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 () and Barry Bradlyn ()
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Kuan-Sen Lin: University of Illinois at Urbana-Champaign
Giandomenico Palumbo: Dublin Institute for Advanced Studies
Zhaopeng Guo: Chinese Academy of Sciences
Yoonseok Hwang: University of Illinois at Urbana-Champaign
Jeremy Blackburn: State University of New York at Binghamton
Daniel P. Shoemaker: University of Illinois at Urbana-Champaign
Fahad Mahmood: University of Illinois at Urbana-Champaign
Zhijun Wang: Chinese Academy of Sciences
Gregory A. Fiete: Northeastern University
Benjamin J. Wieder: Northeastern University
Barry Bradlyn: University of Illinois at Urbana-Champaign

Nature Communications, 2024, vol. 15, issue 1, 1-17

Abstract: Abstract Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ( $${{{{{{{\mathcal{T}}}}}}}}$$ T -) invariant (helical) 3D TCIs—termed higher-order TCIs (HOTIs)—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 $${{{{{{{\mathcal{T}}}}}}}}$$ 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 β-MoTe2 realizes a spin-Weyl state and that α-BiBr hosts both 3D QSHI and T-DAXI regimes.

Date: 2024
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DOI: 10.1038/s41467-024-44762-w

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