Unconventional superconducting gap structure protected by space group symmetry

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 three- or sixfold 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 UPt₃, 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 MoS₂, SrPtAs, UBe₁₃, and PrOs₄Sb₁₂ .