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Lattice models with exactly solvable topological hinge and corner states
Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.ORCID-id: 0000-0002-9739-2930
Antal upphovsmän: 32018 (Engelska)Ingår i: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 97, nr 24, artikel-id 241405Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We devise a generic recipe for constructing D-dimensional lattice models whose d-dimensional boundary states, located on surfaces, hinges, corners, and so forth, can be obtained exactly. The solvability is rooted in the underlying lattice structure and as such does not depend on fine tuning, allowing us to track their evolution throughout various phases and across phase transitions. Most saliently, our models provide boundary solvable examples of the recently introduced higher-order topological phases. We apply our general approach to breathing and anisotropic kagome and pyrochlore lattices for which we obtain exact corner eigenstates, and to periodically driven two-dimensional models as well as to three-dimensional lattices where we present exact solutions corresponding to one-dimensional chiral states at the hinges of the lattice. We relate the higher-order topological nature of these models to reflection symmetries in combination with their provenance from lower-dimensional conventional topological phases.

Ort, förlag, år, upplaga, sidor
2018. Vol. 97, nr 24, artikel-id 241405
Nationell ämneskategori
Fysik
Forskningsämne
teoretisk fysik
Identifikatorer
URN: urn:nbn:se:su:diva-157648DOI: 10.1103/PhysRevB.97.241405ISI: 000434762500002OAI: oai:DiVA.org:su-157648DiVA, id: diva2:1223523
Tillgänglig från: 2018-06-25 Skapad: 2018-06-25 Senast uppdaterad: 2019-12-12Bibliografiskt granskad
Ingår i avhandling
1. Solvable Topological Boundaries
Öppna denna publikation i ny flik eller fönster >>Solvable Topological Boundaries
2019 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Stockholm: Department of Physics, Stockholm University, 2019. s. 91
Nationell ämneskategori
Den kondenserade materiens fysik
Forskningsämne
teoretisk fysik
Identifikatorer
urn:nbn:se:su:diva-166135 (URN)978-91-7797-630-1 (ISBN)978-91-7797-631-8 (ISBN)
Disputation
2019-04-12, sal FB52, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (Engelska)
Opponent
Handledare
Anmärkning

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

Tillgänglig från: 2019-03-20 Skapad: 2019-02-22 Senast uppdaterad: 2019-12-12Bibliografiskt granskad

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Kunst, Flore K.Bergholtz, Emil J.
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