Octupole topological insulating phase protected by a three-dimensional momentum-space nonsymmorphic group

Area of Science:

• Condensed Matter Physics
• Quantum Materials
• Topology in Physics

Background:

• Topological insulators (TIs) are materials exhibiting unique electronic properties.
• Higher-order TIs, like quadrupole and octupole phases, extend topological concepts.
• Conventional TIs often rely on toroidal topology within the Brillouin zone.

Purpose of the Study:

• To discover and characterize a novel octupole topological insulating phase.
• To explore topological phases protected by 3D momentum-space nonsymmorphic groups.
• To investigate topological phenomena within the Brillouin 3D real projective space ([Formula: see text]).

Main Methods:

• Theoretical proposal of a novel octupole TI model and its topological invariant.
• Experimental realization of the insulator using a topological circuit framework.
• Characterization of the octupole phase via localized impedance peaks in the circuit.

Main Results:

• Discovery of a new octupole topological insulating phase protected by a 3D nonsymmorphic group.
• Experimental validation of the octupole phase in a topological circuit.
• Demonstration of a 3D circuit exhibiting both intrinsic and extrinsic topological phases.

Conclusions:

• The findings expand the understanding of topological insulators and their protection mechanisms.
• This work provides insights into band theory within the Brillouin [Formula: see text] space manifold.
• The developed topological circuit serves as a pioneering platform for studying complex topological phases.