Effects of Rashba spin–orbit coupling interface on the orientation-dependent conductance in ferromagnet/spin-triplet superconductor junction

We study theoretically the tunneling charge conductance in ferromagnet/spin-triplet superconductor junction with the spin–orbit coupling interface. It is shown the symmetry of the conductance about the relative angle between the magnetization in ferromagnet and the d-vector in superconductor is broken due to the presence of the interfacial Rashba spin–orbit coupling. We present the conductance for various cases of the angle. For each angle, the spin-active mechanism provided by the interface is investigated. The interface effects for different spin polarization in the ferromagnet is also considered.     

Local transport characteristics of break junction in Sr2RuO4 microbridge

We have measured tunnel conductance of spin-triplet superconductor Sr₂RuO₄ (SRO) break junction which was made by micro fabrication technique with a focused ion beam. This is a new type of tunnel junctions made of SRO, which is different from those made of SRO and other materials. Since the tunnel conductance is sensitive to the internal phase of superconductivity, it enables us to examine the chiral p-wave pairing state, which is the most probable candidate of SRO. The tunnel conductance spectrum of the junction showed a broad zero-bias conductance peak whose shape is different from that of high-T_c cuprate superconductors. The shape of the spectrum is in quite good agreement with the calculated spectrum of a chiral p-wave/insulator/normal metal junction.     

Triplet pairing states with equal spins in ferromagnet/superconductor heterojunctions for noncollinear magnetizations

Four-component Bogoliubov-de Gennes equations are applied to study tunneling conductance spectra of ferromagnet/ferromagnet/d-wave superconductor (F₁/F₂/d-wave S) tunnel junctions and to find out signs of spin-triplet pairing correlations induced in the proximity structure. The pairing correlations with equal spins arises from the novel Andreev reflection (AR), which requires at least three factors: the usual AR at the F₂/S interface, spin flip in the F₂ layer, and superconducting coherence kept up in the F₂ layer. Effects of angle α between magnetizations of the two F layers, polarizations of the F₁ and F₂ layers, the thickness of the F₂ layer, and the orientation of the d-wave S crystal on the tunneling conductance are investigated. A conversion from a zero-bias conductance dip at α = 0 to a zero-bias conductance peak at a certain value of α can be seen as a sign of generated spin-triplet correlations.     

STM spectroscopy of an organic superconductor

Electron tunneling spectroscopy of the organic superconductor κ-(BEDT-TTF)₂Cu(NCS)₂using low temperature scanning tunneling microscope (STM) is reported. The tunneling differential conductance in the superconducting phase was obtained in theb–cplane of a single crystal, by varying the tip position on the sample surface. The differential conductance is reduced near zero bias voltage and enhanced at the gap edge, associated with the superconducting gap structure below[formula] K. The gap width differs slightly from sample to sample, while the overall functional shape of the conductance is sample-independent. The tunneling conductance is reduced to almost zero near zero bias voltage, while it is finite inside the gap edge. The curve obtained cannot be fit to the BCS density of states withs-wave pairing symmetry, even if the life-time broadening of one-electron levels is taken into account. Finite conductance inside the gap edge suggests anisotropy of the gap. However, the conductance curve obtained is not explained by a simpled-wave symmetry for Δ(k). The reduced conductance near zero bias voltage suggests a finite gap. An anisotropic model with a finite gap, in which Δ(k) varies depending on the direction ink-space, is examined. The tunneling conductance in the low-energy region is almost fit by the model with Δ_min = 2 meV and Δ_max = 6 meV. The finite conductance is explained by introducing a small effect of life time broadening. We conclude that the gap is anisotropic and is finite (at least Δ_min = 2 meV) on the entire Fermi surface.     

Theory of the spin-triplet superconductivity in Sr2RuO4 based on perturbation approach to three-band Hubbard model

We investigate a mechanism of the spin-triplet superconductivity in Sr₂RuO₄ by solving Eliashberg equation for three-band Hubbard model, where the effective pairing interaction is expanded perturbatively up to the third order with respect to the Coulomb integrals and the transition temperature is estimated numerically. The most significant momentum dependence of the effective interaction for the spin-triplet p-wave superconductivity does not originate from that of the spin susceptibility, but is brought by the third order vertex corrections. The results show that the p-wave pairing state is stabilized for not so strong inter-orbit couplings.     

Unconventional superconductivity and magnetism in Sr2RuO4 and related materials

We review the normal and superconducting state properties of the unconventional triplet superconductor Sr₂RuO₄ with an emphasis on the analysis of the magnetic susceptibility and the role played by strong electronic correlations. In particular, we show that the magnetic activity arises from the itinerant electrons in the Ru d‐orbitals and a strong magnetic anisotropy occurs (χ^+‐ < χ^zz) due to spin‐orbit coupling. The latter results mainly from different values of the g‐factor for the transverse and longitudinal components of the spin susceptibility (i.e. the matrix elements differ). Most importantly, this anisotropy and the presence of incommensurate antiferromagnetic and ferromagnetic fluctuations have strong consequences for the symmetry of the superconducting order parameter. In particular, reviewing spin fluctuation‐induced Cooper‐pairing scenario in application to Sr₂RuO₄ we show how p‐wave Cooper‐pairing with line nodes between neighboring RuO₂‐planes may occur. We also discuss the open issues in Sr₂RuO₄ like the influence of magnetic and non‐magnetic impurities on the superconducting and normal state of Sr₂RuO₄. It is clear that the physics of triplet superconductivity in Sr₂RuO₄ is still far from being understood completely and remains to be analyzed more in more detail. It is of interest to apply the theory also to superconductivity in heavy‐fermion systems exhibiting spin fluctuations.     

NMR and NQR studies on superconducting Sr2RuO4

We review our nuclear-magnetic resonance (NMR) and nuclear-quadrupole-resonance (NQR) studies in superconducting Sr₂RuO₄, which have been performed in order to investigate the gap structure and the pairing symmetry in the superconducting state and magnetic fluctuations in the normal state. The spin-lattice relaxation rate (1/T₁) of a high-quality sample with shows a sharp decrease without a coherence peak just below T_c, followed by a T³ behavior down to 0.15 K. This result indicates that the superconducting gap in pure Sr₂RuO₄ is a highly anisotropic character with a line-node gap. The Knight shift, which is related to the spin susceptibility, is unchanged in the superconducting state irrespective of the direction of the applied fields and various magnitude of the field. This result strongly suggests that the superconducting pairs are in the spin-triplet state, and the spin direction of the triplet pairs is considered to be changed by small fields of several hundred Oe.     

Twofold spin-triplet pairing states and tunneling conductance in ferromagnet/ferromagnet/iron pnictide superconductor heterojunctions

By applying an extended eight-component Bogoliubov–de Gennes equation, we study theoretically the tunneling conductance in clean ferromagnet/ferromagnet/iron pnictide superconductor (FM/FM/iron-based SC) heterojunctions. Under the condition of noncollinear magnetizations, twofold novel Andreev reflections exist due to the existence of two bands in the SC, in which the incident electron and the two Andreev-reflected holes, belonging to the same spin subband, form twofold spin-triplet pairing states near the FM/iron-based SC interface. It is shown that the conversions of the conductance not only between the zero-bias peak and valley at zero energy but also between the peaks and dips at two gap energies are strongly dependent on both the interband coupling strength in the SC and the spin polarization in the FM. The qualitative differences from tunneling into a conventional s$s$-wave SC are also presented, which may help with experimentally probing and identifying the antiphase s$s$-wave pairing symmetry in the iron-based SC.     

Ferromagnetic features of zero-bias conductance peaks in a ferromagnet/insulator/superconductor junction

We present a general formula for tunneling conductance in ballistic ferromagnet/ferromagnetic insulator/superconductor junctions where the superconducting state has the opposite spin pairing symmetry. The formula shows, correctly, that ferromagnetism has been induced by the effective mass difference between up- and down-spin electrons. This effectively mass mismatched ferromagnet and a standard Stoner ferromagnet have been employed in this paper. As an application of the formulation, we have studied the tunneling effect for junctions including a spin-triplet p-wave superconductor, where we choose a normal insulator for the insulating region, although our formula can be used for a ferromagnetic insulator. Then, we have been able to devote our attention to features of a ferromagnetic metal. The conductance spectra show a clear difference between the two ferromagnets depending upon the method of normalization of the conductance. In particular, an essential difference is seen in the zero-bias conductance peaks, reflecting the characteristics of each ferromagnet. From the obtained results, we suggest that the measurements of the tunneling conductance in the junction provide us with useful information about the mechanism of itinerant ferromagnetism in metals.     

Coherent transmission of nodal Dirac fermions through a graphene-based superconducting double barrier junction

Transport characteristics of relativistic electrons through graphene-based d-wave superconducting double barrier junction and ferromagnet/d-wave superconductor/normal metal double junction have been investigated based on the Dirac–Bogoliubov–de Gennes equation. We have first presented the results of superconducting double barrier junction. In the subgap regime, both the crossed Andreev and nonlocal tunneling conductance all oscillate with the bias voltage due to the formation of Andreev bound states in the normal metal region. Moreover, the critical voltage beyond which the crossed Andreev conductance becomes to zero decreases with increasing value of superconducting pair potential α. In the presence of the ferromagnetism, the MR through graphene-based ferromagnet/ d-wave superconductor/normal metal double junction has been investigated. It is shown that the MR increases from exchange splitting h ₀=0 to h ₀=E _F (Fermi energy), and then it goes down. At h ₀=E _F, MR reaches its maximum 100. In contrast to the case of a single superconducting barrier, Andreev bound states also manifest itself in the zero bias MR, which result in a series of peaks except the maximum one at h ₀=E _F. Besides, the resonance peak of the MR can appear at certain bias voltage and structure parameter. Those phenomena mean that the coherent transmission can be tuned by superconducting pair potential, structure parameter, and external bias voltage, which benefits the spin-polarized electron device based on the graphene materials.     

Tunneling in single-layer Bi2Sr2CuO6+δ single crystals in high magnetic field

In tunneling experiments with high-quality single crystals of a single-layer cuprate superconductor Bi₂Sr₂CuO_6+δ using the break junction and point-contact techniques at T<T _c, the coexistence of the superconducting-state gap and the normal-state gap was observed. The values of the superconducting energy gap 2Δ_p?p are in the range from 13.4 to 15 meV (Δ_p?p=6.7–7.5 meV). The values of 2Δ_p?p are similar for two samples with T _c=4 K and for two samples with T _c=9–10 K and are independent of the carrier concentration. The normal-state gap, with the magnitude approximately equal to 50 meV, persists at T<T _c and in the magnetic field H?H _c2 up to 28 T. After the transition of the sample to the normal state, the intensity of the tunneling conductance rapidly decreases with increasing magnetic field strength and temperature. The observed large broadening of the tunneling spectra and large zero-bias conductances can be caused by a strong angular dependence of the superconducting gap. The tunneling results are in full agreement with the data of the angle-resolved photoemission spectroscopy measurements.     

Asymmetric d-wave superconducting topological insulator in proximity with a magnetic order

In the framework of the Dirac–Bogoliubov–de Gennes formalism, we investigate the transport properties in the surface of a 3-dimensional topological insulator-based hybrid structure, where the ferromagnetic and superconducting orders are simultaneously induced to the surface states via the proximity effect. The superconductor gap is taken to be spin-singlet d-wave symmetry. The asymmetric role of this gap respect to the electron–hole exchange, in one hand, affects the topological insulator superconducting binding excitations and, on the other hand, gives rise to forming distinct Majorana bound states at the ferromagnet/superconductor interface. We propose a topological insulator N/F/FS junction and proceed to clarify the role of d-wave asymmetry pairing in the resulting subgap and overgap tunneling conductance. The perpendicular component of magnetizations in F and FS regions can be at the parallel and antiparallel configurations leading to capture the experimentally important magnetoresistance (MR) of junction. It is found that the zero-bias conductance is strongly sensitive to the magnitude of magnetization in FS region $m_{zfs}$ and orbital rotated angle α of superconductor gap. The negative MR only occurs in zero orbital rotated angle. This result can pave the way to distinguish the unconventional superconducting state in the relating topological insulator hybrid structures.     

Parity violation in a single domain of spin-triplet Sr2RuO4 superconductors

We observed an unconventional parity-violating vortex in single domain Sr₂RuO₄ single crystals using a transport measurement. The current–voltage characteristics of submicron Sr₂RuO₄ show that the induced voltage has anomalous components which are even functions of the bias current. The results may suggest that the vortex itself has a helical internal structure characterized by a Hopf invariant (a topological invariant). We also discuss that the hydrodynamics of such a helical vortex causes the parity violation to retain the topological invariant.     

Chiral superconducting phase transition in 3-K phase of Sr2RuO4

We have investigated the transports of micro-fabricated sample of 3-K phase superconductivity (T_c  3 K) in Sr₂RuO₄–Ru eutectic system in order to clarify the pairing symmetry. Up to now, pure Sr₂RuO₄ (T_c = 1.5 K: 1.5-K phase) is widely recognized to be a spin-triplet odd-parity superconductor. However, the enhancement mechanism of T_c up to 3 K and the pairing symmetry of the 3-K phase have not been cleared yet. By using micro fabrication technique with focused ion beam, we have succeeded to extract individual superconducting channels for the 3-K phase in which only a few pieces of Ru inclusions are contained. Multiple kink structures observed in differential resistance–current (dV/dI − I) characteristics indicate serially connected superconducting filaments in the 3-K phase. We confirm that the 3-K phase is an odd-parity superconductor similar to pure Sr₂RuO₄ from the monotonous temperature dependence of the critical currents. In addition, we observed a quite unusual hysteresis in dV/dI − I below 2 K, which suggests the internal degrees of freedom in the superconducting state: the most probably the chiral p-wave state.     

Nuclear magnetic resonance study of strongly correlated superconductors

This paper introduces nuclear magnetic resonance works in the strongly correlated super-conductors: heavy-Fermion, high-T _C superconductors and Sr₂RuO₄. The analyses strongly support the spin-fluctuation-mediated superconductivity model in a high-T _C superconductor.     

Tunneling conductance study of a metal-superconductor junction in the presence of Rashba spin orbit coupling

The tunneling conductance for a junction device consisting of a normal metal and a singlet superconductor is studied with Rashba spin orbit coupling (RSOC) being present in the metallic lead and the interface separating the two regions via an extended Blonder-Tinkham-Klapwijk (BTK) formalism. Interesting interplay between the RSOC and a number of parameters that have experimental significance, and characterize either the junction or the superconducting leads, such as the barrier transparency, quasiparticle lifetime, Fermi wavevector mismatch, an in-plane magnetic field and their effects on the tunneling conductance are investigated in details for both a s-wave and a d-wave superconductor. In an opaque barrier, in presence of a quasiparticle lifetime, a Fermi wavevector mismatch or an external in-plane magnetic field, RSOC enhances the conductance corresponding to low biasing energies, that is, at energies lesser than the superconducting gap, while the reverse is noted for energies exceeding the magnitude of the gap. Further, there are exciting anomalies noted in the conductance spectrum for the d-wave gap which can be understood by incorporating the interplay between the superconducting gap and the angle of incident of the charge carriers.     

Ballistic conductance of a point contact between a <Emphasis Type="Italic">d</Emphasis>-type superconductor and a ferromagnet

The ballistic conductance of a point contact between a strong ferromagnet and a d-wave superconductor is calculated for arbitrary spin-dependent transmission coefficients. The width of the localized Andreev state level is determined. The possibility of identifying the d-type superconductor by the shape of the voltage dependence of the conductance is analyzed for a point contact with a good metallic conduction.     

A new numerical method for quasi-particle spectroscopy around a pair of vortices in triplet superconductors

Triplet superconductors such as Sr₂RuO₄ and Na_xCoO₂·yH₂O are now found to be p-wave (p_x±ip_y) or f-wave ((p_x±ip_y)coscp_z) superconductors. In conventional singlet superconductors, vortices are quantized because phase of order parameter must rotate by 2π around a vortex. But triplet superconductors have a degree of freedom of spin, which is described by d-vector. The d-vector and phase can rotate by π around a vortex, separately. Therefore appearance of HQVs is predicted. Theoretically, it is found that a pair of HQVs is more stable than a singly quantized vortex, for several parameter regions.In this study, in order to investigate quasi-particle bound states around two vortices in s-wave superconductors, we have developed a new numerical method to solve the BdG equation for two vortices state, using Mathieu functions. We confirmed the validity of this method for two vortices state and applied it in case of a pair of vortices. And we solved it.     

Quasi-two-dimensional Fermi liquid properties of the unconventional superconductor Sr2RuO4

In this paper, we review a large set of experimental data acquired over the past decade by several groups, and demonstrate how it can be used to construct a detailed picture of the low-temperature metallic state of the unconventional superconductor Sr₂RuO₄. We show how the normal state properties can be consistently and quantitatively explained in terms of Landau quasi-particles moving on a quasi-two-dimensional Fermi surface. Besides presenting our full and extensive data sets, we explain the details of some novel data analysis tools that can be used within the general context of quasi-two-dimensional metals. We then use the experimental Fermi surface and band dispersion to reassess several issues relevant to the unconventional superconductivity in Sr₂RuO₄, such as the spin-fluctuation spectrum, quasi-particle renormalization, interlayer dispersion and pressure dependence.     

Spin-triplet pairing states in ferromagnet/ferromagnet/d-wave superconductor heterojunctions with noncollinear magnetizations

Tunneling conductance in clean ferromagnet/ ferromagnet/d-wave superconductor (F/F/d-wave S) double tunnel junctions is studied by use of four-component Bogoliubov-de Gennes equations. The novel Andreev reflection appears due to noncollinear magnetizations, in which the incident electron and the Andreev-reflected hole come from the same spin subband, resulting in spin-triplet pairing states near the F/S interface. In the highly polarized Fs case, the conductance within the energy gap exhibits a conversion from a zero-bias dip in the parallel magnetizations to a spilt zero-bias peak in the perpendicular magnetizations.