Octupole topological insulating phase protected by a three-dimensional momentum-space nonsymmorphic group
S. L. Qiu, Jinbing Hu, Yi Yang, Ce Shang, Shuo Liu, Tie Jun Cui
Abstract
Recent advancements in quantum polarization theory have propelled the exploration of topological insulators (TIs) into the realm of higher-order systems, leading to the study of the celebrated two-dimensional (2D) quadrupole and 3D octupole TIs. Traditionally, these topological phases have been associated with the toroidal topology of the conventional Brillouin zone. This paper reports the discovery of a novel octupole topological insulating phase protected by a 3D momentum-space nonsymmorphic group emerging within the framework of the Brillouin 3D real projective space ([Formula: see text]). We theoretically propose the model and its corresponding topological invariant, experimentally construct this insulator within a topological circuit framework and capture the octupole insulating phase as a localized impedance peak at the circuit's corner. Furthermore, our [Formula: see text] circuit stands out as a pioneering 3D model to simultaneously exhibit both intrinsic, termination-independent symmetry-protected topological phases and extrinsic, termination-dependent surface-obstructed topological phases within the symmetry-protected topological phases. Our results broaden the topological landscape and provide insights into the band theory within the manifold of the Brillouin [Formula: see text] space.