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Universal higher-order bulk-boundary correspondence of triple nodal points


Lenggenhager, Patrick M; Liu, Xiaoxiong; Neupert, Titus; Bzdušek, Tomáš (2022). Universal higher-order bulk-boundary correspondence of triple nodal points. Physical review B, 106(8):085129.

Abstract

Triple nodal points are degeneracies of energy bands in momentum space at which three Hamiltonian eigenstates coalesce at a single eigenenergy. For spinless particles, the stability of a triple nodal point requires two ingredients: rotational symmetry of order three, four, or six; combined with mirror or space-time-inversion symmetry. However, despite ample studies of their classification, robust boundary signatures of triple nodal points have until now remained elusive. In this work, we first show that pairs of triple nodal points in semimetals and metals can be characterized by Stiefel-Whitney and Euler monopole invariants, of which the first one is known to facilitate higher-order topology. Motivated by this observation, we then combine symmetry indicators for corner charges and for the Stiefel-Whitney invariant in two dimensions with the classification of triple nodal points for spinless systems in three dimensions. The result is a complete higher-order bulk-boundary correspondence, where pairs of triple nodal points are characterized by fractional jumps of the hinge charge. We present minimal models of the various species of triple nodal points carrying higher-order topology, and illustrate the derived correspondence on Sc3AlC which becomes a higher-order triple-point metal in applied strain. The generalization to spinful systems, in particular to the WC-type triple-point material class, is briefly outlined.

Abstract

Triple nodal points are degeneracies of energy bands in momentum space at which three Hamiltonian eigenstates coalesce at a single eigenenergy. For spinless particles, the stability of a triple nodal point requires two ingredients: rotational symmetry of order three, four, or six; combined with mirror or space-time-inversion symmetry. However, despite ample studies of their classification, robust boundary signatures of triple nodal points have until now remained elusive. In this work, we first show that pairs of triple nodal points in semimetals and metals can be characterized by Stiefel-Whitney and Euler monopole invariants, of which the first one is known to facilitate higher-order topology. Motivated by this observation, we then combine symmetry indicators for corner charges and for the Stiefel-Whitney invariant in two dimensions with the classification of triple nodal points for spinless systems in three dimensions. The result is a complete higher-order bulk-boundary correspondence, where pairs of triple nodal points are characterized by fractional jumps of the hinge charge. We present minimal models of the various species of triple nodal points carrying higher-order topology, and illustrate the derived correspondence on Sc3AlC which becomes a higher-order triple-point metal in applied strain. The generalization to spinful systems, in particular to the WC-type triple-point material class, is briefly outlined.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Language:English
Date:18 August 2022
Deposited On:05 Sep 2022 15:05
Last Modified:27 Jun 2024 01:39
Publisher:American Physical Society
ISSN:2469-9950
OA Status:Green
Publisher DOI:https://doi.org/10.1103/physrevb.106.085129
Project Information:
  • : FunderSNSF
  • : Grant IDPZ00P2_185806
  • : Project TitleTopological band theory of driven and dissipative systems
  • : FunderEuropean Research Council
  • : Grant ID
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  • : FunderChina Scholarship Council
  • : Grant ID
  • : Project Title
  • : FunderNational Center of Competence in Research Materials’ Revolution: Computational Design and Discovery of Novel Materials
  • : Grant ID
  • : Project Title
  • Content: Published Version
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)