Photonic obstructed atomic insulator

TL;DR

This paper demonstrates that in a 2D magnetic photonic obstructed atomic insulator, corner states are determined by Wyckoff positions and are independent of time-reversal symmetry, revealing real-space atomic arrangements' role in higher-order topology.

Contribution

It reveals the link between Wyckoff positions and corner states in magnetic photonic obstructed atomic insulators, highlighting the significance of real-space atomic distribution in higher-order topological phases.

Findings

Corner states depend on exposed Wyckoff positions.

Time-reversal symmetry is not essential for corner states.

Real-space atomic distribution influences higher-order topology.

Abstract

Topological quantum chemistry (TQC) classifies the topological phases by real-space invariants in which obstructed atomic insulators belong to the trivial case but sometimes show the feature of higher-order topological insulator. Here, for a two-dimensional magnetic photonic obstructed atomic insulator, we show that the emergence of corner states is associated with the Wyckoff positions. In such a square lattice with four +$M$ elements and four -$M$ elements, corner states appear when the superlattice exposes $2b$ Wyckoff positions. And the corner states will decrease when the number of exposed $2b$ Wyckoff positions decreases and disappears when $2b$ Wyckoff positions no longer stand at the edge. By arranging all the magnetic rods into one magnetization direction, we find that time-reversal symmetry is not important for corner states. Our finding indicates that the real-space distribution of atoms determines the feature of higher-order topological insulators for obstructed atomic insulators in TQC.