Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of...

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Published inNature communications Vol. 11; no. 1; pp. 627 - 13
Main Authors Wieder, Benjamin J., Wang, Zhijun, Cano, Jennifer, Dai, Xi, Schoop, Leslie M., Bradlyn, Barry, Bernevig, B. Andrei
Format Journal Article
LanguageEnglish
Published London Nature Publishing Group UK 31.01.2020
Nature Publishing Group
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639/301/119/995
639/766/119/2792/4128
Condensed matter physics
Eigenvalues
Fermions
Humanities and Social Sciences
Metalloids
multidisciplinary
Physics
Quadrupoles
Questions
Science
Science & Technology - Other Topics
Science (multidisciplinary)
Solid state
Symmetry
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Abstract Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s – d -hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- ( α ) and intermediate-temperature ( α ″ ) phases of Cd 3 As 2 , KMgBi, and rutile-structure ( β ′ -) PtO 2 . The existence of a topological bulk-boundary correspondence for Dirac semimetals has remained an open question. Here, Wieder et al. predict one-dimensional hinge states originating from bulk three-dimensional Dirac points in solid-state Dirac semimetals, revealing condensed matter Dirac fermions to be higher-order topological.
AbstractList Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s-d-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw-Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- (α) and intermediate-temperature (α″) phases of Cd3As2, KMgBi, and rutile-structure ([Formula: see text]-) PtO2.Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s-d-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw-Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- (α) and intermediate-temperature (α″) phases of Cd3As2, KMgBi, and rutile-structure ([Formula: see text]-) PtO2.
Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s – d -hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- ( α ) and intermediate-temperature ( α ″ ) phases of Cd 3 As 2 , KMgBi, and rutile-structure ( $$ \beta ^{\prime} $$ β ′ -) PtO 2 .
Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s-d-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw-Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- (α) and intermediate-temperature (α″) phases of Cd As , KMgBi, and rutile-structure ([Formula: see text]-) PtO .
Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s – d -hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- ( α ) and intermediate-temperature ( α ″ ) phases of Cd 3 As 2 , KMgBi, and rutile-structure ( β ′ -) PtO 2 . The existence of a topological bulk-boundary correspondence for Dirac semimetals has remained an open question. Here, Wieder et al. predict one-dimensional hinge states originating from bulk three-dimensional Dirac points in solid-state Dirac semimetals, revealing condensed matter Dirac fermions to be higher-order topological.
Abstract Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s – d -hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- ( α ) and intermediate-temperature ( α ″ ) phases of Cd 3 As 2 , KMgBi, and rutile-structure ( $$ \beta ^{\prime} $$ β ′ -) PtO 2 .
Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s–d-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- (α) and intermediate-temperature (α″) phases of Cd3As2, KMgBi, and rutile-structure (β′-) PtO2.The existence of a topological bulk-boundary correspondence for Dirac semimetals has remained an open question. Here, Wieder et al. predict one-dimensional hinge states originating from bulk three-dimensional Dirac points in solid-state Dirac semimetals, revealing condensed matter Dirac fermions to be higher-order topological.
The existence of a topological bulk-boundary correspondence for Dirac semimetals has remained an open question. Here, Wieder et al. predict one-dimensional hinge states originating from bulk three-dimensional Dirac points in solid-state Dirac semimetals, revealing condensed matter Dirac fermions to be higher-order topological.
Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s – d -hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- ( α ) and intermediate-temperature ( α ″ ) phases of Cd 3 As 2 , KMgBi, and rutile-structure ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \beta ^{\prime} $$\end{document} β ′ -) PtO 2 . The existence of a topological bulk-boundary correspondence for Dirac semimetals has remained an open question. Here, Wieder et al. predict one-dimensional hinge states originating from bulk three-dimensional Dirac points in solid-state Dirac semimetals, revealing condensed matter Dirac fermions to be higher-order topological.
ArticleNumber 627
Author Schoop, Leslie M.
Cano, Jennifer
Bradlyn, Barry
Bernevig, B. Andrei
Wieder, Benjamin J.
Wang, Zhijun
Dai, Xi
Author_xml – sequence: 1
  givenname: Benjamin J.
  orcidid: 0000-0003-2540-6202
  surname: Wieder
  fullname: Wieder, Benjamin J.
  email: bwieder@princeton.edu
  organization: Department of Physics, Princeton University
– sequence: 2
  givenname: Zhijun
  orcidid: 0000-0003-2169-8068
  surname: Wang
  fullname: Wang, Zhijun
  organization: Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, University of Chinese Academy of Sciences
– sequence: 3
  givenname: Jennifer
  orcidid: 0000-0003-1528-4344
  surname: Cano
  fullname: Cano, Jennifer
  organization: Department of Physics and Astronomy, Stony Brook University, Center for Computational Quantum Physics, The Flatiron Institute
– sequence: 4
  givenname: Xi
  surname: Dai
  fullname: Dai, Xi
  organization: Physics Department, Hong Kong University of Science and Technology
– sequence: 5
  givenname: Leslie M.
  orcidid: 0000-0003-3459-4241
  surname: Schoop
  fullname: Schoop, Leslie M.
  organization: Department of Chemistry, Princeton University
– sequence: 6
  givenname: Barry
  orcidid: 0000-0001-6327-1076
  surname: Bradlyn
  fullname: Bradlyn, Barry
  email: bbradlyn@illinois.edu
  organization: Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Donostia International Physics Center
– sequence: 7
  givenname: B. Andrei
  surname: Bernevig
  fullname: Bernevig, B. Andrei
  email: bernevig@princeton.edu
  organization: Department of Physics, Princeton University, Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, Max Planck Institute of Microstructure Physics
BackLink https://www.ncbi.nlm.nih.gov/pubmed/32005893$$D View this record in MEDLINE/PubMed
https://www.osti.gov/biblio/1619476$$D View this record in Osti.gov
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Snippet Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the...
Abstract Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological...
The existence of a topological bulk-boundary correspondence for Dirac semimetals has remained an open question. Here, Wieder et al. predict one-dimensional...
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SubjectTerms 639/301/119/995
639/766/119/2792/4128
Condensed matter physics
Eigenvalues
Fermions
Humanities and Social Sciences
Metalloids
multidisciplinary
Physics
Quadrupoles
Questions
Science
Science & Technology - Other Topics
Science (multidisciplinary)
Solid state
Symmetry
Topology
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Title Strong and fragile topological Dirac semimetals with higher-order Fermi arcs
URI https://link.springer.com/article/10.1038/s41467-020-14443-5
https://www.ncbi.nlm.nih.gov/pubmed/32005893
https://www.proquest.com/docview/2349174926
https://www.proquest.com/docview/2350093002
https://www.osti.gov/biblio/1619476
https://pubmed.ncbi.nlm.nih.gov/PMC6994491
https://doaj.org/article/005cb234a601446b90d6c3cda622d37e
Volume 11
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