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  • Letter
  • Open Access

PT-symmetric non-Hermitian Hopf metal

Seik Pak1, Cheol Hun Yeom1,2, Sonu Verma3,*, and Moon Jip Park1,†

  • 1Department of Physics, Hanyang University, Seoul 04763, Republic of Korea
  • 2Department of Physics, Konkuk University, Seoul 05029, Republic of Korea
  • 3Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Korea

  • *sonu.vermaiitk@gmail.com
  • †moonjippark@hanyang.ac.kr
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Phys. Rev. Research 6, L012053 – Published 8 March, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L012053

Abstract

The Hopf insulator is a representative class of three-dimensional topological insulators beyond the standard topological classification methods based on K theory. In this Letter, we describe the metallic counterpart of the Hopf insulator in non-Hermitian systems. While the Hopf invariant is not a stable topological index due to the additional non-Hermitian degree of freedom, we show that the PT symmetry stabilizes the Hopf invariant even in the presence of the non-Hermiticity. In sharp contrast to the Hopf insulator phase in the Hermitian counterpart, we describe an interesting result that the non-Hermitian Hopf bundle exhibits topologically protected non-Hermitian degeneracy, characterized by the two-dimensional surface of exceptional points. Despite the non-Hermiticity, the Hopf metal has the quantized Zak phase, which results in bulk-boundary correspondence by showing drumheadlike surface states at the boundary. Finally, we show that, by breaking PT symmetry, the nodal surface deforms into knotted exceptional lines. Our description of the Hopf metal phase confirms the existence of the non-Hermitian topological phase outside the framework of the standard topological classifications.

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Phys. Rev. Research 6, L012053– Published 8 March, 2024
  • Received 3 November 2023
  • Revised 5 February 2024
  • Accepted 13 February 2024
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