PT-symmetric Non-Hermitian Hopf Metal

• URL: http://arxiv.org/abs/2311.02155v1
• Date: Fri, 3 Nov 2023 18:00:01 GMT
• Title: PT-symmetric Non-Hermitian Hopf Metal
• Authors: Seik Pak and Cheol Hun Yeom and Sonu Verma and Moon Jip Park
• Abstract summary: We discover the metallic counterpart of the Hopf insulator in the non-Hermitian systems. We show that the PT-symmetry stabilizes the Hopf invariant even in the presence of the non-Hermiticity. Our discovery 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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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 discover the metallic counterpart of the Hopf insulator in the 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 discover an interesting result that the non-Hermitian Hopf bundle exhibits the 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 drumhead-like surface states at the boundary. Finally, we show that, by breaking PT-symmetry, the nodal surface deforms into the knotted exceptional lines. Our discovery of the Hopf metal phase firstly confirms the existence of the non-Hermitian topological phase outside the framework of the standard topological classifications.

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