A groundbreaking study led by researchers from Southeast University, the Chinese Academy of Sciences, the University of Hong Kong, and the University of Shanghai for Science and Technology, has unveiled a new class of topological insulator, the octupole topological insulating phase, which is protected by a three-dimensional momentum-space nonsymmorphic symmetry (k-NS) group. This breakthrough, published in National Science Review, offers a fresh perspective on the study of topological materials and significantly enhances the understanding of higher-order topological insulators.
In the study, the team presented a novel 3D higher-order topological insulator (HOTI) exhibiting an octupole insulating phase within the framework of the Brillouin 3D real projective space. The distinctive 3D Brillouin manifold is constructed by introducing k-NS symmetries in three directions, resulting in three pairs of twisted boundaries. These unconventional symmetries partition the 3D Brillouin zone (BZ) into 64 blocks, which are further grouped into eight categories. A reduced BZ can be defined from any eight uniquely grouped blocks that are enclosed, which inherits all the topological information from the original one.
The study also reveals that the HOTI demonstrates the coexistence of symmetry-protected topological phases (SPTPs), induced by bulk gap closures, and surface-obstructed topological phases (SOTPs), which are dependent on the boundary termination. This intrinsic and extrinsic HOTI feature was verified by numerically calculating the Wannier values and surface polarizations within the cylindrical geometry of the HOTI.
To further validate the octupole topological phase, the team constructed a topological circuit model and confirmed the presence of octupole topological states by measuring impedance spectra of the circuit. The impedance peak was localized at the circuit's corner, aligning with theoretical predictions of the topological properties.
"This work expands the topological landscape by considering more complex geometries and symmetries, thereby providing new opportunities for both theoretical investigations and practical applications in topological materials and circuits," said the researchers.
The findings not only broaden the comprehension of higher-order topological phases but also provide new insights into the band theory within the manifold of the Brillouin real projective space.
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Octupole topological insulating phase protected by three-dimensional momentum-space nonsymmorphic group
