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2021 | OriginalPaper | Chapter

4. Superconducting Gap Classification on High-Symmetry Lines

Author : Dr. Shuntaro Sumita

Published in: Modern Classification Theory of Superconducting Gap Nodes

Publisher: Springer Singapore

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Abstract

In Chap. 3, the condition for nonsymmorphic-symmetry-protected line nodes, which are beyond the results of the Sigrist–Ueda method, has been elucidated by using the modern classification of superconducting gap on high-symmetry \(\varvec{k}\) planes. In this chapter, on the other hand, we show nontrivial gap structures using the gap classification on high-symmetry \(\varvec{k}\) lines, namely the n-fold rotational axes (\(n = 2\), 3, 4, and 6). In the following part, we neglect nonsymmorphic symmetry for simplicity; symmorphic PM space groups are assumed. Nevertheless, nontrivial superconducting gap structures resulting from the angular momentum of a normal Bloch state appear on high-symmetry lines.In Sects. 4.1 and 4.2, we present the general classification table on high-symmetry axes using group theory and topology, respectively. Furthermore, some candidate superconductors are shown: UPt\(_3\) (Sect. 4.3), SrPtAs (Sect. 4.4), CeCoIn\(_5\) (Sect. 4.5), UCoGe (Sect. 4.6), MoS\(_2\) (Sect. 4.7), UBe\(_{13}\) (Sect. 4.8), and PrOs\(_4\)Sb\(_{12}\) (Sect. 4.9).

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previous chapter Superconducting Gap Classification on High-Symmetry Planes
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Appendix
Available only for authorised users
Footnotes
1
All representatives in \(\mathcal {M}^{\varvec{k}}_n / \mathbb {T}\) can be chosen to have no translation operation since we assume symmorphic space groups. This does not mean the unimportance of nonsymmorphic symmetry on high-symmetry lines. Indeed, recent theoretical study has pointed out that the gap classification on \(C_{2v}\)-symmetric hinges of the BZ with glide symmetry is different from that with mirror symmetry [1].
 
2
For example, see Ref. [1].
 
3
Symmetry breaking by a weak crystal distortion has been reported [27], although its reliability is under debate. We here assume the high symmetry space group \(P6_{3}/mmc\).
 
4
Here, we dub the ASOC coupling constant as \(\alpha \) according to the convention. Although the symbol is the same as that of the normal Bloch state, the difference is obvious from the context.
 
5
The same result is obtained for the \([1 {-1} 0]\) plane.
 
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Metadata
Title
Superconducting Gap Classification on High-Symmetry Lines
Author
Dr. Shuntaro Sumita
Copyright Year
2021
Publisher
Springer Singapore
Book
Modern Classification Theory of Superconducting Gap Nodes

Print ISBN: 978-981-334-263-7

Electronic ISBN: 978-981-334-264-4

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-981-33-4264-4_4

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