We theoretically study superconductivity in UTe2, which is a recently discovered strong candidate for an oddparity spin-triplet superconductor. Theoretical studies for this compound faced difficulty because first-principles calculations predict an insulating electronic state, incompatible with superconducting instability. To overcome this problem, we take into account electron correlation effects by a GGA+U method and show the insulatormetal transition by Coulomb interaction. Using Fermi surfaces obtained as a function of U , we clarify topological properties of possible superconducting states. Fermi surface formulas for the three-dimensional winding number and three two-dimensional Z2 numbers indicate topological superconductivity at an intermediate U for all the odd-parity pairing symmetry in the Immm space group. Symmetry and topology of superconducting gap nodes are analyzed and the gap structure of UTe2 is predicted. Topologically protected low-energy excitations are highlighted, and experiments by bulk and surface probes are proposed to link Fermi surfaces and pairing symmetry. Based on the results, we also discuss multiple superconducting phases under magnetic fields, which were implied by recent experiments. arXiv:1908.04004v3 [cond-mat.supr-con] 1 Nov 2019

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 jz-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 jz. 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 jz as effective orbital angular momentum by site permutation. We also discuss superconducting gap structures in MoS2, SrPtAs, UBe13, and PrOs4Sb12. arXiv:1801.03293v3 [cond-mat.supr-con]

Discoveries of marked similarities to high-T_{c} cuprate superconductors point to the realization of superconductivity in the doped J_{eff}=1/2 Mott insulator Sr_{2}IrO_{4}. Contrary to the mother compound of cuprate superconductors, several stacking patterns of in-plane canted antiferromagnetic moments have been reported, which are distinguished by the ferromagnetic components as -++-, ++++, and -+-+. In this paper, we clarify unconventional features of the superconductivity coexisting with -++- and -+-+ structures. Combining the group theoretical analysis and numerical calculations for an effective J_{eff}=1/2 model, we show unusual superconducting gap structures in the -++- state protected by nonsymmorphic magnetic space group symmetry. Furthermore, our calculation shows that the Fulde-Ferrell-Larkin-Ovchinnikov superconductivity is inevitably stabilized in the -+-+ state since the odd-parity magnetic -+-+ order makes the band structure asymmetric by cooperating with spin-orbit coupling. These unusual superconducting properties are signatures of magnetic multipole order in nonsymmorphic crystal.

Stimulated by recent studies of superconductivity and magnetism with local and global broken inversion symmetry, we investigate the superconductivity in magnetic multipole states in locally noncentrosymmetric metals. We consider a one-dimensional zigzag chain with sublattice-dependent antisymmetric spin-orbit coupling and suppose three magnetic multipole orders: monopole order, dipole order, and quadrupole order. It is demonstrated that the Bardeen-Cooper-Schrieffer state, the pair-density wave (PDW) state, and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are stabilized by these multipole orders, respectively. We show that the PDW state is a topological superconducting state specified by the nontrivial $\mathbb{Z}_2$ number and winding number. The origin of the FFLO state without macroscopic magnetic moment is attributed to the asymmetric band structure induced by the magnetic quadrupole order and spin-orbit coupling.Comment: 13 pages, 9 figure

Recent development in exact classification of a superconducting gap has elucidated various unconventional gap structures, which have not been predicted by the classification of order parameter based on the point group. One of the important previous results is that all symmetry-protected line nodes are characterized by nontrivial topological numbers. Another intriguing discovery is the gap structures depending on the angular momentum jz of normal Bloch states on threefold and sixfold rotational-symmetric lines in the Brillouin zone. Stimulated by these findings, we classify irreducible representations of the Bogoliubov-de Gennes Hamiltonian at each k point on a highsymmetry n-fold (n = 2, 3, 4, and 6) axis for centrosymmetric and paramagnetic superconductors, by using the combination of group theory and K theory. This leads to the classification of all crystal symmetry-protected nodes (including jz-dependent nodes) on the axis that crosses a normal-state Fermi surface. As a result, it is shown that the classification by group theory completely corresponds with the topological classification. Based on the obtained results, we discuss superconducting gap structures in SrPtAs, CeCoIn5, UPt3, and UCoGe. arXiv:1811.08627v2 [cond-mat.supr-con]