Abstract
Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- (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 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.
| Original language | English (US) |
|---|---|
| Article number | 550 |
| Journal | Nature communications |
| Volume | 15 |
| Issue number | 1 |
| Early online date | Jan 16 2024 |
| DOIs | |
| State | Published - Dec 2024 |
ASJC Scopus subject areas
- General Chemistry
- General Biochemistry, Genetics and Molecular Biology
- General Physics and Astronomy
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- 10.1038/s41467-024-44762-wLicense: CC BY
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In: Nature communications, Vol. 15, No. 1, 550, 12.2024.
Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Spin-resolved topology and partial axion angles in three-dimensional insulators
AU - Lin, Kuan Sen
AU - Palumbo, Giandomenico
AU - Guo, Zhaopeng
AU - Hwang, Yoonseok
AU - Blackburn, Jeremy
AU - Shoemaker, Daniel P.
AU - Mahmood, Fahad
AU - Wang, Zhijun
AU - Fiete, Gregory A.
AU - Wieder, Benjamin J.
AU - Bradlyn, Barry
N1 - We thank Andrey Gromov and Inti Sodemann for insightful discussions during the early stages of this study. We further acknowledge helpful discussions with Frank Schindler, Senthil Todadri, and Fan Zhang. Concurrent with the preparation of this work, a bulk spin-magnetoelectric response and anomalous surface halves of 2D TI states were detected in helical HOTIs in ref. through numerical studies of the charge and spin bound to threaded magnetic flux. During the preparation of this work, spin-resolved topology was also explored in 2D antimonene and bismuthene. Additionally, during the preparation of this work, a semiclassical treatment of a spinor-axion response was explored in relation to HOTIs in ref. . After the initial submission of this work, nontrivial (pseudo)spin-resolved partial axion angles were also identified in magnetic helical TCIs in ref. by implementing the method proposed in the present work. Lastly, after the submission of this work, the spin texture of α-BiBr was measured through spin-ARPES experiments, and showed close agreement with the DFT-based spin gap calculations performed in this work. The numerical calculations performed for and experimental proposals introduced in this work were supported by the Center for Quantum Sensing and Quantum Materials, an Energy Frontier Research Center funded by the U. S. Department of Energy, Office of Science, Basic Energy Sciences under Award DE-SC0021238. The analytical calculations performed by K.-S. L. and B. B. were additionally supported by the Alfred P. Sloan foundation and the National Science Foundation under Grant DMR-1945058. K.-S. L. also acknowledges the Graduate Fellowship Program at the Kavli Institute for Theoretical Physics, University of California, Santa Barbara, supported in part by the National Science Foundation under Grant No. NSF PHY-1748958 and NSF PHY-2309135, the Heising-Simons Foundation, and the Simons Foundation (216179, LB), during which this work was finalized. The work of Y. H. on the electromagnetic response of HOTI phases was supported by the Air Force Office of Scientific Research under award number FA9550-21-1-0131. Y. H. received additional support from the US Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) Grant N00014-20-1-2325 on Robust Photonic Materials with High-Order Topological Protection. This work made use of the Illinois Campus Cluster, a computing resource that is operated by the Illinois Campus Cluster Program (ICCP) in conjunction with the National Center for Supercomputing Applications (NCSA) and which is supported by funds from the University of Illinois at Urbana-Champaign. J. B. was supported through the National Science Foundation under Grant IIS-2046590 and provided additional computing resources via iDRAMA.cloud, funded by the National Science Foundation under Grant CNS-2247867. Z. G. and Z. W. were supported by the National Natural Science Foundation of China (Grants No. 11974395, No. 12188101), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB33000000), the China Postdoctoral Science Foundation funded project (Grant No. 2021M703461), and the Center for Materials Genome. B. J. W. acknowledges support from the European Union’s Horizon Europe research and innovation program (ERC-StG-101117835-TopoRosetta). G. A. F. and B. J. W. were additionally supported by the Department of Energy (BES) Award No. DE-SC0022168 and the National Science Foundation Grant No. DMR-2114825. B. J. W. further acknowledges the Laboratoire de Physique des Solides, Orsay for hosting during some stages of this work. , We thank Andrey Gromov and Inti Sodemann for insightful discussions during the early stages of this study. We further acknowledge helpful discussions with Frank Schindler, Senthil Todadri, and Fan Zhang. Concurrent with the preparation of this work, a bulk spin-magnetoelectric response and anomalous surface halves of 2D TI states were detected in helical HOTIs in ref.24through numerical studies of the charge and spin bound to threaded magnetic flux. During the preparation of this work, spin-resolved topology was also explored in 2D antimonene and bismuthene102 ,103. Additionally, during the preparation of this work, a semiclassical treatment of a spinor-axion response was explored in relation to HOTIs in ref.104. After the initial submission of this work, nontrivial (pseudo)spin-resolved partial axion angles were also identified in magnetic helical TCIs in ref.105by implementing the method proposed in the present work. Lastly, after the submission of this work, the spin texture of α -BiBr was measured through spin-ARPES experiments106, and showed close agreement with the DFT-based spin gap calculations performed in this work. The numerical calculations performed for and experimental proposals introduced in this work were supported by the Center for Quantum Sensing and Quantum Materials, an Energy Frontier Research Center funded by the U. S. Department of Energy, Office of Science, Basic Energy Sciences under Award DE-SC0021238. The analytical calculations performed by K.-S. L. and B. B. were additionally supported by the Alfred P. Sloan foundation and the National Science Foundation under Grant DMR-1945058. K.-S. L. also acknowledges the Graduate Fellowship Program at the Kavli Institute for Theoretical Physics, University of California, Santa Barbara, supported in part by the National Science Foundation under Grant No. NSF PHY-1748958 and NSF PHY-2309135, the Heising-Simons Foundation, and the Simons Foundation (216179, LB), during which this work was finalized. The work of Y. H. on the electromagnetic response of HOTI phases was supported by the Air Force Office of Scientific Research under award number FA9550-21-1-0131. Y. H. received additional support from the US Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) Grant N00014-20-1-2325 on Robust Photonic Materials with High-Order Topological Protection. This work made use of the Illinois Campus Cluster, a computing resource that is operated by the Illinois Campus Cluster Program (ICCP) in conjunction with the National Center for Supercomputing Applications (NCSA) and which is supported by funds from the University of Illinois at Urbana-Champaign. J. B. was supported through the National Science Foundation under Grant IIS-2046590 and provided additional computing resources via iDRAMA.cloud, funded by the National Science Foundation under Grant CNS-2247867. Z. G. and Z. W. were supported by the National Natural Science Foundation of China (Grants No. 11974395, No. 12188101), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB33000000), the China Postdoctoral Science Foundation funded project (Grant No. 2021M703461), and the Center for Materials Genome. B. J. W. acknowledges support from the European Union’s Horizon Europe research and innovation program (ERC-StG-101117835-TopoRosetta). G. A. F. and B. J. W. were additionally supported by the Department of Energy (BES) Award No. DE-SC0022168 and the National Science Foundation Grant No. DMR-2114825. B. J. W. further acknowledges the Laboratoire de Physique des Solides, Orsay for hosting during some stages of this work.
PY - 2024/12
Y1 - 2024/12
N2 - Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- (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 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.
AB - Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- (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 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.
UR - http://www.scopus.com/inward/record.url?scp=85182433082&partnerID=8YFLogxK
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U2 - 10.1038/s41467-024-44762-w
DO - 10.1038/s41467-024-44762-w
M3 - Article
C2 - 38228584
AN - SCOPUS:85182433082
SN - 2041-1723
VL - 15
JO - Nature communications
JF - Nature communications
IS - 1
M1 - 550
ER -