Spin-resolved topology and partial axion angles in three-dimensional insulators.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Materials

Background:

• Symmetry-protected topological crystalline insulators (TCIs) are typically identified by boundary states.
• Helical 3D TCIs (higher-order TCIs or HOTIs) can exhibit complex 1D hinge states.
• Characterizing bulk topological properties of spinful insulators is crucial.

Purpose of the Study:

• To develop novel tools for characterizing intrinsic bulk topological properties of spinful 3D insulators.
• To classify the distinct spin-resolved phases realized by helical HOTIs.
• To identify material candidates exhibiting these topological phases.

Main Methods:

• Introduction of nested spin-resolved Wilson loops.
• Development of layer construction techniques.
• Ab-initio calculations for material characterization.

Main Results:

• Identification of three distinct spin-resolved phases for helical HOTIs.
• Discovery of spin-Weyl semimetals and T-doubled axion insulator (T-DAXI) states.
• Robustness of these phases to bulk spin-orbital texture deformations.
• Observation of 3D quantum spin Hall insulators (QSHIs), spin-Weyl, and T-DAXI regimes in specific materials.

Conclusions:

• Helical HOTIs host diverse topological phases with unique bulk responses.
• The developed methods provide a robust framework for classifying these complex topological states.
• β-MoTe2 and α-BiBr are identified as promising materials realizing predicted topological phases.