Microwave conductivity and penetration depth in the heavy fermion superconductor CeCoIn5

Observation of the non-linear Meissner effect

A long-standing theoretical prediction is that in clean, nodal unconventional superconductors the magnetic penetration depth λ, at zero temperature, varies linearly with magnetic field. This non-linear Meissner effect is an equally important manifestation of the nodal state as the well studied linear-in-T dependence of λ, but has never been convincingly experimentally observed. Here we present measurements of the nodal superconductors CeCoIn5 and LaFePO which clearly show this non-linear Meissner effect. We further show how the effect of a small dc magnetic field on λ(T) can be used to distinguish gap nodes from non-nodal deep gap minima. Our measurements of KFe2As2 suggest that this material has such a non-nodal state.

Dielectric resonator method for determining gap symmetry of superconductors through anisotropic nonlinear Meissner effect

We present a new measurement method which can be used to image the gap nodal structure of superconductors whose pairing symmetry is under debate. This technique utilizes a high quality factor microwave resonance involving the sample of interest. While supporting a circularly symmetric standing wave current pattern, the sample is perturbed by a scanned laser beam, creating a photoresponse that was previously shown to reveal the superconducting gap anisotropy. Simulation and the measurement of the photoresponse of an unpatterned Nb film show less than 8% anisotropy, as expected for a superconductor with a nearly isotropic energy gap along with expected systematic uncertainty. On the other hand, measurement of a YBa₂Cu₃O_7-δ thin film shows a clear 4-fold symmetric image with ∼12.5% anisotropy, indicating the well-known 4-fold symmetric d_x²-y² gap nodal structure in the ab-plane. The deduced gap nodal structure can be further cross-checked by low temperature surface impedance data, which are simultaneously measured. The important advantage of the presented method over the previous spiral resonator method is that it does not require a complicated lithographic patterning process which limits one from testing various kinds of materials due to photoresponse arising from patterning defects. This advantage of the presented technique, and the ability to measure unpatterned samples such as planar thin films and single crystals, enables one to survey the pairing symmetry of a wide variety of unconventional superconductors.

From Kondo lattices to Kondo superlattices

The realization of new classes of ground states in strongly correlated electron systems continues to be a major issue in condensed matter physics. Heavy fermion materials, whose electronic structure is essentially three-dimensional, are one of the most suitable systems for obtaining novel electronic states because of their intriguing properties associated with many-body effects. Recently, a state-of-the-art molecular beam epitaxy technique was developed to reduce the dimensionality of heavy electron systems by fabricating artificial superlattices that include heavy fermion compounds; this approach can produce a new type of electronic state in two-dimensional (2D) heavy fermion systems. In artificial superlattices of the antiferromagnetic heavy fermion compound CeIn3 and the conventional metal LaIn3, the magnetic order is suppressed by a reduction in the thickness of the CeIn3 layers. In addition, the 2D confinement of heavy fermions leads to enhancement of the effective electron mass and deviation from the standard Fermi liquid electronic properties, which are both associated with the dimensional tuning of quantum criticality. In the superconducting superlattices of the heavy fermion superconductor CeCoIn5 and nonmagnetic metal YbCoIn5, signatures of superconductivity are observed even at the thickness of one unit-cell layer of CeCoIn5. The most remarkable feature of this 2D heavy fermion superconductor is that the thickness reduction of the CeCoIn5 layers changes the temperature and angular dependencies of the upper critical field significantly. This result is attributed to a substantial suppression of the Pauli pair-breaking effect through the local inversion symmetry breaking at the interfaces of CeCoIn5 block layers. The importance of the inversion symmetry breaking in this system has also been supported by site-selective nuclear magnetic resonance spectroscopy, which can resolve spectroscopic information from each layer separately, even within the same CeCoIn5 block layer. In addition, recent experiments involving CeCoIn5/YbCoIn5 superlattices have shown that the degree of the inversion symmetry breaking and, in turn, the Rashba splitting are controllable, offering the prospect of achieving even more fascinating superconducting states. Thus, these Kondo superlattices pave the way for the exploration of unconventional metallic and superconducting states.

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.

Nodal quasiparticle dynamics in the heavy fermion superconductor CeCoIn₅ revealed by precision microwave spectroscopy

CeCoIn₅ is a heavy fermion superconductor with strong similarities to the high-Tc cuprates, including quasi-two-dimensionality, proximity to antiferromagnetism and probable d-wave pairing arising from a non-Fermi-liquid normal state. Experiments allowing detailed comparisons of their electronic properties are of particular interest, but in most cases are difficult to realize, due to their very different transition temperatures. Here we use low-temperature microwave spectroscopy to study the charge dynamics of the CeCoIn₅ superconducting state. The similarities to cuprates, in particular to ultra-clean YBa₂Cu₃O(y), are striking: the frequency and temperature dependence of the quasiparticle conductivity are instantly recognizable, a consequence of rapid suppression of quasiparticle scattering below T(c); and penetration-depth data, when properly treated, reveal a clean, linear temperature dependence of the quasiparticle contribution to superfluid density. The measurements also expose key differences, including prominent multiband effects and a temperature-dependent renormalization of the quasiparticle mass.

Do organic and other exotic superconductors fail universal scaling relations?

Universal scaling relations are of tremendous importance in science, as they reveal fundamental laws of nature. Several such scaling relations have recently been proposed for superconductors; however, they are not really universal in the sense that some important families of superconductors appear to fail the scaling relations, or obey the scaling with different scaling pre-factors. In particular, a large group of materials called organic (or molecular) superconductors are a notable example. Here, we show that such apparent violations are largely due to the fact that the required experimental parameters were collected on different samples, with different experimental techniques. When experimental data is taken on the same sample, using a single experimental technique, organic superconductors, as well as all other studied superconductors, do in fact follow universal scaling relations.

Anomalous superfluid density in quantum critical superconductors

When a second-order magnetic phase transition is tuned to zero temperature by a nonthermal parameter, quantum fluctuations are critically enhanced, often leading to the emergence of unconventional superconductivity. In these "quantum critical" superconductors it has been widely reported that the normal-state properties above the superconducting transition temperature T(c) often exhibit anomalous non-Fermi liquid behaviors and enhanced electron correlations. However, the effect of these strong critical fluctuations on the superconducting condensate below T(c) is less well established. Here we report measurements of the magnetic penetration depth in heavy-fermion, iron-pnictide, and organic superconductors located close to antiferromagnetic quantum critical points, showing that the superfluid density in these nodal superconductors universally exhibits, unlike the expected T-linear dependence, an anomalous 3/2 power-law temperature dependence over a wide temperature range. We propose that this noninteger power law can be explained if a strong renormalization of effective Fermi velocity due to quantum fluctuations occurs only for momenta k close to the nodes in the superconducting energy gap Δ(k). We suggest that such "nodal criticality" may have an impact on low-energy properties of quantum critical superconductors.

Electronic tuning and uniform superconductivity in CeCoIn5

We report a globally reversible effect of electronic tuning on the magnetic phase diagram in CeCoIn(5) driven by electron (Pt and Sn) and hole (Cd, Hg) doping. Consequently, we are able to extract the superconducting pair breaking component for hole and electron dopants with pressure and codoping studies, respectively. We find that these nominally nonmagnetic dopants have a remarkably weak pair breaking effect for a d-wave superconductor. The pair breaking is weaker for hole dopants, which induce magnetic moments, than for electron dopants. Furthermore, both Pt and Sn doping have a similar effect on superconductivity despite being on different dopant sites, arguing against the notion that superconductivity lives predominantly in the CeIn(3) planes of these materials. In addition, we shed qualitative understanding on the doping dependence with density functional theory calculations.

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.

Microwave surface-impedance measurements of the magnetic penetration depth in single crystal Ba1-xKxFe2As2 superconductors: evidence for a disorder-dependent superfluid density

We report high-sensitivity microwave measurements of the in-plane penetration depth lambda_{ab} and quasiparticle scattering rate 1/tau in several single crystals of the hole-doped Fe-based superconductor Ba(1-x)K(x)Fe(2)As(2) (x approximately 0.55). While a power-law temperature dependence of lambda_{ab} with a power approximately 2 is found in crystals with large 1/tau, we observe an exponential temperature dependence of the superfluid density consistent with the existence of fully opened two gaps in the cleanest crystal we studied. The difference may be a consequence of different levels of disorder inherent in the crystals. We also find a linear relation between the low-temperature scattering rate and the density of quasiparticles, which shows a clear contrast to the case of d-wave cuprate superconductors with nodes in the gap. These results demonstrate intrinsically nodeless order parameters in the Fe arsenides.

Microwave penetration depth and quasiparticle conductivity of PrFeAsO1-y single crystals: evidence for a full-gap superconductor

In-plane microwave penetration depth lambda_{ab} and quasiparticle conductivity at 28 GHz are measured in underdoped single crystals of the Fe-based superconductor PrFeAsO_{1-y} (T_{c} approximately 35 K) by using a sensitive superconducting cavity resonator. lambda_{ab}(T) shows flat dependence at low temperatures, which is incompatible with the presence of nodes in the superconducting gap Delta(k). The temperature dependence of the superfluid density demonstrates that the gap is nonzero (Delta/k_{B}T_{c} greater, similar1.6) all over the Fermi surface. The microwave conductivity below T_{c} exhibits an enhancement larger than the coherence peak, reminiscent of high-T_{c} cuprate superconductors.

Field dependence of the ground state in the exotic superconductor CeCoIn5: a nuclear magnetic resonance investigation

We report 115In nuclear magnetic resonance (NMR) measurements in CeCoIn5 at low temperature (T approximately 70 mK) as a function of the magnetic field (H0) from 2 to 13.5 T applied perpendicular to the c axis. A NMR line shift reveals that below 10 T the spin susceptibility increases as sqrt[H0]. We associate this with an increase of the density of states due to the Zeeman and Doppler-shifted quasiparticles extended outside the vortex cores in a d-wave superconductor. Above 10 T a new superconducting state is stabilized, possibly the modulated phase predicted by Fulde, Ferrell, Larkin, and Ovchinnikov. This phase is clearly identified by a strong and linear increase of the NMR shift with the field, before a jump at the first order transition to the normal state.

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.

effects of rattling phonons on the dynamics of quasiparticle excitation in the beta-pyrochlore KOs(2)O(6) Superconductor

Microwave penetration depth lambda and surface resistance at 27 GHz are measured in high quality crystals of KOs(2)O(6). Firm evidence for fully gapped superconductivity is provided from lambda(T). Below the second transition at T(p) approximately 8 K, the superfluid density shows a steplike change with a suppression of effective critical temperature T(c). Concurrently, the extracted quasiparticle scattering time shows a steep enhancement, indicating a strong coupling between the anomalous rattling motion of K ions and quasiparticles. The results imply that the rattling phonons help to enhance superconductivity, and that K sites freeze to an ordered state with long quasiparticle mean free path below T(p).

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.

Texture in the superconducting order parameter of CeCoIn5 revealed by nuclear magnetic resonance

We present a 115In NMR study of the quasi-two-dimensional heavy-fermion superconductor CeCoIn5 believed to host a Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state. In the vicinity of the upper critical field and with a magnetic field applied parallel to the ab plane, the NMR spectrum exhibits a dramatic change below T*(H) which well coincides with the position of reported anomalies in specific heat and ultrasound velocity. We argue that our results provide the first microscopic evidence for the occurrence of a spatially modulated superconducting order parameter expected in a FFLO state. The NMR spectrum also implies an anomalous electronic structure of vortex cores.

Field-induced quantum critical point in CeCoIn5

The resistivity of the heavy-fermion superconductor CeCoIn5 was measured as a function of temperature, down to 25 mK and in magnetic fields of up to 16 T applied perpendicular to the basal plane. With increasing field, we observe a suppression of the non-Fermi liquid behavior, rho approximately T, and the development of a Fermi liquid state, with its characteristic rho=rho(0)+AT2 dependence. The field dependence of the T2 coefficient shows critical behavior with an exponent of 1.37. This is evidence for a field-induced quantum critical point (QCP), occurring at a critical field which coincides, within experimental accuracy, with the superconducting critical field H(c2). We discuss the relation of this field-tuned QCP to a change in the magnetic state, seen as a change in magnetoresistance from positive to negative, at a crossover line that has a common border with the superconducting region below approximately 1 K.

Hexagonal and square flux line lattices in CeCoIn5

Using small-angle neutron scattering, we have imaged the magnetic flux line lattice (FLL) in the d-wave heavy-fermion superconductor CeCoIn5. At low fields we find a hexagonal FLL. Around 0.6 T this undergoes what is most likely a first-order transition to square symmetry, with the nearest neighbors oriented along the gap node directions. This orientation of the square FLL is consistent with theoretical predictions based on the d-wave order parameter symmetry.

Superconductivity caused by the pairing of plutonium 5f Eelectrons in PuCoGa5

On the basis of electronic structure calculations we identify the superconductivity in the novel, high-temperature superconductor PuCoGa5 to be caused by the pairing of Pu 5f electrons. Assuming delocalized Pu 5f states, we compute theoretical crystallographic constants very near to the experimental ones, and the calculated specific heat coefficient compares reasonably to the measured coefficient. The theoretical Fermi surface is quasi-two-dimensional and the material appears to be close to a magnetic phase instability.