonstrate band crossings and topological bands protected by local support crystalline and time-reversal symmetries, and further present a realistic material realization in a fluorinated biphenylene network, where a band crossing is protected by a local support C$_2$ symmetry.