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Register a new userThe direction of the $d$-vector in a nematic triplet superconductor
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We investigate the states of triplet pairing in a candidate nematic superconductor versus typical material parameters, using the mean field theory for two- and three-dimensional tight-binding models with local triplet pairing in the $E_u$ representation. In the two-dimensional model, the system favors the fully gapped chiral state for weaker warping or lower filling level, while a nodal and nematic $Delta_{4x}$ state is favorable for stronger warping or higher filling, with the $d$-vector aligned along the principle axis. In the presence of lattice distortion, relative elongation along one of the principle axes, ${bf a}$, tends to rotate the nematic $d$-vector orthogonal to ${bf a}$, resulting in the nematic $Delta_{4y}$ state at sufficient elongation. Three-dimensionality is seen to suppress the chiral state in favor of the nematic ones. Our results may explain the variety in the probed direction of the $d$-vector in existing experiments.
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Recent experiments show strong evidences of nematic triplet superconductivity in doped Bi$_2$Se$_3$ and in Bi$_2$Te$_3$ thin film on a superconducting substrate, but with varying identifications of the direction of the $d$-vector of the triplet that is essential to the topology of the underlying superconductivity. Here we show that the $d$-vector can be directly visualized by scanning tunneling measurements: At subgap energies the $d$-vector is along the leading peak wave-vector in the quasi-particle-interference pattern for potential impurities, and counter-intuitively along the elongation of the local density-of-state profile of the vortex. The results provide a useful guide to experiments, the result of which would in turn pose a stringent constraint on the pairing symmetry.
The field dependence of the specific heat gamma(H) at lower temperatures in Sr2RuO4 is analyzed by solving microscopic Eilenberger equation numerically. We find that systematic gamma(H) behaviors from a concaved sqrt H to a convex H^{alpha} (alpha>1) under H orientation change are understood by taking account of the Pauli paramagnetic effect. The magnetizations are shown to be consistent with it. This implies either a singlet pairing or a triplet one with d-vector locked in the basal plane, which allows us to explain other mysteries of this compound in a consistent way.
In this work, we study even-parity spin-singlet orbital-triplet pairing states for a two-band superconductor. An orbital $mathbf{d}_o(mathbf{k})$-vector is introduced to characterize orbital-dependent pairings, in analogy to the spin $mathbf{d}_s(mathbf{k})$-vector that describes spin-triplet pairings in $^3$He superfluid. Naively, one might think the double degeneracy of orbitals would be lifted by inter-orbital hybridizations due to crystal fields or electron-electron repulsive interactions, then spin-singlet orbital-dependent pairings may be severely suppressed. However, we demonstrate that orbital-triplet pairing, represented by the orbital $mathbf{d}_o(mathbf{k})$-vector, could exist under some circumstances. Remarkably, it could even coexist with nematic orders or charge-density-wave orders induced by interactions. The generalization to a single-band superconductor with two valleys (e.g.~honeycomb lattice with two sublattices) is also discussed. Moreover, the complex orbital $mathbf{d}_o$-vector spontaneously breaks time-reversal symmetry (TRS), which might give rise to the TRS-breaking orbital-polarization, analogous to the spin magnetism.
The theory of superconductor-ferromagnet (S-F) heterostructures with two ferromagnetic layers predicts the generation of a long-range, odd-in-frequency triplet pairing at non-collinear alignment (NCA) of the magnetizations of the F-layers. This triplet pairing has been detected in a Nb/Cu41Ni59/nc-Nb/Co/CoOx spin-valve type proximity effect heterostructure, in which a very thin Nb film between the F-layers serves as a normal conducting (nc) spacer. The resistance of the sample as a function of an external magnetic field shows that for not too high fields the system is superconducting at a collinear alignment of the Cu41Ni59 and Co layer magnetic moments, but switches to the normal conducting state at a NCA configuration. This indicates that the superconducting transition temperature Tc for NCA is lower than the fixed measuring temperature. The existence of a minimum Tc, at the NCA regime below that one for parallel or antiparallel alignments of the F-layer magnetic moments, is consistent with the theoretical prediction of a singlet superconductivity suppression by the long-range triplet pairing generation.
Motivated by a recent angle-resolved thermal conductivity experiment that shows a twofold gap symmetry in the high-field and low-temperature C phase in the heavy-fermion superconductor UPt$_3$, we group-theoretically identify the pairing functions as $E_{1u}$ with the $f$-wave character for all the three phases. The pairing functions are consistent with the observation as well as with a variety of existing measurements. By using a microscopic quasi-classical Eilenberger equation with the identified triplet pairing function under applied fields, we performed detailed studies of the vortex structures for three phases, including the vortex lattice symmetry, the local density of states, and the internal field distribution. These quantities are directly measurable experimentally by SANS, STM/STS, and NMR, respectively. It is found that, in the B phase of low $H$ and low $T$, the double-core vortex is stabilized over a singular vortex. In the C phase, thermal conductivity data are analyzed to confirm the gap structure proposed. We also give detailed comparisons of various proposed pair functions, concluding that the present scenario of $E_{1u}$ with the $f$-wave, which is an analogue to the triplet planar state, is better than the $E_{2u}$ or $E_{1g}$ scenario. Finally, we discuss the surface topological aspects of Majorana modes associated with the $E_{1u}^f$ state of planar like features.
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