Exceptional topology of non-Hermitian systems

By E. Bergholtz, J. C. Budich, Flore K. Kunst. Reviews of Modern Physics, 2019

963 citations recorded by the source corpus.

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed. In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, leads to phenomena drastically distinct from the familiar Hermitian realm is discussed. An immediate consequence is the ubiquitous occurrence of nodal NH topological phases with concomitant open Fermi-Seifert surfaces, where conventional band-touching points are replaced by the aforementioned exceptional degeneracies. Furthermore, new notions of gapped phases including topological phases in single-band systems are detailed, and the manner in which a given physical context may affect the symmetry-based topological classification is clarified. A unique property of NH systems with relevance beyond the field of topological phases consists of the anomalous relation between bulk and boundary physics, stemming from the striking sensitivity of NH matrices to boundary conditions. Unifying several complementary insights recently reported in this context, a picture of intriguing phenomena such as the NH bulk-boundary correspondence and the NH skin effect is put together. Finally, applications of NH topology in both classical systems including optical setups with gain and loss, electric circuits, and mechanical systems and genuine quantum systems such as electronic transport settings at material junctions and dissipative cold-atom setups are reviewed.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/c0787e8f1b73d13cea6fc2dffe4f2566106fae71

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In Atomic and Molecular Physics, and Optics

1. K. Kawabata
2. Masatoshi Sato
3. Ken Shiozaki
4. N. Okuma
5. Chen Fang
6. V. Vitelli
7. Kun Ding
8. Guancong Ma

Citations in the corpus

• Higher-order non-Hermitian skin effect (2020, background): “Topological phases and their boundary physics are enriched also by non-Hermiticity [29, 30].”
• Non-Hermitian topology and exceptional-point geometries (2022, background): “(15) This phase factor is the gauge-invariant multi-band Berry phase(48).”
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class (2020, methodology): “To understand the role of topology in non-Hermitian systems, topological characterization of non-Hermitian systems [14, 15] has recently been developed both in theory [16–58] and experiments [59–70].”
• Topological active matter (2020, background): “Active matter shares striking similarities with other kinds of drivendissipative systems [38, 39] ranging from optics [40] to open quantum systems [41–45], that are however outside the scope of this review.”