Spin-triplet Superconductor Sr2RuO4 Research Articles

Anomalous anisotropic behaviour of spin-triplet proximity effect in Au/SrRuO3/Sr2RuO4 junctions

Spin-polarized supercurrents can be generated with magnetic inhomogeneity at a ferromagnet/spin-singlet-superconductor interface. In such systems, complex magnetic inhomogeneity makes it difficult to functionalise the spin-polarized supercurrents. However, spin-polarized supercurrents in ferromagnet/spin-triplet-superconductor junctions can be controlled by the angle between magnetization and spin of Copper pairs (d-vector), that can effectively be utilized in developing of a field of research known as superconducting spintronics. Recently, we found induction of spin-triplet correlation into a ferromagnet SrRuO3 epitaxially deposited on a spin-triplet superconductor Sr2RuO4, without any electronic spin-flip scattering. Here, we present systematic magnetic field dependence of the proximity effect in Au/SrRuO3/Sr2RuO4 junctions. It is found that induced triplet correlations exhibit strongly anisotropic field response. Such behaviour is attributed to the rotation of the d-vector of Sr2RuO4. This anisotropic behaviour is in contrast with the vortex dynamic. Our results will stimulate study of interaction between ferromagnetism and unconventional superconductivity.

Thermal Hall conductivity in the spin-triplet superconductor with broken time-reversal symmetry

Motivated by the spin-triplet superconductor Sr2RuO4, the thermal Hall conductivity is investigated for several pairing symmetries with broken time-reversal symmetry. In the chiral p-wave phase with a fully opened quasiparticle excitation gap, the temperature dependence of the thermal Hall conductivity has a temperature linear term associated with the topological property directly, and an exponential term, which shows a drastic change around the Lifshitz transition. Examining f-wave states as alternative candidates with $\bm d=\Delta_0\hat{z}(k_x^2-k_y^2)(k_x\pm ik_y)$ and $\bm d=\Delta_0\hat{z}k_xk_y(k_x\pm ik_y)$ with gapless quasiparticle excitations, we study the temperature dependence of the thermal Hall conductivity, where for the former state the thermal Hall conductivity has a quadratic dependence on temperature, originating from the linear dispersions, in addition to linear and exponential behavior. The obtained result may enable us to distinguish between the chiral p-wave and f-wave states in Sr2RuO4.

Thermal Hall Conductivity in a Multiband Chiral p-Wave Superconductor

For the spin-triplet superconductor Sr2RuO4, multiband effects on the thermal Hall conductivity are investigated in the superconducting phase. While the gap functions of all bands (α–β and γ) are assumed to have chiral p-wave symmetry, the thermal Hall conductivity at very low temperatures is dominated by the γ band due to its topological nontrivial state and the presence of nodeless quasiparticle excitation gaps.

Thermal Hall conductivity and topological transition in a chiralp-wave superconductor forSr2RuO4

The interplay between the thermal transport property and the topological aspect is investigated in a spin-triplet chiral p-wave superconductor Sr2RuO4 with the strong two-dimensionality. We show the thermal Hall conductivity is well described by the temperature linear term and the exponential term in the low temperature region. While the former term is proportional to the so-called Chern number directly, the latter is associated with the superconducting gap amplitude of the gamma band. We also demonstrate that the coefficient of the exponential term changes the sign around Lifshitz transition. Our obtained result may enable us access easily the physical quantities and the topological property of Sr2RuO4 in detail.

Topological aspect and transport property in multi-band spin-triplet chiral p-wave superconductor Sr2RuO4

Considering the superconductor Sr2RuO4, we analyze a three-band tight-binding model with one hole-like and two electron-like Fermi surfaces corresponding to the α, β and γ bands of Sr2RuO4 by means of a self-consistent Bogoliubov-de Gennes approach for ribbonshaped system to investigate topological properties and edge states. In the superconducting phase two types of gapless edge states can be identified, one of which displays an almost flat dispersion at zero energy, while the other, originating from the γ band, has a linear dispersion and constitutes a genuine chiral edge states. Not only a charge current appears at the edges but also a spin current due to the multi-band effect in the superconducting phase. In particular, the chiral edge state from the γ band is closely tied to topological properties, and the chiral p-wave superconducting states are characterized by an integer topological number, the so-called Chern number. We show that the γ band is close to a Lifshitz transition. Since the sign of the Chern number may be very sensitive to the surface condition, we consider the effect of the surface reconstruction observed in Sr2RuO4 on the topological property and show the possibility of the hole-like Fermi surface at the surface.

Ferromagnetic Properties of SrRuO3 Thin Films Deposited on the Spin-Triplet Superconductor Sr2RuO4

We report magnetic properties of epitaxial thin films of the itinerant ferromagnet SrRuO3 deposited on the cleaved ab surface of the spin-triplet superconductor Sr2RuO4. The films exhibit ferromagnetic transition near 160K as in the bulk SrRuO3, although the films are under 1.7% compressive strain. The observed magnetization is even higher than that of the bulk SrRuO3. In addition, we newly found that the magnetization relaxation after field removal is strongly anisotropic: two relaxation processes are involved when magnetic domains are aligned along the ab-plane.

Effect of Lishitz Transition on Thermal Transport Properties in Sr2RuO4

Inspired by specific features of the spin-triplet superconductor Sr2RuO4, we investigate thermal transport properties for a generic chiral p-wave superconductor. One of the bands of Sr2RuO4 lies close to a Lifshitz transition which would lead to a change of the Fermi surface topology and influence also topological properties of the chiral superconducting phase characterized by the so-called Chern number. Treating superconductivity based on a two-dimensional tight-binding model for the relevant γ band and a self-consistent Bogoliubov-de Gennes approach, we study thermal transport properties. We focus particularly on the connection between topological properties of the superconducting phase and thermal Hall conductivity. Our results show that low-temperature thermal Hall conductivity can be decomposed into a T -linear contribution and an thermally activated correction, whereby the latter incorporates information about the size of the superconducting gap and the Lifshitz transition.

Effect of the RuO6 Octahedron Rotation at the Sr2RuO4 Surface on Topological Property

We investigate the rotation effect of the RuO$_6$ octahedron around the $c$ axis on the topological and transport properties near the surface of the spin-triplet superconductor Sr$_2$RuO$_4$. While the Fermi level of bulk Sr$_2$RuO$_4$ is near the Lifshitz transition, the RuO$_6$ rotation realized near the surface leads to the change of the Fermi surface topology. The edge current resulting from the time-reversal symmetry breaking in the chiral $p$-wave phase with fully opened excitation gap is less affected around Lifshitz transition. The topological property and the edge state are sensitive to the rotation angle and the amplitude of the nearest neighbor interaction, and the superconducting gap is strongly reduced in the larger next nearest neighbor interaction region. Although the edge state in Sr$_2$RuO$_4$ is topologically protected, it is not robust to the disorder such as impurity or defect.

Ferromagnetic SrRuO3 thin-film deposition on a spin-triplet superconductor Sr2RuO4 with a highly conducting interface

Ferromagnetic SrRuO3 thin films are deposited on the ab surface of single crystals of the spin-triplet superconductor (TSC) Sr2RuO4 as substrates using pulsed laser deposition. The films are under a severe in-plane compressive strain. Nevertheless, the films exhibit ferromagnetic order with the easy axis along the c-direction below the Curie temperature of 158 K. The electrical transport reveals that the SrRuO3/Sr2RuO4 interface is highly conducting, in contrast with the interface between other normal metals and the ab surface of Sr2RuO4. Our results stimulate investigations on proximity effects between a ferromagnet and a TSC.

Topological and edge state properties of a three-band model for Sr2RuO4

Modeling the spin-triplet superconductor Sr2RuO4 through a three-orbital tight-binding model we investigate topological properties and edge states assuming chiral p-wave pairing. In concordance with experiments the three Fermi surfaces consist of two electron-like and one hole-like one corresponding to the alpha-, beta- and gamma-band on the level of a two-dimensional system. The quasi-particle spectra and other physical quantities of the superconducting phase are calculated by means of a self-consistent Bogoliubov-de Gennes approach for a ribbon shaped system. While a full quasiparticle excitation gap is realized in the bulk system, at the edges gapless states appear some of which have linear and others nearly flat dispersion around zero energy. This study shows the interplay between spin-orbit coupling induced spin currents, chiral edge currents and correlation driven surface magnetism. The topological nature of the chiral p-wave state manifests itself in the gamma-band characterized by an integer Chern number. As the gamma-band is close to a Lifshitz transition in Sr2RuO4, changing the sign of the Chern number, the topological nature may be rather fragile.

Topological aspects and transport properties of edge states in the multi-band superconductor Sr2RuO4

Motivated by the spin-triplet superconductor Sr2RuO4, we investigate the edge states by using a two-band tight-binding model with interorbital hybridization and spin-orbit coupling. In particular we focus on the topological aspects and the transport properties in the chiral spin-triplet superconducting phase. The Fermi surfaces correspond to the ones of Sr2RuO4 where the α and the β bands have hole- and electron-like characters, respectively. Although a full quasiparticle excitation gap is present in the bulk system, gapless edge states appear and affect both the spin and the charge currents. We study the interplay between electron- and hole-like particles in the formation of these edge states and edge currents. Topologically the two bands compensate for each other such that the edge state is not topologically protected. The repulsive interaction yields a spin polarization near the edges and lifts the degeneracy of the subgap edge states. The net spontaneous magnetization generated through both the edge charge current and the spin polarization may be small due to canceling effects. The lifting of the spin degeneracy could likely be detected by quasiparticle tunneling for the surface density of states.

Unconventional quantum oscillations in mesoscopic rings of spin-triplet superconductor Sr2RuO4

Odd-parity, spin-triplet superconductor Sr2RuO4 has been found to feature exotic vortex physics including half-flux quanta trapped in a doubly connected sample and the formation of vortex lattices at low fields. The consequences of these vortex states on the low-temperature magnetoresistive behavior of mesoscopic samples of Sr2RuO4 were investigated in this work using ring device fabricated on mechanically exfoliated single crystals of Sr2RuO4 by photolithography and focused ion beam. With the magnetic field applied perpendicular to the in-plane direction, thin-wall rings of Sr2RuO4 were found to exhibit pronounced quantum oscillations with a conventional period of the full-flux quantum even though the unexpectedly large amplitude and the number of oscillations suggest the observation of vortex-flow-dominated magnetoresistance oscillations rather than a conventional Little-Parks effect. For rings with a thick wall, two distinct periods of quantum oscillations were found in high and low field regimes, respectively, which we argue to be associated with the "lock-in" of a vortex lattice in these thick-wall rings. No evidence for half-flux-quantum resistance oscillations were identified in any sample measured so far without the presence of an in-plane field.

Field-temperature phase diagram of superconductivity in Sr2RuO4-Ru under out-of-plane uniaxial pressure

One of the interesting issues on the spin-triplet superconductor Sr2RuO4 (Tc = 1.5 K) is the origin of the Tc enhancement up to about 3 K in the eutectic system Sr2RuO4-Ru. We have recently revealed a striking fact that Tc of pure Sr2RuO4 is also enhanced up to 3.2 K by uniaxial pressure along the c axis (P||c). When P||c is applied to Sr2RuO4-Ru, there is a crossover at P*||c ~ 0.4 GPa from behavior attributable to interfacial superconductivity (SC) to behavior similar to that in pure Sr2RuO4 under P||c. We focus on the field-temperature phase diagrams of Sr2RuO4-Ru above and below P*||c. We revealed that the H-T curves of Sr2RuO4-Ru both above and below P*||c are concave-up. This fact suggests that the P||c-originated SC above P*||c as well as the interfacial SC below P*||c are granular-like. We also found that the H-T curves of these SCs do not scale with Tc's, which is possibly related to a difference in the spatial distribution of superconducting regions.

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-Tc 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.

Atomic structure of functional interfaces in Sr2RuO4/Sr3Ru2O7 eutectic crystals

Sr 2 RuO 4 / Sr 3 Ru 2 O 7 eutectic system is investigated by transmission electron microscopy (TEM) and high angle annular dark field scanning TEM (STEM). The Sr2RuO4/Sr3Ru2O7 lamellar structure allows studying tunneling and proximity effects between spin-triplet superconductor Sr2RuO4 and metamagnetic normal metal Sr3Ru2O7. Our analyses reveal two typologies of interfaces within the eutectic: interfaces parallel to the growth direction are sharp and defect-free whereas interfaces perpendicular to the growth direction appear wavy and decorated with Ru precipitates. These results indicate that interfaces parallel to the growth direction are the best candidates for Sr2RuO4/Sr3Ru2O7 natural junctions to study the unusual superconductivity of Sr2RuO4.

A nodeless superconducting gap in Sr2RuO4 from tunneling spectroscopy

We report on tunneling spectroscopy measurements using a scanning tunneling microscope (STM) on the spin triplet superconductor Sr2RuO4. A fully open gap, close to the Bardeen–Cooper–Schrieffer (BCS) value, is found, which disappears at the bulk Tc=1.5 K. The results are discussed in the framework of recent multigap scenarios for an unconventional spin triplet superconductor.

Pairing state at an interface of Sr2RuO4: parity-mixing, restored time-reversal symmetry and topological superconductivity

We investigate pairing states realized at the (001) interface of a spin-triplet superconductor Sr2RuO4 on the basis of microscopic calculations. Because of a Rashba-type spin–orbit interaction induced at the interface, strong parity-mixing of Cooper pairs between a spin-singlet state and a spin-triplet state occurs in this system. There are also strong inter-band pair correlations between the spin–orbit split bands, in spite of the considerably large spin–orbit splitting. This is due to frustration between the spin–orbit interaction and pairing interactions. In this pairing state, time-reversal symmetry is restored, in contrast to the bulk Sr2RuO4, which is believed to be a chiral p+ip superconductor with broken time-reversal symmetry. It is demonstrated that, because of these features, the pairing state at the interface is a promising candidate for the recently proposed time-reversal invariant topological superconductor.

Unusual temperature dependence of the in-plane critical field in Sr2RuO4

We have studied the upper critical field Hc2 of the spin-triplet superconductor Sr2RuO4. For H || c, Hc2 increases linearly with decreasing temperature down to well below Tc = 1.5 K, consistent with the orbital depairing effect. However, for H || ab, the increase of Hc2 is strongly suppressed below 1 K. The origin of this in-plane Hc2 limit has been actively discussed, but its mechanism is still unclear. In the present study, we performed ac susceptibility measurements in the applied fields with higher accuracy than in previous studies to obtain the field-temperature phase diagrams for H || c and H || ab. We revealed that Hc2 || ab (T) does not exhibit a linear temperature dependence even above 1 K, which indicates that the Hc2 suppression is operative even close to Tc. In addition, we found that the Hc2 anisotropy ratio Hc2 || ab/Hc2 || c decreases monotonically from 60 to 20 with decreasing temperature.

Observation of vortex coalescence, vortex chains and crossing vortices in the anisotropic spin-triplet superconductor Sr2RuO4

Scanning μSQUID force microscopy is used to study magnetic flux structures in single crystals of the layered spin-triplet superconductor Sr2RuO4. Images of the magnetic flux configuration above the a→b→-face of the cleaved crystal are acquired, mostly after field-cooling the sample. For low applied magnetic fields, individual vortices are observed, each carrying a single quantum of flux. Above 1G, coalescence of vortices is discovered. The coalescing vortices may indicate the presence of domains of a chiral order parameter.When the applied field is tilted from the c→-axis, we observe a gradual transition from vortex domains to vortex chains. The in-plane component of the applied magnetic field transforms the vortex domains to vortex chains by aligning them along the field direction.This behavior and the inter-chain distance varies in qualitative agreement with the Ginzburg–Landau theory of anisotropic 3D superconductors. The effective mass anisotropy of Sr2RuO4, γ=20, is the highest observed in three-dimensional superconductors.When the applied field is closely in-plane, the vortex form flux channels confined between the crystal-layers. Residual Abrikosov vortices are pinned preferentially on these channels. Thus the in-plane vortices are decorated by crossing Abrikosov vortices: two vortex orientations are apparent simultaneously, one along the layers and the other perpendicular to the layers.

High Resolution Polar Kerr Effect Measurements ofSr2RuO4: Evidence for Broken Time-Reversal Symmetry in the Superconducting State

The polar Kerr effect in the spin-triplet superconductor Sr2RuO4 was measured with high precision using a Sagnac interferometer with a zero-area Sagnac loop. We observed nonzero Kerr rotations as big as 65 nanorad appearing below Tc in large domains. Our results imply a broken time-reversal symmetry state in the superconducting state of Sr2RuO4, similar to 3He-A.