Unconventional superconducting gap structure protected by space group symmetry

TL;DR

This paper classifies unconventional superconducting gap structures protected by space group symmetries, revealing new features like $j_z$-dependent point nodes and their realization in materials such as UPt$_3$.

Contribution

It provides a comprehensive classification of symmetry-protected gap structures in superconductors, including nonsymmorphic systems and $j_z$-dependent nodes, with applications to real materials.

Findings

Line nodes are constrained to primitive or orthorhombic base-centered lattices.

Identification of $j_z$-dependent point nodes on 3- or 6-fold axes.

Proposal of UPt$_3$ as a candidate for realizing these unconventional gap structures.

Abstract

Recent superconducting gap classifications based on space group symmetry have revealed nontrivial gap structures that were not shown by point group symmetry. First, we review a comprehensive classification of symmetry-protected line nodes within the range of centrosymmetric space groups. Next, we show an additional constraint; line nodes peculiar to nonsymmorphic systems appear only for primitive or orthorhombic base-centered Bravais lattice. Then, we list useful classification tables of 59 primitive or orthorhombic base-centered space groups for the superconducting gap structures. Furthermore, our gap classification reveals the $j_z$-dependent point nodes (gap opening) appearing on a 3- or 6-fold axis, which means that the presence (absence) of point nodes depends on the Bloch-state angular momentum $j_z$. We suggest that this unusual gap structure is realized in a heavy-fermion superconductor UPt$_3$, using a group-theoretical analysis and a numerical calculation. The calculation demonstrates that a Bloch phase contributes to $j_z$ as effective orbital angular momentum by site permutation. We also discuss superconducting gap structures in MoS$_2$, SrPtAs, UBe$_{13}$, and PrOs$_4$Sb$_{12}$.