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  • Letter
  • Open Access

Generalization of the nested Wilson loop formalism in topological Dirac semimetals with higher-order Fermi arcs

Hui Zeng1, Wenhui Duan1,2,3,4, and Huaqing Huang4,5,6,*

  • 1State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
  • 2Institute for Advanced Study, Tsinghua University, Beijing 100084, China
  • 3Frontier Science Center for Quantum Information, Beijing 100084, China
  • 4Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
  • 5School of Physics, Peking University, Beijing 100871, China
  • 6Center for High Energy Physics, Peking University, Beijing 100871, China

  • *Corresponding author: huaqing.huang@pku.edu.cn
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Phys. Rev. Research 5, L042003 – Published 3 October, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L042003

Abstract

We generalize the nested Wilson loop formalism, which has been playing an important role in the study of topological quadrupole insulators, to two-dimensional (2D) and 3D nonsymmorphic materials with higher-order topology. In particular, certain 3D Dirac semimetals exhibit 1D higher-order Fermi arc (HOFA) states localizing on hinges where two surfaces meet and connecting the projections of the bulk Dirac points. We discover that the generalized nested Berry phase (gNBP) derived from this formalism is the bulk topological indicator determining the existence or absence of HOFAs, revealing a direct bulk-hinge correspondence in 3D Dirac semimetals. Finally, we study the Dirac semimetals NaCuSe and KMgBi based on first-principles calculations and explicitly show that the change in the gNBP adjacent to the Dirac point corresponds to the termination of HOFAs at the projection of Dirac points on the hinge. Our findings not only improve the understanding of the bulk-hinge correspondence in topological Dirac semimetals but also provide a general formalism for studying the higher-order topology in nonsymmorphic systems.

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Outline

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Phys. Rev. Research 5, L042003– Published 3 October, 2023
  • Received 29 May 2023
  • Accepted 25 August 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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