Topological protection by local support symmetry and destructive interference

TL;DR

The paper shows that topological features can be protected by symmetries that exist only in part of a system, not requiring full system-wide symmetry.

Contribution

The novel contribution is the concept of local support symmetries that can protect topological phases even when global symmetry is broken.

Findings

Local support symmetries can protect topological features despite symmetry-breaking couplings.

Destructive interference of Bloch wave functions is crucial for this protection.

A fluorinated biphenylene network demonstrates a material realization of this concept.

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 C2 symmetry.

Symmetry-protected topological phases are conventionally considered to be protected by global symmetries. Here, the authors demonstrate that topological protections can persist even when symmetries are preserved only within a partial region of the system, which they term local support symmetries.

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