Periodic table for topological bands with non-Hermitian symmetries

By Hengyun Zhou, Jong Yeon Lee. Physical review B, 2018

310 citations recorded by the source corpus.

Classifications of symmetry-protected topological (SPT) phases provide a framework to systematically understand the physical properties and potential applications of topological systems. While such classifications have been widely explored in the context of Hermitian systems, a complete understanding of the roles of more general non-Hermitian symmetries and their associated classification is still lacking. Here, we derive a periodic table for non-interacting SPTs with general non-Hermitian symmetries. Our analysis reveals novel non-Hermitian topological classes, while also naturally incorporating the entire classification of Hermitian systems as a special case of our scheme. Building on top of these results, we derive two independent generalizations of Kramers' theorem to the non-Hermitian setting, which constrain the spectra of the system and lead to new topological invariants. To elucidate the physics behind the periodic table, we provide explicit examples of novel non-Hermitian topological invariants, focusing on the symmetry classes in zero, one and two dimensions with new topological classifications (e.g. $\mathbb{Z}$ in 0D, $\mathbb{Z}_2$ in 1D, 2D). These results thus provide a framework for the design and engineering of non-Hermitian symmetry-protected topological systems.

Subfields: Atomic and Molecular Physics, and Optics, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/881bae981a4dd97d79c285195717e0c5943237fe

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In Atomic and Molecular Physics, and Optics

In Organic Chemistry

Citations in the corpus

Roadmap on topological photonics (2022, unknown): “10 3125 [19] Ozawa T, Price HM, Goldman N, Zilberberg O and Carusotto I 2016 Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics Phys.”
Symmetry and Topology in Non-Hermitian Physics (2018, methodology): “— After this work had been submitted, a related work by Zhou and Lee appeared [231].”