Modern Classification Theory of Superconducting Gap Nodes

Author: Dr. Shuntaro Sumita

Publisher: Springer Singapore

Book Series : Springer Theses

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

About this book

This book puts forward a modern classification theory for superconducting gap nodes, whose structures can be observed by experiments and are essential for understanding unconventional superconductivity. In the first part of the book, the classification method, based on group theory and K theory, is introduced in a step-by-step, pedagogical way. In turn, the latter part presents comprehensive classification tables, which include various nontrivial gap (node) structures, which are not predicted by the Sigrist-Ueda method, but are by the new method. The results obtained here show that crystal symmetry and/or angular momentum impose critical constraints on the superconducting gap structures. Lastly, the book lists a range of candidate superconductors for the nontrivial gap nodes.

The classification methods and tables presented here offer an essential basis for further investigations into unconventional superconductivity. They indicate that previous experimental studies should be reinterpreted, while future experiments should reflect the new excitation spectrum.

Frontmatter

Chapter 1. Introduction

Abstract

In this chapter, we review the conventional classification theory of superconducting order parameter. Although the method is convenient and has been used in many researches of unconventional superconductivity, it may fail to predict actual gap structures in superconductors with multi-degrees of freedom. In the review, the inadequacies of the conventional method are explicitly pointed out. Furthermore, we introduce some recent progressive studies elucidating unconventional superconducting gap structures beyond the method.

Shuntaro Sumita

Chapter 2. Method

Abstract

In this chapter, we introduce modern gap classification theory using group theory (representation theory) and topological argument. First, in Sect. 2.1, we make a remark about some terminologies and notations of finite-group representation theory, which are used throughout the thesis, for the avoidance of confusion. In Sect. 2.2, we introduce the group-theoretical analysis of the superconducting gap on high-symmetry points in the BZ [1‐11]. Next, we explain the topological classification of nodes on the high-symmetry points by using the Wigner criteria and the orthogonality test in Sect. 2.3 [12‐15]. Also, an intuitive understanding of the classification methods is given by showing simple examples (Sect. 2.4).

Shuntaro Sumita

Chapter 3. Superconducting Gap Classification on High-Symmetry Planes

Abstract

In this chapter, using the classification theory introduced in Chap. 2, we completely classify the superconducting gap structures on high-symmetry (namely mirror- or glide-invariant) planes in the BZ. From the group-theoretical analysis, the classification tables for all possible symmetries are given in Sect. 3.1. The tables clarify the condition for nontrivial line nodes or gap opening on the BZ boundary, which are protected by nonsymmorphic symmetry. Next, in Sect. 3.2, we see a one-to-one correspondence between the group-theoretical and topological classification: all crystal-symmetry-protected line nodes on high-symmetry planes are also characterized by 0D and/or 1D topological numbers. Furthermore, we discuss the possibility of Majorana flat bands as surface states corresponding to the 1D topological number. Finally, as an example, we demonstrate nonsymmorphic-symmetry-protected gap structures in the model of Sr\(_2\)IrO\(_4\) (Sect. 3.3).

Shuntaro Sumita

Chapter 4. Superconducting Gap Classification on High-Symmetry Lines

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).

Shuntaro Sumita

Chapter 5. Conclusion

Abstract

We provide summary and outlooks of the researches presented in this thesis.

Shuntaro Sumita

Backmatter

Title: Modern Classification Theory of Superconducting Gap Nodes
Author: Dr. Shuntaro Sumita
Publisher: Springer Singapore
Electronic ISBN: 978-981-334-264-4
Print ISBN: 978-981-334-263-7
DOI: https://doi.org/10.1007/978-981-33-4264-4

Springer Professional

Modern Classification Theory of Superconducting Gap Nodes

About this book

Table of Contents

Frontmatter

Chapter 1. Introduction

Chapter 2. Method

Chapter 3. Superconducting Gap Classification on High-Symmetry Planes

Chapter 4. Superconducting Gap Classification on High-Symmetry Lines

Chapter 5. Conclusion

Backmatter

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