In chiral p-wave superconductors, magnetic flux patterns may appear spontaneously when translational symmetry is broken such as at surfaces, domain walls, or impurities. However, in the candidate material Sr2RuO4 no direct signs of such magnetic fields have been detected experimentally. In this paper, the flux pattern at the edge of a disk-shaped sample is examined using the phenomenological Ginzburg Landau approach. The detailed shape of the flux pattern, including self-screening, is computed numerically for different surface types by systematically scanning a range of boundary conditions. Moreover, specific features of the electronic structure are included qualitatively through the coefficients in the Ginzburg Landau functional. Both the shape and the magnitude of the flux pattern are found to be highly sensitive to all considered parameters. In conclusion, such spontaneous magnetic flux patterns are not a universal feature of chiral p-wave superconductors.

Eutectic Sr 2 RuO 4 -Ru samples with μm-sized Ru-metal inclusions support inhomogeneous superconductivity above the bulk transition of Sr 2 RuO 4 in the so-called 3-Kelvin phase. In Pb/Ru/Sr 2 RuO 4 Josephson junctions as realized by Maeno et al., a Pb film is indirectly coupled to the superconductor Sr 2 RuO 4 mediated by the proximity-induced superconducting Ru inclusions, yielding an extended Josephson contact through the interface between Ru and Sr 2 RuO 4 . Motivated by this experimental setup, we formulate a sine-Gordon model for the Josephson phase of the interface, assuming a simple cylindrical shape for the Ru inclusion hosting the proximityinduced s-wave superconducting phase. Considering the Sr 2 RuO 4 as a chiral p-wave superconductor, we discuss two types of Josephson junctions, a frustrated one due to the nature of the order parameter in Sr 2 RuO 4 and an unfrustrated one for the topologically trivial 3-Kelvin phase. While the latter situation displays standard junction behavior, the former yields an unusual limiting mechanism for the critical current, based on a pinning-depinning transition of a spontaneously induced magnetic flux driven by an externally applied current. We analyze different coupling limits and show that different critical currents can arise for the two topologies. This concept fits well to recent experimental data obtained for the above setup showing an anomalous temperature dependence of the critical current at the transition temperature T c of bulk Sr 2 RuO 4 .

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The evolution of the filamentary 3-Kelvin (3K) superconducting phase at the interface between Sr2RuO4 and Ru-metal inclusions is discussed for Pb-Ru-Sr2RuO4 contacts. Using the GinzburgLandau model, the influence of proximity-induced superconductivity in Ru on the topology of the 3K phase is analyzed. Because the s-wave order parameter in Ru favors a 3K state of trivial topology, the onset temperature of the phase with a non-trivial topology, which is compatible with the bulk phase of Sr2RuO4, is essentially reduced to the bulk transition temperature. Because the topology of the superconducting state in Sr2RuO4 is crucial for the Josephson effect through Pb-Ru-Sr2RuO4 contacts, this model qualitatively reproduces the experimental observation of the anomalous temperature dependence on the critical current. PACS numbers: 74.20. De,74.45.+c,74.70.Pq, 74.25.Dw Besides the intriguing superconducting phase appearing in the quasi-two-dimensional strongly correlated metal Sr 2 RuO 4 (SRO) below its bulk transition temperature T c,SRO = 1.5 K 1-4 , the filamentary superconductivity nucleating at T * ≈ 3 K in eutectic Ru-SRO samples bears further fascinating features [5][6][7][8][9][10][11][12] . For the bulk state of SRO in the zero-magnetic field, multiple studies 1-4 , in particular, the observation of the polar Kerr effect 13 and intrinsic magnetism in µSR experiments 14 , count as evidence for the realization of a time-reversal symmetry breaking (TRSB) chiral p-wave state 1-4 . On the other hand, several experimental attempts to observe spontaneous edge currents expected for the chiral p-wave state led to negative results 15-17 and have triggered several theoretical studies exploring potential reasons for this conflicting result [18][19][20] . Microscopic calculations concerning the pairing symmetry show a close competition between a chiral and helical p-wave state, the former having inplane-and the latter c-axis equal-spin pairing 21 . Both of these phase are compatible with NMR-data, if we assume that the pinning of the spin configuration by spin-orbit coupling is weak 22,23 . Also the observation of half-flux-quantum vortices 24 is probably most easily explained with an almost freely twistable d-vector. On the other hand, recent functional renormalization group studies support the spin triplet pairing dominantly in the γ-band which favors the chiral p-wave channel due to spin-orbit coupling 21,25,26 . In the following we will assume that the bulk superconducting phase of SRO has the chiral p-wave symmetry.In eutectic systems, where excess Ru segregates from bulk SRO into micrometer-sized Ru-metal inclusions, superconductivity is believed to appear first at the interfaces between Ru and SRO at temperatures as high as T * ≈ 3 K 5,27,28 . This so-called "3-Kelvin" (3K) phase evolves into the bulk phase when the temperature is reduced. However, because the phase nucleating at T * does not break the time-reversal symmetry, the transition from the filamentary to the bulk phase involves an additional phase transition ...

Chiral superconductors are two-fold degenerate and domains of opposite chirality can form, separated by domain walls. There are indications of such domain formation in the quasi two-dimensional putative chiral p-wave superconductor Sr2RuO4, yet no experiment has explicitly resolved individual domains in this material. In this work, c-axis domain walls lying parallel to the layers in chiral p-wave superconductors are explored from a theoretical point of view. First, using both a phenomenological Ginzburg–Landau and a quasiclassical Bogoliubov-de Gennes approach, a consistent qualitative description of the domain wall structure is obtained. While these domains are decoupled in the isotropic limit, there is a finite coupling in anisotropic systems and the domain wall can be treated as an effective Josephson junction. In the second part, the formation and structure of half-quantum vortices on such c-axis domain walls are discussed.