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

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.

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.

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.

Evidence for fully gapped strong coupling s-wave superconductivity in Bi4O4S3

We report on the superconducting gap and pairing symmetry in the layered superconductor Bi4O4S3. The measurement of temperature dependence of magnetic penetration depth was carried out using the tunnel diode oscillator technique. It is observed that Bi4O4S3 is a conventional s-wave type superconductor with a fully developed gap. The zero-temperature value of the superconducting energy gap Δ0 was found to be 1.54 meV, corresponding to the ratio 2Δ0/k(B)T(c) = 7.2 which is much higher than the BCS value of 3.53. In the superconducting range, superfluid density is very well described by the single gap s-wave model.

Superfluid density and energy gap function of superconducting PrPt4Ge12

The filled skutterudite superconductor PrPt4Ge12 was studied in muon-spin rotation (muSR), specific heat, and electrical resistivity experiments. The continuous increase of the superfluid density with decreasing temperature and the dependence of the magnetic penetration depth lambda on the magnetic field obtained by means of muSR, as well as the observation of a T3 dependence of the electronic specific heat indicate the presence of pointlike nodes in the superconducting energy gap. The gap and the specific heat are found to be well described by two models with point nodes, similar to results obtained for the unconventional heavy fermion skutterudite superconductor PrOs4Sb12.

Superconductivity and disorder in PrOs(4)Sb(12)

The specific heat, and dc and ac magnetic susceptibility are reported for a large single crystal of PrOs(4)Sb(12) and, after grinding, its powder. The physical properties of the crystal are typical of the majority of reported PrOs(4)Sb(12) samples. The room temperature effective paramagnetic moment of the crystal was consistent with the Pr(3+) ionic configuration and full (or nearly full) occupancy of the Pr sublattice. The crystal showed two distinct anomalies in the specific heat and an overall discontinuity in C/T of approximately 1000 mJ K(-2) mol(-1). The upper transition (at T(c1)) was characteristically rounded. The anomaly at T(c2) was very sharp, consistent with a good quality for the crystal. We observed a shoulder in χ(') and two peaks in χ('') below T(c1). However, there were no signatures in χ(') of the lower temperature transition. Grinding to powder size smaller than 50 µm completely suppresses the upper superconducting transition in both the specific heat and magnetic susceptibility. It also strongly reduces ΔC/T(c) at T(c2). Stress annealing brings back some of this lost ΔC/T(c) but does not restore the upper temperature transition. Possible explanations of the existence of two superconducting specific heat anomalies for single crystals are discussed.

Unconventional London penetration depth in single-crystal Ba(Fe0.93Co0.07)2As2 superconductors

The London penetration depth lambda(T) has been measured in single crystals of Ba(Fe0.93Co0.07)2As2. The observed low-temperature variation of lambda(T) follows a power law, Deltalambda(T) approximately T(n) with n approximately 2.4+/-0.1, indicating the existence of normal quasiparticles down to at least 0.02T(c). This is in contrast with previous penetration depth measurements on single crystals of NdFeAsO1-xFx and SmFeAsO1-xFx, which indicate an anisotropic but nodeless gap. We discuss possible explanations of the observed power law behavior.

Superconducting PrOs4Sb12: a thermal conductivity study

The superconducting state of the heavy fermion PrOs4Sb12 is studied by heat transport measurements on a highly homogeneous single crystal exhibiting only one transition peak in the specific heat. The field and temperature dependence of the thermal conductivity confirm multiband superconductivity and point to fully open gaps on the whole Fermi surface.

Multiband superconductivity in the heavy fermion compound PrOs4Sb12

The thermal conductivity of the heavy fermion superconductor Pr(Os(4)Sb(12) was measured down to T(c)/40 throughout the vortex state. At lowest temperatures and for magnetic fields H approximately 0.07H(c2), already 40% of the normal state thermal conductivity is restored. This behavior (similar to that observed in MgB2) is a clear signature of multiband superconductivity in this compound.

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).

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.