Symmetry-Enforced Line Nodes in Unconventional Superconductors

Tunable zero-energy Dirac and Luttinger nodes in a two-dimensional topological superconductor

Cooper pairing in ultrathin films of topological insulators, induced intrinsically or by proximity effect, can produce an energetically favorable spin-triplet superconducting state. The spin-orbit coupling acts as an SU(2) gauge field and stimulates the formation of a spin-current vortex lattice in this superconducting state. Here we study the Bogoliubov quasiparticles in such a state and find that the quasiparticle spectrum consists of a number of Dirac nodes pinned to zero energy by the particle-hole symmetry. Some nodes are 'accidental' and move through the first Brillouin zone along high-symmetry directions as the order parameter magnitude or the strength of the spin-orbit coupling are varied. At special parameter values, nodes forming neutral quadruplets merge and become gapped out, temporarily producing a quadratic band-touching spectrum. All these features are tunable by controlling the order parameter magnitude via a gate voltage in a heterostructure device. In addition to analyzing the spectrum at the mean-field level, we briefly discuss a few experimental signatures of this spectrum.

Topological Structure of the Order Parameter of Unconventional Superconductors Based on d- and f- Elements

The superconducting order parameter (SOP) of a triplet superconductor UTe2 was constructed using the topological space group approach, in which, in contrast to phenomenological and topological approaches, the single pair function and phase winding in condensate are different quantities. The connection between them is investigated for the D2h point group and the m′m′m magnetic group. It is shown how a non-unitary pair function of UTe2 can be constructed using one-dimensional real irreducible representations and Ginzburg–Landau phase winding. It is also shown that the total phase winding is non-zero in magnetic symmetry only. Experimental data on the superconducting order parameter of topological superconductors UPt3, Sr2RuO4, LaPt3P, and UTe2 are considered and peculiarities of their nodal structures are connected with the theoretical results of the topological space group approach.

Recent progress on superconductors with time-reversal symmetry breaking

Superconductivity and magnetism are adversarial states of matter. The presence of spontaneous magnetic fields inside the superconducting state is, therefore, an intriguing phenomenon prompting extensive experimental and theoretical research. In this review, we discuss recent experimental discoveries of unconventional superconductors which spontaneously break time-reversal symmetry and theoretical efforts in understanding their properties. We discuss the main experimental probes and give an extensive account of theoretical approaches to understand the order parameter symmetries and the corresponding pairing mechanisms, including the importance of multiple bands.

Insulator-Metal Transition and Topological Superconductivity in UTe_{2} from a First-Principles Calculation

We theoretically study superconductivity in UTe_{2}, which is a recently discovered strong candidate for an odd-parity 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 insulator-metal 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 Z_{2} 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 UTe_{2} 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.

Multipole Superconductivity in Nonsymmorphic Sr_{2}IrO_{4}

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.