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

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