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Anatomy of topological surface states: Exact solutions from destructive interference on frustrated lattices
Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Freie Universität Berlin, Germany.
Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Freie Universität Berlin, Germany.ORCID-id: 0000-0002-9739-2930
Rekke forfattare: 32017 (engelsk)Inngår i: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 96, nr 8, artikkel-id 085443Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

The hallmark of topological phases is their robust boundary signature whose intriguing properties-such as the one-way transport on the chiral edge of a Chern insulator and the sudden disappearance of surface states forming open Fermi arcs on the surfaces of Weyl semimetals-are impossible to realize on the surface alone. Yet, despite the glaring simplicity of noninteracting topological bulk Hamiltonians and their concomitant energy spectrum, the detailed study of the corresponding surface states has essentially been restricted to numerical simulation. In this work, however, we show that exact analytical solutions of both topological and trivial surface states can be obtained for generic tight-binding models on a large class of geometrically frustrated lattices in any dimension without the need for fine-tuning of hopping amplitudes. Our solutions derive from local constraints tantamount to destructive interference between neighboring layer lattices perpendicular to the surface and provide microscopic insights into the structure of the surface states that enable analytical calculation of many desired properties including correlation functions, surface dispersion, Berry curvature, and the system size dependent gap closing, which necessarily occurs when the spatial localization switches surface. This further provides a deepened understanding of the bulkboundary correspondence. We illustrate our general findings on a large number of examples in two and three spatial dimensions. Notably, we derive exact chiral Chern insulator edge states on the spin-orbit-coupled kagome lattice, and Fermi arcs relevant for recently synthesized slabs of pyrochlore-based Eu2Ir2O7 and Nd2Ir2O7, which realize an all-in-all-out spin configuration, as well as for spin-ice-like two-in-two-out and one-in-three-out configurations, which are both relevant for Pr2Ir2O7. Remarkably, each of the pyrochlore examples exhibit clearly resolved Fermi arcs although only the one-in-three-out configuration features bulk Weyl nodes in realistic parameter regimes. Our approach generalizes to symmetry protected phases, e.g., quantum spin Hall systems and Dirac semimetals with time-reversal symmetry, and can furthermore signal the absence of topological surface states, which we illustrate for a class of models akin to the trivial surface of Hourglass materials KHgX where the exact solutions apply but, independently of Hamiltonian details, yield eigenstates delocalized over the entire sample.

sted, utgiver, år, opplag, sider
2017. Vol. 96, nr 8, artikkel-id 085443
Emneord [en]
edge states, frustrated magnetism, surfaces states, topological materials
HSV kategori
Forskningsprogram
teoretisk fysik
Identifikatorer
URN: urn:nbn:se:su:diva-147048DOI: 10.1103/PhysRevB.96.085443ISI: 000408623700007OAI: oai:DiVA.org:su-147048DiVA, id: diva2:1142999
Tilgjengelig fra: 2017-09-20 Laget: 2017-09-20 Sist oppdatert: 2019-12-12bibliografisk kontrollert
Inngår i avhandling
1. Solvable Topological Boundaries
Åpne denne publikasjonen i ny fane eller vindu >>Solvable Topological Boundaries
2019 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
Stockholm: Department of Physics, Stockholm University, 2019. s. 91
HSV kategori
Forskningsprogram
teoretisk fysik
Identifikatorer
urn:nbn:se:su:diva-166135 (URN)978-91-7797-630-1 (ISBN)978-91-7797-631-8 (ISBN)
Disputas
2019-04-12, sal FB52, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (engelsk)
Opponent
Veileder
Merknad

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

Tilgjengelig fra: 2019-03-20 Laget: 2019-02-22 Sist oppdatert: 2019-12-12bibliografisk kontrollert

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