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Register a new userHigher angular momentum pairings in inter-orbital shadowed-triplet superconductors: Application to Sr$_{2}$RuO$_{4}$
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Even-parity inter-orbital spin-triplet pairing emerges as an intriguing candidate in multi-orbital superconductors with significant Hunds and spin-orbit coupling. Within such a state, the pairing is dominated by the intra-band pseudospin-singlet component via the spin-orbit coupling, distinguishing it from a pure spin triplet and motivating the name, shadowed triplet. With atomic spin-orbit coupling, it was shown that this pairing exhibits anisotropic $s$-wave character, while higher angular momentum pairing symmetries such as $d$- or $g$-wave have been proposed based on phenomenological analyses in candidate systems. A natural question is then whether higher angular momentum pairings may arise with this form of spin-triplet pairing. Here, we examine the interplay between spin-orbit coupling and the electronic dispersions in correlated metals and demonstrate how they can be realized. We apply this idea to Sr$_{2}$RuO$_{4}$ and determine the competition among different pairing states as multiple spin-orbit coupling parameters are tuned. The presence of both $d$- and $g$-wave pairings, including a $d+ig$ state are found when momentum-dependent spin-orbit coupling with $d$-wave character is increased. Implications of the theory and future directions are also discussed.
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The mechanism of superconductivity in ${rm Sr}_{2}{rm RuO}_{4}$ is studied using a degenerate Hubbard model within the weak coupling theory. When the system approaches the orbital instability which is realized due to increasing the on-site Coulomb interaction between the electrons in the different orbitals, it is shown that the triplet superconductivity appears. This superconducting mechanism is only available in orbitally degenerate systems with multiple Fermi surfaces.
The quasiparticle interference (QPI) in Sr$_{2}$RuO$_{4}$ is theoretically studied based on two different pairing models in order to propose an experimental method to test them. For a recently proposed two-dimensional model with pairing primarily from the $gamma$ band, we found clear QPI peaks evolving with energy and their locations can be determined from the tips of the constant-energy contour (CEC). On the other hand, for a former quasi-one-dimensional model with pairing on the $alpha$ and $beta$ bands, the QPI spectra are almost dispersionless and may involve off-shell contributions to the scatterings beyond the CEC. The different behaviors of the QPI in these two models may help to resolve the controversy of active/passive bands and whether Sr$_{2}$RuO$_{4}$ is a topological superconductor.
Sr$_{2}$RuO$_{4}$ is one of the most promising candidates of a topological superconductor with broken time-reversal symmetry, because a number of experiments have revealed evidences for a spin-triplet chiral $p$-wave superconductivity. In order to clarify the time-reversal symmetry of Sr$_{2}$RuO$_{4}$, we introduce a novel test that examines the invariance of the Josephson critical current under the inversion of both the current and magnetic fields, in contrast to the detection of a spontaneous magnetic field employed in past experiments. Analyses of the transport properties of the planar and corner Josephson junctions formed between Sr$_{2}$RuO$_{4}$ and Nb reveal the time-reversal invariant superconductivity, most probably helical $p$-wave, of Sr$_{2}$RuO$_{4}$. This state corresponds to a yet-to-be confirmed $topological crystalline superconductivity$ that can host two Majorana edge modes at the surface protected by crystalline mirror symmetry.
Differential resistance measurements are conducted for point contacts (PCs) between tungsten tip approaching along the $c$ axis direction and the $ab$ plane of Sr$_{2}$RuO$_{4}$ single crystal. Three key features are found. Firstly, within 0.2 mV there is a dome like conductance enhancement due to Andreev reflection at the normal-superconducting interface. By pushing the W tip further, the conductance enhancement increases from 3% to more than 20%, much larger than that was previously reported, probably due to the pressure exerted by the tip. Secondly, there are also superconducting like features at bias higher than 0.2 mV which persists up to 6.2 K, resembling the enhanced superconductivity under uniaxial pressure for bulk Sr$_{2}$RuO$_{4}$ crystals but more pronounced here. Third, the logarithmic background can be fitted with the Altshuler-Aronov theory of tunneling into quasi two dimensional electron system, consistent with the highly anisotropic electronic system in Sr$_{2}$RuO$_{4}$.
We investigate the bulk orbital angular momentum (AM) in a two-dimensional hole-doped topological superconductor (SC) which is composed of a hole-doped semiconductor thin film, a magnetic insulator, and an $s$-wave SC and is characterized by the Chern number $C = -3$. In the topological phase, $L_z/N$ is strongly reduced from the intrinsic value by the non-particle-hole-symmetric edge states as in the corresponding chiral $f$-wave SCs when the spin-orbit interactions (SOIs) are small, while this reduction of $L_z/N$ does not work for the large SOIs. Here $L_z$ and $N$ are the bulk orbital AM and the total number of particles at zero temperature, respectively. As a result, $L_z/N$ is discontinuous or continuous at the topological phase transition depending on the strengths of the SOIs. We also discuss the effects of the edge states by calculating the radial distributions of the orbital AM.
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