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Band structures of topological crystalline insulators
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.
2018 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Bandstrukturer för topologiska kristallina isolatorer (Swedish)
Abstract [en]

Topological insulators and topological crystalline insulators are materials that have a bulk band structure that is gapped, but that also have toplogically protected non-gapped surface states. This implies that the bulk is insulating, but that the material can conduct electricity on some of its surfaces. The robustness of these surface states is a consequence of time-reversal symmetry, possibly in combination with invariance under other symmetries, like that of the crystal itself. In this thesis we review some of the basic theory for such materials. In particular we discuss how topological invariants can be derived for some specific systems. We then move on to do band structure calculations using the tight-binding method, with the aim to see the topologically protected surface states in a topological crystalline insulator. These calculations require the diagonalization of block tridiagonal matrices. We finish the thesis by studying the properties of such matrices in more detail and derive some results regarding the distribution and convergence of their eigenvalues.

Place, publisher, year, edition, pages
2018. , p. 87
Keywords [en]
Topological insulator, Band structure, Block tridiagonal matrix
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:kau:diva-65536OAI: oai:DiVA.org:kau-65536DiVA, id: diva2:1171075
Educational program
Engineering: Engineering Physics (300 ECTS credits)
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Examiners
Available from: 2018-01-09 Created: 2018-01-05 Last updated: 2018-01-09Bibliographically approved

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CiteExportLink to record
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