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Non-Hermitian systems and topology: A transfer-matrix perspective
Stockholm University, Faculty of Science, Department of Physics.
Number of Authors: 22019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 24, article id 245116Article in journal (Refereed) Published
Abstract [en]

Topological phases of Hermitian systems are known to exhibit intriguing properties such as the presence of robust boundary states and the famed bulk-boundary correspondence. These features can change drastically for their non-Hermitian generalizations, as exemplified by a general breakdown of bulk-boundary correspondence and a localization of all states at the boundary, termed the non-Hermitian skin effect. In this paper, we present a completely analytical unifying framework for studying these systems using generalized transfer matrices, a real-space approach suitable for systems with periodic as well as open boundary conditions. We show that various qualitative properties of these systems can be easily deduced from the transfer matrix. For instance, the connection between the breakdown of the conventional bulk-boundary correspondence and the existence of a non-Hermitian skin effect, previously observed numerically, is traced back to the transfer matrix having a determinant not equal to unity. The vanishing of this determinant signals real-space exceptional points, whose order scales with the system size. We also derive previously proposed topological invariants such as the biorthogonal polarization and the Chern number computed on a complexified Brillouin zone. Finally, we define an invariant for and thereby clarify the meaning of topologically protected boundary modes for non-Hermitian systems.

Place, publisher, year, edition, pages
2019. Vol. 99, no 24, article id 245116
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-170798DOI: 10.1103/PhysRevB.99.245116ISI: 000470840800003OAI: oai:DiVA.org:su-170798DiVA, id: diva2:1338352
Available from: 2019-07-22 Created: 2019-07-22 Last updated: 2019-07-22Bibliographically approved

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