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Calculating Topological Invariants with Z2Pack


Gresch, Dominik; Soluyanov, Alexey (2018). Calculating Topological Invariants with Z2Pack. In: Soluyanov, Alexey. Topological Matter : Lectures from the Topological Matter School 2017. Cham: Springer (Bücher), 63-92.

Abstract

The topological phase of non-interacting electronic bandstructure can be classified by calculating integer invariants. In this chapter, we introduce the Chern invariant that classifies 2D materials in the absence of symmetry. We then show that this invariant can be used as the building block for the classification of topological insulators, semimetals, and symmetry-protected topological phases. We show how this classification is performed in practice by introducing Z2Pack, a tool which allows calculating topological invariants from k⋅p and tight-binding models, as well as first-principles calculations.

Abstract

The topological phase of non-interacting electronic bandstructure can be classified by calculating integer invariants. In this chapter, we introduce the Chern invariant that classifies 2D materials in the absence of symmetry. We then show that this invariant can be used as the building block for the classification of topological insulators, semimetals, and symmetry-protected topological phases. We show how this classification is performed in practice by introducing Z2Pack, a tool which allows calculating topological invariants from k⋅p and tight-binding models, as well as first-principles calculations.

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Additional indexing

Item Type:Book Section, not_refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Language:English
Date:4 October 2018
Deposited On:20 Dec 2018 12:29
Last Modified:29 Jul 2020 08:28
Publisher:Springer (Bücher)
Series Name:Springer Series in Solid-State Sciences
ISSN:0171-1873
ISBN:9783319763873
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/978-3-319-76388-0_3

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