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arXiv · 2207.10099

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

Kuan-Sen Lin·Giandomenico Palumbo·Zhaopeng Guo·Yoonseok Hwang·Jeremy Blackburn·Daniel P. Shoemaker·Fahad Mahmood·Zhijun Wang·Gregory A. Fiete·Benjamin J. Wieder·Barry Bradlyn
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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.

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Kuan-Sen Lin, Giandomenico Palumbo, Zhaopeng Guo, Yoonseok Hwang, Jeremy Blackburn, Daniel P. Shoemaker, Fahad Mahmood, Zhijun Wang, Gregory A. Fiete, Benjamin J. Wieder, Barry Bradlyn. 2022-07-20. Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators. https://doi.org/10.1038/s41467-024-44762-w

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