Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators

Abstract

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($\mathcal{T}$-) invariant (helical) 3D TCI$\unicode{x2014}$termed higher-order TCIs (HOTIs)$\unicode{x2014}$the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), "spin-Weyl" semimetals, and $\mathcal{T}$-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that $\beta$-MoTe${}_2$ realizes a spin-Weyl state and that $\alpha$-BiBr hosts both 3D QSHI and T-DAXI regimes.

Final version: 22+146 pages, 8+44 figures. Nested and spin-resolved Wilson loop code with example scripts and documentation freely available at https://github.com/kuansenlin/nested_and_spin_resolved_Wilson_loop

References in corpus (24)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Crystalline Insulators
• Dissipationless Quantum Spin Current at Room Temperature
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• On A Proper Definition of Spin Current
• Robustness of the Spin-Chern number
• Layer Hall effect in a 2D topological Axion antiferromagnet
• Angle-resolved photoemission spectroscopy and its application to topological materials
• Towards a microscopic theory of toroidal moments in bulk periodic crystals
• Purely rotational symmetry-protected topological crystalline insulator $\alpha$-Bi4Br4
• Surface theorem for the Chern-Simons axion coupling
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Measurement of spin Chern numbers in quantum simulated topological insulators
• Topological electronic structure and spin texture of quasi-one-dimensional higher-order topological insulator Bi4Br4
• Magnetic band representations, Fu-Kane-like symmetry indicators and magnetic topological materials
• Competing Adiabatic Thouless Pumps in Enlarged Parameter Spaces
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators

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• Coincidence detection techniques for direct measurement of many-body correlations in strongly correlated electron systems
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