Chern dartboard insulator: sub-Brillouin zone topology and skyrmion multipoles

TL;DR

This paper introduces Chern dartboard insulators with sub-Brillouin zone topology, revealing new surface states and pseudospin textures, and demonstrates their realization in photonic crystals.

Contribution

It defines the reduced Chern number in subregions of the Brillouin zone and constructs a family of insulators with unique topological properties protected by mirror symmetries.

Findings

Presence of exotic gapless edge states like Möbius fermions

Observation of (anti)skyrmion pseudospin textures in the sBZ

Realization of CDIs in photonic crystal systems

Abstract

Topology plays a crucial role in many physical systems, leading to interesting states at the surface. The paradigmatic example is the Chern number defined in the Brillouin zone that leads to the robust gapless edge states. Here we introduce the reduced Chern number, defined in subregions of the Brillouin zone (BZ), and construct a family of Chern dartboard insulators (CDIs) with quantized reduced Chern numbers in the sub-BZ (sBZ) but with trivial bulk topology. CDIs are protected by mirror symmetries and exhibit distinct pseudospin textures, including (anti)skyrmions, inside the sBZ. These CDIs host exotic gapless edge states, such as M\"{o}bius fermions and midgap corner states, and can be realized in photonic crystals. Our work opens up new possibilities for exploring sBZ topology and nontrivial surface responses in topological systems.