Spectroscopic evidence for multiple order parameter components in the heavy fermion superconductor CeCoIn5

Critical analysis of soft point contact Andreev reflection spectra between superconducting films and pressed In

We present a critical analysis of an alternative technique of point contact Andreev reflection (PCAR) spectroscopy used to extract energy resolved information of superconductors which is based on making 'soft-contacts' between superconductors and indium. This technique is not sensitive to mechanical vibrations and hence can be used in a cryogen free platform increasing its accessibility to users having no access to cryogenic liquids. Through our experiments on large number of superconducting films we show that the PCAR spectra below the T _c of In show sub-harmonic gap structures consistent with the theory of multiple Andreev reflection (MAR) and a zero bias conductance (ZBC) anomaly associated with the Josephson supercurrent. Furthermore, we demonstrate that large contact resistance with low transparency ballistic contacts in the PCAR regime are required to obtain reliable spectroscopic data. One limitation of the technique arises for low contact resistance junctions where the superconducting proximity effect (SPE) reduces the value of the superconducting energy gap.

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.

Nodal to nodeless superconducting energy-gap structure change concomitant with fermi-surface reconstruction in the heavy-fermion compound CeCoIn(5)

The London penetration depth λ(T) was measured in single crystals of Ce_{1-x}R_{x}CoIn_{5}, R=La, Nd, and Yb down to T_{min}≈50  mK (T_{c}/T_{min}∼50) using a tunnel-diode resonator. In the cleanest samples Δλ(T) is best described by the power law Δλ(T)∝T^{n}, with n∼1, consistent with the existence of line nodes in the superconducting gap. Substitutions of Ce with La, Nd, and Yb lead to similar monotonic suppressions of T_{c}; however, the effects on Δλ(T) differ. While La and Nd substitution leads to an increase in the exponent n and saturation at n∼2, as expected for a dirty nodal superconductor, Yb substitution leads to n>3, suggesting a change from nodal to nodeless superconductivity. This superconducting gap structure change happens in the same doping range where changes of the Fermi-surface topology were reported, implying that the nodal structure and Fermi-surface topology are closely linked.

Multi-channel Andreev reflection in Co-W nanocontacts fabricated using focused electron/ion beam induced deposition

We report multi-channel electron transport in nano-contacts fabricated using focused electron beam induced deposited (FEBID) cobalt and focused ion beam induced deposited (FIBID) tungsten. Anomalous Andreev reflection (AR) effect is observed to which the conventional Blonder-Tinkham-Klapwijk (BTK) fit cannot be applied. In specific, we have observed multiple number of shoulders near the AR peak, whose origin is unknown in literature. We explain this effect based on a simple model that takes into account the material properties of the FIBID grown W superconductor, as well as the specific interface properties that are an outcome of using FEBID/FIBID as a fabrication technique. We show that numerical calculations using the BTK approximation based on the consideration of multiple channels generate similar shoulders as we observed in the AR experiments. Electrical measurements and x-ray photoemission spectroscopy carried out on FIBID W deposits puts additional evidence towards multi-channel current transport occuring at the interface of the nanocontacts.

Magnetic field splitting of the spin resonance in CeCoIn5

Neutron scattering in strong magnetic fields is used to show the spin resonance in superconducting CeCoIn(5) (T(c)=2.3 K) is a doublet. The underdamped resonance (ħΓ=0.069±0.019 meV) Zeeman splits into two modes at E(±)=ħΩ(0)±αμ(B)μ(0)H with α=0.96±0.05. A linear extrapolation of the lower peak reaches zero energy at 11.2±0.5 T, near the critical field for the incommensurate "Q phase." Kenzelmann et al. [Science 321, 1652 (2008)] This, taken with the integrated weight and polarization of the low-energy mode (E(-)), indicates that the Q phase can be interpreted as a Bose condensate of spin excitons.

Superconducting gap structure of the 115s revisited

Density functional theory calculations of the electronic structure of Ce- and Pu-based heavy fermion superconductors in the so-called 115 family are performed. The gap equation is used to consider which superconducting order parameters are most favorable assuming a pairing interaction that is peaked at (π, π, qz)—the wavevector for the antiferromagnetic ordering found in close proximity. In addition to the commonly accepted dx2−y2 order parameter, there is evidence that an extended s-wave order parameter with nodes is also plausible. We discuss whether these results are consistent with current observations and possible measurements that could help distinguish between these scenarios.

New anomaly in the transverse acoustic impedance of superfluid 3He-B with a wall coated by several layers of 4He

We measured the transverse acoustic impedance of superfluid 3He-B with a wall coated by several layers of 4He. The coating is known to enhance the specularity in quasiparticle scattering by the wall. We found a new anomaly, a bump and a peak, in the temperature dependence of the transverse acoustic impedance. This agrees with a theoretical calculation using a partially specular wall boundary condition. The new anomaly is shown to arise from a change in the surface density of states by coating and the scattering of thermally occupied surface bound states to other states. The change is towards the density of states of Majorana cone in the specular limit.

Andreev reflection and order parameter symmetry in heavy-fermion superconductors: the case of CeCoIn(5)

We review the current status of Andreev reflection spectroscopy on the heavy fermions, mostly focusing on the case of CeCoIn(5), a heavy-fermion superconductor with a critical temperature of 2.3 K. This is a well-established technique to investigate superconducting order parameters via measurements of the differential conductance from nanoscale metallic junctions. Andreev reflection is clearly observed in CeCoIn(5) as in other heavy-fermion superconductors. Considering the large mismatch in Fermi velocities, this observation seemingly appears to disagree with the Blonder-Tinkham-Klapwijk (BTK) theory. The measured Andreev signal is highly reduced to the order of maximum ∼13% compared to the theoretically predicted value (100%). The background conductance exhibits a systematic evolution in its asymmetry over a wide temperature range from above the heavy-fermion coherence temperature down to well below the superconducting transition temperature. Analysis of the conductance spectra using the extended BTK model provides a qualitative measure for the superconducting order parameter symmetry, which is determined to be the d(x(2)-y(2)) wave in CeCoIn(5). It is found that existing models do not quantitatively account for the data, which we attribute to the intrinsic properties of the heavy fermions. A substantial body of experimental data and extensive theoretical analysis point to the existence of two-fluid components in CeCoIn(5) and other heavy-fermion compounds. A phenomenological model is proposed employing a Fano interference effect between two conductance channels in order to explain both the conductance asymmetry and the reduced Andreev signal. This model appears plausible not only because it provides good fits to the data but also because it is highly likely that the electrical conduction occurs via two channels, one into the heavy-electron liquid and the other into the conduction electron continuum. Further experimental and theoretical investigations will shed new light on the mechanism of how the coherent heavy-electron liquid emerges out of the Kondo lattice, a prototypical strongly correlated electron system. Unresolved issues and future directions are also discussed.

Superfluid density in gapless superconductor CeCoIn(5)

Temperature dependence of the London penetration depth λ measured in single crystals of CeCoIn(5) is interpreted as being caused by a strong pair-breaking scattering that makes the superconductivity in this compound gapless. For a gapless d-wave superconductor, we derive λ = λ(0)(1-T(2)/T(c)(2))(-1/2) caused by the combined effect of magnetic and non-magnetic scattering, in excellent agreement with the data in the full temperature range and with the gapless s-wave case of Abrikosov and Gor'kov. We also obtain the slope of the upper critical field at T(c) that compares well with the measured slope.

Multigap superconductivity in the heavy-Fermion system CeCoIn5

New thermal conductivity experiments on the heavy-fermion superconductor CeCoIn5 down to 10 mK rule out the suggested existence of unpaired electrons. Moreover, they reveal strong multigap effects with a remarkably low "critical" field Hc2S for the small gap band, showing that the complexity of heavy-fermion band structure has a direct impact on their response under magnetic field.

Spin resonance in the d-wave superconductor CeCoIn5

Neutron scattering is used to probe antiferromagnetic spin fluctuations in the d-wave heavy fermion superconductor CeCoIn5 (T_(c)=2.3 K). Superconductivity develops from a state with slow (variant Planck's over 2piGamma=0.3+/-0.15 meV) commensurate [Q_(0)=(1/2,1/2,1/2)] antiferromagnetic spin fluctuations and nearly isotropic spin correlations. The characteristic wave vector in CeCoIn5 is the same as CeIn3 but differs from the incommensurate wave vector measured in antiferromagnetically ordered CeRhIn5. A sharp spin resonance (variant Planck's over 2piGamma<0.07 meV) at variant Planck's over 2piomega=0.60+/-0.03 meV develops in the superconducting state removing spectral weight from low-energy transfers. The presence of a resonance peak is indicative of strong coupling between f-electron magnetism and superconductivity and consistent with a d-wave gap order parameter satisfying Delta(q+Q0)=-Delta(q).

Theory of tunneling spectroscopy in the Larkin-Ovchinnikov state

We present a theory of tunneling spectroscopy for normal metal/Larkin-Ovchinnikov state junctions in which the spatial periodic modulation in the pair potential amplitude is taken into account. The tunneling spectra show the characteristic line shapes reflecting the minigap structures under the periodic pair potentials depending on the boundary condition of the pair potentials at the junction interface. These features are qualitatively different from the tunneling spectra of the Fulde-Ferrell state. We propose an experimental setup which identifies the superconducting state of CeCoIn5.

Fulde-Ferrell-Larkin-Ovchinnikov state in a perpendicular field of quasi-two-dimensional CeCoIn5

A Fulde-Ferrell-Larkin-Ovchinnkov (FFLO) state was previously reported in the quasi-2D heavy fermion CeCoIn5 when a magnetic field was applied parallel to the ab plane. Here, we conduct 115In NMR studies of this material in a perpendicular field, and provide strong evidence for FFLO in this case as well. Although the topology of the phase transition lines in the H-T phase diagram is identical for both configurations, there are several remarkable differences between them. Compared to H parallelab, the FFLO phase for H perpendicularab is confined in a much narrower region at the low-T-high-H corner in the H-T plane, and the critical field separating the FFLO and non-FFLO superconducting states almost ceases to have a temperature dependence. Moreover, directing H perpendicularab results in a notable change in the quasiparticle excitation spectrum within the planar node associated with the FFLO transition.

Field dependent coherence length in the superclean, high-kappa superconductor CeCoIn5

Using small-angle neutron scattering, we have studied the flux-line lattice (FLL) in the superclean, high-kappa superconductor CeCoIn5. The FLL undergoes a first-order symmetry and reorientation transition at approximately 0.55 T at 50 mK. In addition, the FLL form factor in this material is found to be independent of the applied magnetic field, in striking contrast to the exponential decrease usually observed in superconductors. This result is consistent with a strongly field-dependent coherence length, proportional to the vortex separation.

Unpaired electrons in the heavy-fermion superconductor CeCoIn5

Thermal conductivity and specific heat were measured in the superconducting state of the heavy-fermion material Ce(1-x)La(x)CoIn5. With increasing impurity concentration x, the suppression of T(c) is accompanied by the increase in residual electronic specific heat expected of a d-wave superconductor, but it occurs in parallel with a decrease in residual electronic thermal conductivity. This contrasting behavior reveals the presence of uncondensed electrons coexisting with nodal quasiparticles. An extreme multiband scenario is proposed, with a d-wave superconducting gap on the heavy-electron sheets of the Fermi surface and a negligible gap on the light, three-dimensional pockets.