Time-reversal symmetry-breaking superconductivity in heavy-fermion PrOs4Sb12 detected by muon-spin relaxation

Unconventional superconductivity in topological Kramers nodal-line semimetals

Crystalline symmetry is a defining factor of the electronic band topology in solids, where many-body interactions often induce a spontaneous breaking of symmetry. Superconductors lacking an inversion center are among the best systems to study such effects or even to achieve topological superconductivity. Here, we demonstrate that TRuSi materials (with T a transition metal) belong to this class. Their bulk normal states behave as three-dimensional Kramers nodal-line semimetals, characterized by large antisymmetric spin-orbit couplings and by hourglass-like dispersions. Our muon-spin spectroscopy measurements show that certain TRuSi compounds spontaneously break the time-reversal symmetry at the superconducting transition, while unexpectedly showing a fully gapped superconductivity. Their unconventional behavior is consistent with a unitary (s + ip) pairing, reflecting a mixture of spin singlets and spin triplets. By combining an intrinsic time-reversal symmetry-breaking superconductivity with nontrivial electronic bands, TRuSi compounds provide an ideal platform for investigating the rich interplay between unconventional superconductivity and the exotic properties of Kramers nodal-line/hourglass fermions.

Distinct Kondo Screening Behaviors in Heavy Fermion Filled Skutterudites with 4f^{1} and 4f^{2} Configurations

CeOs_{4}Sb_{12} (COS) and PrOs_{4}Sb_{12} (POS) are two representative compounds that provide the ideal vantage point to systematically study the physics of multi-f-electron systems. COS with Ce 4f^{1}, and POS with Pr 4f^{2} configurations show distinct properties of Kondo insulating and heavy fermion superconductivity, respectively. We unveiled the underlying microscopic origin by angle-resolved photoemission spectroscopy studies. Their eV-scale band structure matches well, representing the common characters of conduction electrons in ROs_{4}Sb_{12} systems (R=rare earth). However, f electrons interact differently with conduction electrons in COS and POS. Strong hybridization between conduction electrons and f electrons is observed in COS with band dependent hybridization gaps, and the development of a Kondo insulating state is directly revealed. Although the ground state of POS is a singlet, finite but incoherent hybridization exists, which can be explained by the Kondo scattering with the thermally excited triplet crystalline electric field state. Our results help us to understand the intriguing properties in COS and POS, and provide a clean demonstration of the microscopic differences in heavy fermion systems with 4f^{1} and 4f^{2} configurations.

Recent progress on superconductors with time-reversal symmetry breaking

Superconductivity and magnetism are adversarial states of matter. The presence of spontaneous magnetic fields inside the superconducting state is, therefore, an intriguing phenomenon prompting extensive experimental and theoretical research. In this review, we discuss recent experimental discoveries of unconventional superconductors which spontaneously break time-reversal symmetry and theoretical efforts in understanding their properties. We discuss the main experimental probes and give an extensive account of theoretical approaches to understand the order parameter symmetries and the corresponding pairing mechanisms, including the importance of multiple bands.

Transport and Point Contact Measurements on Pr1-xCexPt4Ge12 Superconducting Polycrystals

We performed a detailed investigation of the superconducting properties of polycrystalline Pr1-xCexPt4Ge12 pellets. We report the effect of Ce substitution, for x = 0.07, on magnetic field phase diagram H-T. We demonstrate that the upper critical field is well described by the Ginzburg-Landau model and that the irreversibility field line has a scaling behaviour similar to cuprates. We also show that for magnetic fields lower than 0.4 T, the activation energy follows a power law of the type ?-1/2, suggesting a collective pinning regime with a quasi-2D character for the Ce-doped compound with x = 0.07. Furthermore, by means of a point contact Andreev reflection spectroscopy setup, we formed metal/superconductor nano-junctions as small as tens of nanometers on the PrPt4Ge12 parent compound (x = 0). Experimental results showed a wide variety of conductance features appearing in the dI/dV vs. V spectra, all explained in terms of a modified Blonder-Tinkham-Klapwijk model considering a superconducting order parameter with nodal directions as well as sign change in the momentum space for the sample with x = 0. The numerical simulations of the conductance spectra also demonstrate that s-wave pairing and anisotropic s-waves are unsuitable for reproducing experimental data obtained at low temperature on the un-doped compound. Interestingly, we show that the polycrystalline nature of the superconducting PrPt4Ge12 sample can favour the formation of an inter-grain Josephson junction in series with the point contact junction in this kind of experiments.

Simultaneous Nodal Superconductivity and Time-Reversal Symmetry Breaking in the Noncentrosymmetric Superconductor CaPtAs

By employing a series of experimental techniques, we provide clear evidence that CaPtAs represents a rare example of a noncentrosymmetric superconductor which simultaneously exhibits nodes in the superconducting gap and broken time-reversal symmetry (TRS) in its superconducting state (below T_{c}≈1.5  K). Unlike in fully gapped superconductors, the magnetic penetration depth λ(T) does not saturate at low temperatures, but instead it shows a T^{2} dependence, characteristic of gap nodes. Both the superfluid density and the electronic specific heat are best described by a two-gap model comprising of a nodeless gap and a gap with nodes, rather than by single-band models. At the same time, zero-field muon-spin relaxation spectra exhibit increased relaxation rates below the onset of superconductivity, implying that TRS is broken in the superconducting state of CaPtAs, hence indicating its unconventional nature. Our observations suggest CaPtAs to be a new remarkable material that links two apparently disparate classes, that of TRS-breaking correlated magnetic superconductors with nodal gaps and the weakly correlated noncentrosymmetric superconductors with broken TRS, normally exhibiting only a fully gapped behavior.

Symmetry of Order Parameters in Multiband Superconductors LaRu_{4}As_{12} and PrOs_{4}Sb_{12} Probed by Local Magnetization Measurements

The temperature dependencies of the lower critical field H_{c1}(T) of several filled-skutterudite superconductors were investigated by local magnetization measurements. While LaOs_{4}As_{12} and PrRu_{4}As_{12} exhibit the H_{c1}(T) dependencies consistent with the single-band BCS prediction, for LaRu_{4}As_{12} (the superconducting temperature T_{c}=10.4  K) with a similar three-dimensional Fermi surface, we observe a sudden increase in H_{c1}(T) deep in a superconducting state below about 0.32T_{c}. Remarkably, a rapid rise of H_{c1}(T) at approximately the same reduced temperature 0.27T_{c} is also found for the heavy-fermion compound PrOs_{4}Sb_{12} (T_{c}≃1.78  K), in fair accord with the earlier macroscopic study. We attribute the unusual H_{c1}(T) dependencies of LaRu_{4}As_{12} and PrOs_{4}Sb_{12} to a kink structure in their superfluid densities due to different contributions from two nearly decoupled bands. Whereas LaRu_{4}As_{12} is established as a two-band isotropic s-wave superconductor, nonsaturating behavior of H_{c1}(T) is observed for PrOs_{4}Sb_{12}, indicative of an anisotropic structure of a smaller gap. For this superconductor with broken time-reversal symmetry, our findings suggest a superconducting state with multiple symmetries of the order parameters.

Nodeless s-wave superconductivity in the [Formula: see text]-Mn structure type noncentrosymmetric superconductor TaOs: a [Formula: see text]SR study

Noncentrosymmetric superconductors can lead to a variety of exotic properties in the superconducting state such as line nodes, multigap behavior, and time-reversal symmetry breaking. In this paper, we report the properties of a new noncentrosymmetric superconductor TaOs, using muon spin relaxation and rotation measurements. It is shown using the zero-field muon experiment that TaOs preserve the time-reversal symmetry in the superconducting state. From the transverse field muon measurements, we extract the temperature dependence of [Formula: see text], which is proportional to the superfluid density. This data can be fit with a fully gapped s-wave model for [Formula: see text]  =  2.01 [Formula: see text] 0.02. Furthermore, the value of magnetic penetration depth is found to be 5919 [Formula: see text] 45 [Formula: see text], which is consistent with the value obtained from the bulk measurements.

Time Reversal Symmetry Breaking Superconductors: Sr2RuO4 and Beyond

Recent work done on the time reversal symmetry (TRS) breaking superconductors is reviewed in this paper. The special attention is paid to Sr 2 RuO 4 believed to be spin triplet chiral p-wave superconductor which break TRS and is expected to posses non-trivial topological properties. The family of TRS breaking superconductors is growing relatively fast, with many of its newly discovered members being non-centrosymmetric. However not only Sr 2 RuO 4 but also many other superconductors which possess center of inversion also break TRS. The TRS is often identified by means of the muon spin relaxation ( μ SR) and the Kerr effect. Both methods effectively measure the appearance of the spontaneous bulk magnetic field below superconducting transition temperature. This compound provides an example of the material whose many band, multi-condensate modeling has enjoyed a number of successes, but the full understanding has not been achieved yet. We discuss in some details the properties of the material. Among them is the Kerr effect and by understanding has resulted in the discovery of the novel mechanism of the phenomenon. The mechanism is universal and thus applicable to all systems with multi-orbital character of states at the Fermi energy.

Time-Reversal Symmetry Breaking in Re-Based Superconductors

To trace the origin of time-reversal symmetry breaking (TRSB) in Re-based superconductors, we performed comparative muon-spin rotation and relaxation (μSR) studies of superconducting noncentrosymmetric Re_{0.82}Nb_{0.18} (T_{c}=8.8  K) and centrosymmetric Re (T_{c}=2.7  K). In Re_{0.82}Nb_{0.18}, the low-temperature superfluid density and the electronic specific heat evidence a fully gapped superconducting state, whose enhanced gap magnitude and specific-heat discontinuity suggest a moderately strong electron-phonon coupling. In both Re_{0.82}Nb_{0.18} and pure Re, the spontaneous magnetic fields revealed by zero-field μSR below T_{c} indicate time-reversal symmetry breaking and thus unconventional superconductivity. The concomitant occurrence of TRSB in centrosymmetric Re and noncentrosymmetric ReT (T=transition metal), yet its preservation in the isostructural noncentrosymmetric superconductors Mg_{10}Ir_{19}B_{16} and Nb_{0.5}Os_{0.5}, strongly suggests that the local electronic structure of Re is crucial for understanding the TRSB superconducting state in Re and ReT. We discuss the superconducting order parameter symmetries that are compatible with the experimental observations.

Thermal transport studies on charge density wave materials LaPt2Si2 and PrPt2Si2

We measured the thermal properties of polycrystalline samples of LaPt₂Si₂ and PrPt₂Si₂ using thermopower (S) along with thermal conductivity (κ) in the temperature range 10 K-300 K. Significant anomalies related to charge density waves (CDW) around 112 K and 88 K respectively have been observed in [Formula: see text] in both systems. Analysis of thermopower by a two band model suggests that the observations are consistent with a reduction of electron charge density. A change in slope accompanied by a drop in the value of thermal conductivity has been observed around T _CDW in case of LaPt₂Si₂. Analysis of thermal conductivity of this material suggests that the CDW mainly affects electronic contribution to thermal transport. Only a slight change of slope has been detected in temperature dependent thermal conductivity in the case of PrPt₂Si₂ around T _CDW, while its resistivity shows a clear anomaly which shows that electronic part of thermal conductivity is mainly influenced by the CDW in this case also. It is interesting to note that the lattice contribution to thermal conductivity remains unaffected by the CDWs in both materials.

Polar Kerr Effect from Time-Reversal Symmetry Breaking in the Heavy-Fermion Superconductor PrOs_{4}Sb_{12}

We present polar Kerr effect measurements of the filled skutterudite superconductor PrOs_{4}Sb_{12}. Simultaneous ac susceptibility measurements allow us to observe the superconducting transition under the influence of heating from the optical beam. A nonzero Kerr angle θ_{K} develops below the superconducting transition, saturating at ∼300  nrad at low temperatures. This result is repeated across several measurements of multiple samples. By extrapolating the measured θ_{K}(T) to zero optical power, we are able to show that the Kerr angle onset temperature in one set of measurements is consistent with the transition to the B phase at T_{C2}. We discuss the possible explanations for this result and its impact on the understanding of multiphase and inhomogeneous superconductivity in PrOs_{4}Sb_{12}.

Discovery of slow magnetic fluctuations and critical slowing down in the pseudogap phase of YBa2Cu3O y

The origin of the pseudogap region below a temperature T* is at the heart of the mysteries of cuprate high-temperature superconductors. Unusual properties of the pseudogap phase, such as broken time-reversal and inversion symmetry are observed in several symmetry-sensitive experiments: polarized neutron diffraction, optical birefringence, dichroic angle-resolved photoemission spectroscopy, second harmonic generation, and polar Kerr effect. These properties suggest that the pseudogap region is a genuine thermodynamic phase and are predicted by theories invoking ordered loop currents or other forms of intra-unit-cell (IUC) magnetic order. However, muon spin rotation (μSR) and nuclear magnetic resonance (NMR) experiments do not see the static local fields expected for magnetic order, leaving room for skepticism. The magnetic resonance probes have much longer time scales, however, over which local fields could be averaged by fluctuations. The observable effect of the fluctuations in magnetic resonance is then dynamic relaxation. We have measured dynamic muon spin relaxation rates in single crystals of YBa₂Cu₃O _y (6.72 < y < 6.95) and have discovered "slow" fluctuating magnetic fields with magnitudes and fluctuation rates of the expected orders of magnitude that set in consistently at temperatures T_mag ≈ T*. The absence of any static field (to which μSR would be linearly sensitive) is consistent with the finite correlation length from neutron diffraction. Equally important, these fluctuations exhibit the critical slowing down at T_mag expected near a time-reversal symmetry breaking transition. Our results explain the absence of static magnetism and provide support for the existence of IUC magnetic order in the pseudogap phase.

Superconducting gap structure in the electron doped BiS2-based superconductor

The influence of electron doping on semimetallic SrFBiS₂ has been investigated by means of resistivity, zero and transverse  -  field (ZF/TF) muon spin relaxation/rotation (μSR) experiments. SrFBiS₂ is semimetallic in its normal state and small amounts of La doping results in bulk superconductivity at 2.8 K, at ambient pressure. The temperature dependence of the superfluid density as determined by TF-μSR can be best modelled by an isotropic s  -  wave type superconducting gap. We have estimated the magnetic penetration depth [Formula: see text] nm, superconducting carrier density [Formula: see text] carriers m^-3 and effective-mass enhancement m ^*  =  1.558 m _e. Additionally, there is no clear sign of the occurrence of spontaneous internal magnetic fields below [Formula: see text], which implies that the superconducting state in this material can not be categorized by the broken time-reversal symmetry which is in agreement with the previous theoretical prediction.

Bogoliubov Fermi Surfaces in Superconductors with Broken Time-Reversal Symmetry

It is commonly believed that, in the absence of disorder or an external magnetic field, there are three possible types of superconducting excitation gaps: The gap is nodeless, it has point nodes, or it has line nodes. Here, we show that, for an even-parity nodal superconducting state which spontaneously breaks time-reversal symmetry, the low-energy excitation spectrum generally does not belong to any of these categories; instead, it has extended Bogoliubov Fermi surfaces. These Fermi surfaces can be visualized as two-dimensional surfaces generated by "inflating" point or line nodes into spheroids or tori, respectively. These inflated nodes are topologically protected from being gapped by a Z_{2} invariant, which we give in terms of a Pfaffian. We also show that superconducting states possessing these Fermi surfaces can be energetically stable. A crucial ingredient in our theory is that more than one band is involved in the pairing; since all candidate materials for even-parity superconductivity with broken time-reversal symmetry are multiband systems, we expect these Z_{2}-protected Fermi surfaces to be ubiquitous.

Three-dimensional Majorana fermions in chiral superconductors

Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum J formed by Bloch electrons with angular momentum j in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs4Sb12 and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions.

Theory of Andreev reflection spectroscopy for tetrahedral and non-unitary superconductors

A general formula for point contact conductance from a normal metal tip into a superconductor is derived using the Blonder-Tinkham-Klapwijk theory of Andreev reflection, with special emphasis on non-unitary superconductors. The results of a comprehensive set of conductance spectrum calculations are presented: all symmetry-allowed gap functions for superconductors with tetrahedral symmetry, such as PrOs4Sb12, are considered, including several non-unitary cases.

Unconventional Superconductivity in La(7)Ir(3) Revealed by Muon Spin Relaxation: Introducing a New Family of Noncentrosymmetric Superconductor That Breaks Time-Reversal Symmetry

The superconductivity of the noncentrosymmetric compound La(7)Ir(3) is investigated using muon spin rotation and relaxation. Zero-field measurements reveal the presence of spontaneous static or quasistatic magnetic fields below the superconducting transition temperature T(c)=2.25  K-a clear indication that the superconducting state breaks time-reversal symmetry. Furthermore, transverse-field rotation measurements suggest that the superconducting gap is isotropic and that the pairing symmetry of the superconducting electrons is predominantly s wave with an enhanced binding strength. The results indicate that the superconductivity in La(7)Ir(3) may be unconventional and paves the way for further studies of this family of materials.

Unconventional superconductivity in Y5Rh6Sn18 probed by muon spin relaxation

Conventional superconductors are robust diamagnets that expel magnetic fields through the Meissner effect. It would therefore be unexpected if a superconducting ground state would support spontaneous magnetics fields. Such broken time-reversal symmetry states have been suggested for the high—temperature superconductors, but their identification remains experimentally controversial. We present magnetization, heat capacity, zero field and transverse field muon spin relaxation experiments on the recently discovered caged type superconductor Y₅Rh₆Sn₁₈ ( T_C= 3.0 K). The electronic heat capacity of Y₅Rh₆Sn₁₈ shows a T³ dependence below T_c indicating an anisotropic superconducting gap with a point node. This result is in sharp contrast to that observed in the isostructural Lu₅Rh₆Sn₁₈ which is a strong coupling s—wave superconductor. The temperature dependence of the deduced superfluid in density Y₅Rh₆Sn₁₈ is consistent with a BCS s—wave gap function, while the zero-field muon spin relaxation measurements strongly evidences unconventional superconductivity through a spontaneous appearance of an internal magnetic field below the superconducting transition temperature, signifying that the superconducting state is categorized by the broken time-reversal symmetry.

Detection of time-reversal symmetry breaking in the noncentrosymmetric superconductor Re6Zr using muon-spin spectroscopy

We have investigated the superconducting state of the noncentrosymmetric compound Re6Zr using magnetization, heat capacity, and muon-spin relaxation or rotation (μSR) measurements. Re6Zr has a superconducting transition temperature, Tc=6.75±0.05  K. Transverse-field μSR experiments, used to probe the superfluid density, suggest an s-wave character for the superconducting gap. However, zero and longitudinal-field μSR data reveal the presence of spontaneous static magnetic fields below Tc indicating that time-reversal symmetry is broken in the superconducting state and an unconventional pairing mechanism. An analysis of the pairing symmetries identifies the ground states compatible with time-reversal symmetry breaking.

Nonunitary triplet pairing in the centrosymmetric superconductor LaNiGa2

Muon spin rotation and relaxation experiments on the centrosymmetric intermetallic superconductor LaNiGa2 are reported. The appearance of spontaneous magnetic fields coincides with the onset of superconductivity, implying that the superconducting state breaks time reversal symmetry, similarly to noncentrosymmetric LaNiC2. Only four triplet states are compatible with this observation, all of which are nonunitary triplets. This suggests that LaNiGa2 is the centrosymmetric analogue of LaNiC2. We argue that these materials are representatives of a new family of paramagnetic nonunitary superconductors.

Quadrupolar waves in uranium dioxide

In presence of active orbital degrees of freedom, elementary excitations around a broken-symmetry state may include multipolar waves, but none of these exotic dispersive excitation branches has ever been identified. We show that quadrupolar waves constitute a major component of the dynamics of uranium dioxide in its magnetoquadrupolar ordered phase, and that many unexplained features in existing inelastic neutron scattering data, including a whole excitation branch, are associated with these propagating quadrupolar fluctuations. Our model permits us to separate the role of Jahn-Teller and superexchange mechanisms as sources of quadrupolar interactions.

Investigation of the heavy fermion state and superconductivity in Pr(1-x)La(x)Os4Sb12 by the upper critical field slope at Tc

Measurements of the upper critical field H(c2) near T(c) of Pr(1 - x)La(x)Os(4)Sb(12) were performed by specific heat. The results support the hypothesis of a non-single-ion origin of m* enhancement in PrOs(4)Sb(12), derived from the analysis of the C/T discontinuity at T(c). Both sets of measurements indicate the existence of a crossover concentration, x(cr)≈0.2-0.3, separating heavy fermion-like alloys (x < x(cr)) from normal metals (x > x(cr)). Heavy fermion-like alloys exhibit field-induced long-range antiferro-quadrupolar (AFQ) anomalies in the specific heat, while those with x > x(cr) do not. The curvature in H(c2) versus T near T(c), observed in different measurements on pure PrOs(4)Sb(12), is sample- and method-dependent.

Excitation spectrum of PrOs(4)Sb(12) under a magnetic field

The evolution of the magnetic excitation spectrum of the heavy fermion superconductor PrOs(4)Sb(12) was studied by inelastic neutron scattering on crossing the critical field H(c2) for superconductivity at low temperature. The peak positions in energy and the peak intensities of the modes of the triplet split by magnetic field confirm the known crystal field parameters for PrOs(4)Sb(12) in T(h) symmetry. A selective broadening of the lineshape occurs on increasing the magnetic field: the linewidth of the upper mode of the triplet increases while the one of the middle mode does not.

Evidence for time-reversal symmetry breaking in the noncentrosymmetric superconductor LaNiC2

Muon spin relaxation experiments on the noncentrosymmetric intermetallic superconductor LaNiC2 are reported. We find that the onset of superconductivity coincides with the appearance of spontaneous magnetic fields, implying that in the superconducting state time-reversal symmetry is broken. An analysis of the possible pairing symmetries suggests only four triplet states compatible with this observation, all of them nonunitary. They include the intriguing possibility of triplet pairing with the full point group symmetry of the crystal, which is possible only in a noncentrosymmetric superconductor.

Absence of broken time-reversal symmetry in the pseudogap state of the high temperature La(2-x)SrxCuO4 superconductor from muon-spin-relaxation measurements

We have performed zero-field muon-spin-relaxation measurements on single crystals of La(2-x)SrxCuO4 to search for spontaneous currents in the pseudogap state. By comparing measurements on materials across the phase diagram, we put strict upper limits on any possible time-reversal symmetry breaking fields that could be associated with the pseudogap. Comparison between experimental limits and the proposed circulating current states effectively eliminates the possibility that such states exist in this family of materials.

Time-reversal symmetry breaking by a (d+id) density-wave state in underdoped cuprate superconductors

It was proposed that the id(x(2)-y(2)) density-wave state (DDW) may be responsible for the pseudogap behavior in the underdoped cuprates. Here we show that the admixture of a small d(xy) component to the DDW state breaks the symmetry between the counterpropagating orbital currents of the DDW state and, thus, violates the macroscopic time-reversal symmetry. This symmetry breaking results in a nonzero polar Kerr effect, which has recently been observed in the pseudogap phase.

Direct observation of quadrupolar excitons in the heavy-fermion superconductor PrOs4Sb12

We report inelastic neutron scattering experiments performed to investigate the low energy magnetic excitations on single crystals of the heavy-fermion superconductor PrOs(4)Sb(12). The observed excitation clearly softens at a wave vector Q=(1,0,0), which is the same as the modulation vector of the field-induced antiferro-quadrupolar ordering, and its intensity at Q=(1,0,0) is smaller than that around the zone center. This result directly evidences that this excitonic behavior is derived mainly from nonmagnetic quadrupolar interactions. Furthermore, the narrowing of the linewidths of the excitations below the superconducting transition temperature indicates the close connection between the superconductivity and the excitons.

Pronounced enhancement of the lower critical field and critical current deep in the superconducting state of PrOs4Sb12

We have observed an unexpected enhancement of the lower critical field H(c1)(T) and the critical current I(c)(T) deep in the superconducting state below T approximately 0.6 K (T/T(c) approximately 0.3) in the filled skutterudite heavy fermion superconductor PrOs(4)Sb(12). From a comparison of the behavior of H(c1)(T) with that of the heavy fermion superconductors U(1-x)Th(x)Be(13) and UPt(3), we speculate that the enhancement of H(c1)(T) and I(c)(T) in PrOs(4)Sb(12) reflects a transition into another superconducting phase that occurs below T/T(c) approximately 0.3. An examination of the literature reveals unexplained anomalies in other physical properties of PrOs(4)Sb(12) near T/T(c) approximately 0.3 that correlate with the features we have observed in H(c1)(T) and I(c)(T).

Magnetic fluctuations of filled skutterudites emerging in the transition region between singlet and triplet states

In order to clarify magnetic properties of filled skutterudites, we analyze the Anderson model including seven f orbitals hybridized with an au conduction band using a numerical technique. For n=2 corresponding to Pr-based filled skutterudites, where n is the local f-electron number, even if the ground state is a singlet, there remain significant magnetic fluctuations from a triplet state with a small excitation energy. This result can be understood by the fact that f-electron states are clearly distinguished as itinerant and localized ones in the filled skutterudite structure. This picture also explains the complex results for f-electron magnetic susceptibility and entropy for n=1-13.

Flux-line lattice distortion in PrOs4Sb12

We report that the flux-line lattice in the cubic superconductor Pr(Os4Sb12 is strongly distorted from an ideal hexagonal lattice at very low temperatures in a small applied field. We attribute this to the presence of gap nodes in the superconducting state on at least some Fermi-surface sheets.

Vortex state in double transition superconductors

The novel vortex phase and nature of the double transition field are investigated by two-component Ginzburg-Landau theory in a situation where fourfold-twofold symmetric superconducting double transition occurs. The deformation from 60 degrees triangular vortex lattice and a possibility of the vortex sheet structure are discussed. In the presence of the gradient coupling, the transition changes to a crossover at finite field. These characters are important to identify the multiple superconducting phase in PrOs4Sb12.

Probing the superconducting gap symmetry of PrOs4Sb12: a penetration depth study

We report measurements of the magnetic penetration depth lambda in single crystals of PrOs4Sb12 down to 0.1 K, with the ac field applied along the a, b, and c directions. In all three field orientations, lambda approximately T2 and superfluid density rho(s) approximately T2 for T<0.3T(c). Data are best fit by the 3He A-phase-like gap with multidomains, each having two point nodes along a cube axis, and parameter Delta(0)(0)/k(B)T(c)=2.6, suggesting that PrOs4Sb12 is a strong-coupling superconductor with two point nodes on the Fermi surface. We also confirm the double transitions at 1.75 and 1.85 K seen in other measurements.