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.
Highlights
An Alice string [1,2] is a topological defect with a very peculiar feature
We find that the Alice string phenomenon in non-Hermitian systems is manifested by nontrivial braiding of band nodes in momentum space
We have shown that band nodes with a Chern number braid nontrivially around exceptional lines in non-Hermitian systems, and that this interplay is naturally explained as an Alice string effect
Summary
An Alice string [1,2] 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. We find that the Alice string phenomenon in non-Hermitian systems is manifested by nontrivial braiding of band nodes in momentum space. The exceptional ring is further stabilized by an additional Z-valued winding number (defined on loops) [56] These two invariants correspond to the line-gap vs the point-gap topological classification of Ref. We rederive these topological charges from homotopy theory, and we show that they interact nontrivially, with the exceptional line playing the role of an Alice string: The Chern number of an exceptional ring flips sign when the ring is braided around another exceptional line. This property makes it impossible to define the Chern number globally These results open a viewpoint on the nonperturbative aspect of band topology in non-Hermitian systems. Note that throughout the paper by closing the energy gap we mean the formation of a band degeneracy, i.e., a situation where two complex band energies agree both in their real and in their imaginary parts
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