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

doi:10.1038/s41467-024-44762-w

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

Nat Commun. 2024 Jan 16;15(1):550. doi: 10.1038/s41467-024-44762-w.

Authors

Kuan-Sen Lin^{1

2}, Giandomenico Palumbo³, Zhaopeng Guo^{4

5}, Yoonseok Hwang⁶, Jeremy Blackburn⁷, Daniel P Shoemaker^{8

9}, Fahad Mahmood^{9

10}, Zhijun Wang^{4

5}, Gregory A Fiete^{11

12}, Benjamin J Wieder^{13

14

15}, Barry Bradlyn¹⁶

Affiliations

¹ Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA. kuansen2@illinois.edu.
² Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106, USA. kuansen2@illinois.edu.
³ School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin, 4, Ireland.
⁴ Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, China.
⁵ University of Chinese Academy of Sciences, 100049, Beijing, China.
⁶ Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA.
⁷ Department of Computer Science, State University of New York at Binghamton, Binghamton, NY, 13902, USA.
⁸ Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA.
⁹ Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA.
¹⁰ Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA.
¹¹ Department of Physics, Northeastern University, Boston, MA, 02115, USA. g.fiete@northeastern.edu.
¹² Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA. g.fiete@northeastern.edu.
¹³ Department of Physics, Northeastern University, Boston, MA, 02115, USA. benjamin.wieder@ipht.fr.
¹⁴ Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA. benjamin.wieder@ipht.fr.
¹⁵ Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, F-91191, Gif-sur-Yvette, France. benjamin.wieder@ipht.fr.
¹⁶ Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA. bbradlyn@illinois.edu.

Abstract

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ([Formula: see text]-) 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 [Formula: see text]-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.

Abstract

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