Alice string in Non-Hermitian Systems

Abstract

Alice string is a topological defect with a very peculiar feature. When a defect with a monopole charge encircles an Alice string, the monopole charge changes sign. In this work, we generalize this notion to momentum space of periodic media with loss and gain. In particular, we find that the generic band-structure node for a three-dimensional non-Hermitian crystalline system acts as an Alice string, which can flip the Chern number charge carried by Weyl points and by exceptional-line rings. We discuss signatures of this topological structure for a lattice model with one tuning parameter, including non-trivial braiding of bulk band nodes, and the spectroscopic features of both the bulk and the surface states. We also explore how an Alice string affects the validity of the Nielsen-Ninomiya theorem, and present a mathematical description of the braiding phenomenon.

13 pages, 6 figures, published version

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• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Geometric approach to fragile topology beyond symmetry indicators
• Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems
• Topological classification of non-Hermitian bands
• Eigenvalue topology of non-Hermitian band structures in two and three dimensions
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Weyl points on non-orientable manifolds
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Exceptional topology on nonorientable manifolds