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Non-Hermitian systems and topology: A transfer matrix perspective
Stockholm University, Faculty of Science, Department of Physics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Non-Hermitian topological systems are known to exhibit features strikingly different from their Hermitian counterparts. We study these systems using a generalized transfer matrix approach, which provides a unifying analytical framework for tight-binding models with periodic as well as open boundary conditions. This leads to an analytical and intuitive understanding of many of the unusual properties of non-Hermitian systems, such as the non-Hermitian skin effect, the breakdown of the conventional bulk-boundary correspondence, and the appearance of exceptional points with an order scaling with system size.

National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-166134OAI: oai:DiVA.org:su-166134DiVA, id: diva2:1289091
Available from: 2019-02-15 Created: 2019-02-15 Last updated: 2019-02-22
In thesis
1. Solvable Topological Boundaries
Open this publication in new window or tab >>Solvable Topological Boundaries
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The hallmark of topological phases of matter is the presence of robust boundary states. In this dissertation, a formalism is developed with which analytical solutions for these states can be straightforwardly obtained by making use of destructive interference, which is naturally present in a large family of lattice models. The validity of the solutions is independent of tight-binding parameters, and as such these lattices can be seen as a subset of solvable systems in the landscape of tight-binding models. The approach allows for a full control of the topological phase of the system as well as the dispersion and localization of the boundary states, which makes it possible to design lattice models possessing the desired topological phase from the bottom up. Further applications of this formalism can be found in the fields of higher-order topological phases—where boundary states localize to boundaries with a codimension larger than one—and of non-Hermitian Hamiltonians—which is a fruitful approach to describe dissipation, and feature many exotic features, such as the possible breakdown of bulk-boundary correspondence—where the access to exact solutions has led to new insights.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2019. p. 91
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-166135 (URN)978-91-7797-630-1 (ISBN)978-91-7797-631-8 (ISBN)
Public defence
2019-04-12, sal FB52, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 7: Submitted. Paper 8: Manuscript.

Available from: 2019-03-20 Created: 2019-02-22 Last updated: 2019-03-15Bibliographically approved

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arXiv:1812.02186

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Citation style
  • apa
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More languages
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