Ion-Selective Scattering Studied Using the Variable-Energy Electron Irradiation in the Ba0.2K0.8Fe2As2 Superconductor

Low-temperature variable-energy electron irradiation was used to induce non-magnetic disorder in a single crystal of a hole-doped iron-based superconductor, Ba1-xKxFe2As2, x = 0.80. To avoid systematic errors, the beam energy was adjusted non-consequently for five values between 1.0 and 2.5 MeV when sample resistance was measured in situ at 22 K. For all energies, the resistivity raises linearly with the irradiation fluence suggesting the creation of uncorrelated dilute point-like disorder (confirmed by simulations). The rate of the resistivity increase peaks at energies below 1.5 MeV. Comparison with calculated partial cross-sections points to the predominant creation of defects in the iron sublattice. Simultaneously, superconducting Tc, measured separately between the irradiation runs, is monotonically suppressed as expected, since it depends on the total scattering rate, hence on the total cross-section, which is a monotonically increasing function of the energy. Our work experimentally confirms an often-made assumption of the dominant role of the iron sub-lattice in iron-based superconductors.

Anisotropic Melting of Frustrated Ising Antiferromagnets

Magnetic frustrations and dimensionality play an important role in determining the nature of the magnetic long-range order and how it melts at temperatures above the ordering transition T_{N}. In this Letter, we use large-scale Monte Carlo simulations to study these phenomena in a class of frustrated Ising spin models in two spatial dimensions. We find that the melting of the magnetic long-range order into an isotropic gaslike paramagnet proceeds via an intermediate stage where the classical spins remain anisotropically correlated. This correlated paramagnet exists in a temperature range T_{N}<T<T^{*}, whose width increases as magnetic frustrations grow. This intermediate phase is typically characterized by short-range correlations; however, the two-dimensional nature of the model allows for an additional exotic feature-formation of an incommensurate liquidlike phase with algebraically decaying spin correlations. The two-stage melting of magnetic order is generic and pertinent to many frustrated quasi-2D magnets with large (essentially classical) spins.

Possible unconventional order parameter in single crystals of SrPt3P superconductor

Anisotropic properties of single crystals of SrPt₃P were studied using London penetration depth and electrical resistivity measurements. The upper critical field,Hc2(T), was determined from four-probe electrical resistivity measurements for three orthogonal directions of a magnetic field with respect to the crystal. The London penetration depth,λ(T), was determined from the magnetic susceptibility of the Meissner-London state measured using a tunnel-diode resonator technique. WhereasHc2(T)and the normal-stateρ(T)are practically identical for all three magnetic field orientations, the London penetration depth shows significant unidirectional anisotropy. The low-temperatureλ(T)is exponentially attenuated when a small excitation radiofrequency magnetic field,H_rf, is applied along thec''-direction, in which case screening currents flow in thea''b''-plane, while for the other two orientations,Hrf∥a''andHrf∥b'', the London penetration depth shows a much stronger,λ(T)∼T2, variation. Such unusual and contrasting behavior of the two anisotropies,γHT=Hc2,ab/Hc2,c=ξab/ξcandγλT=λc/λab, imposes significant constraints on the possible order parameter. Although our measurements are insufficient to derive conclusively the superconducting gap anisotropy, the order parameter with two point nodes and a modulation in the perpendicular direction is qualitatively consistent with the experimental observations.

Low-temperature high-frequency dynamic magnetic susceptibility of classical spin-ice Dy2Ti2O7

Radio-frequency (14.6 MHz) AC magnetic susceptibility,χAC', of Dy₂Ti₂O₇was measured using self-oscillating tunnel-diode resonator. Measurements were made with the excitation AC field parallel to the superimposed DC magnetic field up to 5 T in a wide temperature range from 50 mK to 100 K. At 14.6 MHz, a known broad peak ofχAC'(T)from kHz-range audio-frequency measurements around 15 K for both [111] and [110] directions shifts to 45 K, continuing the Arrhenius activated behavior with the same activation energy barrier ofE_a≈ 230 K. Magnetic field dependence ofχAC'along [111] reproduces previously reported low-temperature two-in-two-out to three-in-one-out spin configuration transition at about 1 T, and an intermediate phase between 1 and 1.5 T. The boundaries of the intermediate phase show reasonable overlap with the literature data and connect at a critical endpoint of the first order transition line, suggesting that these features are frequency independent. An unusual upturn of the magnetic susceptibility atT→ 0 was observed in magnetic fields between 1.5 T and 2 T for both magnetic field directions, before fully polarized configuration sets in above 2 T.

Effect of Controlled Artificial Disorder on the Magnetic Properties of EuFe2(As1-xPx)2 Ferromagnetic Superconductor

Static (DC) and dynamic (AC, at 14 MHz and 8 GHz) magnetic susceptibilities of single crystals of a ferromagnetic superconductor, EuFe2(As1-xPx)2 (x = 0.23), were measured in pristine state and after different doses of 2.5 MeV electron or 3.5 MeV proton irradiation. The superconducting transition temperature, Tc(H), shows an extraordinarily large decrease. It starts at Tc(H=0)≈24K in the pristine sample for both AC and DC measurements, but moves to almost half of that value after moderate irradiation dose. Remarkably, after the irradiation not only Tc moves significantly below the FM transition, its values differ drastically for measurements at different frequencies, ≈16 K in AC measurements and ≈12 K in a DC regime. We attribute such a large difference in Tc to the appearance of the spontaneous internal magnetic field below the FM transition, so that the superconductivity develops directly into the mixed spontaneous vortex-antivortex state where the onset of diamagnetism is known to be frequency-dependent. We also examined the response to the applied DC magnetic fields and studied the annealing of irradiated samples, which almost completely restores the superconducting transition. Overall, our results suggest that in EuFe2(As1-xPx)2 superconductivity is affected by local-moment ferromagnetism mostly via the spontaneous internal magnetic fields induced by the FM subsystem. Another mechanism is revealed upon irradiation where magnetic defects created in ordered Eu2+ lattice act as efficient pairbreakers leading to a significant Tc reduction upon irradiation compared to other 122 compounds. On the other hand, the exchange interactions seem to be weakly screened by the superconducting phase leading to a modest increase of Tm (less than 1 K) after the irradiation drives Tc to below Tm. Our results suggest that FM and SC phases coexist microscopically in the same volume.

Mechanical detwinning device for anisotropic resistivity measurements in samples requiring dismounting for particle irradiation

Uniaxial stress is used to detwin the samples of orthorhombic iron based superconductors to study their intrinsic electronic anisotropy. Here, we describe the development of a new detwinning setup enabling variable-load stress-detwinning with easy sample mounting/dismounting without the need to re-solder the contacts. It enables the systematic study of the anisotropy evolution as a function of an external parameter when the sample is modified between the measurements. In our case, the external parameter is the dose of 2.5 MeV electron irradiation at low temperature. We illustrate the approach by studying resistivity anisotropy in single crystals of Ba_1-xK_xFe₂As₂ at x = 0.25, where the much discussed unusual re-entrance of the tetragonal C₄ phase, C₄ → C₂ → C₄, is observed on cooling. With the described technique, we found a significant anisotropy increase in the C₂ phase after electron irradiation with a dose of 2.35 C/cm².

Disorder-Driven Transition from s_{±} to s_{++} Superconducting Order Parameter in Proton Irradiated Ba(Fe_{1-x}Rh_{x})_{2}As_{2} Single Crystals

Microwave measurements of the London penetration depth and critical temperature T_{c} were used to show evidence of a disordered-driven transition from s_{±} to s_{++} order parameter symmetry in optimally doped Ba(Fe_{1-x}Rh_{x})_{2}As_{2} single crystals, where disorder was induced by means of 3.5 MeV proton irradiation. Signatures of such a transition, as theoretically predicted [V. D. Efremov et al., Phys. Rev. B 84, 180512(R) (2011)PRBMDO1098-012110.1103/PhysRevB.84.180512], are found as a drop in the low-temperature values of the London penetration depth and a virtually disorder-independent superconducting T_{c}. We show how these experimental observations can be described by multiband Eliashberg calculations in which the effect of disorder is accounted for in a suitable way. To this aim, an effective two-band approach is adopted, allowing us to treat disorder in a range between the Born approximation and the unitary limit.

Tunnel diode resonator for precision magnetic susceptibility measurements in a mK temperature range and large DC magnetic fields

Precision radio-frequency measurements of the magnetic susceptibility using the tunnel diode resonator (TDR) technique are used to study the delicate effects in magnetic and superconducting materials. High resolution (in ppb range) measurements are particularly important for studies of the London and Campbell penetration depths in a superconductor and for the investigation of magnetic transitions in (anti)ferromagnets. Due to the small rf magnetic-excitation in a mOe range, the TDR is especially useful at low-temperatures in a mK range, if Joule heating generated in the TDR circuitry is efficiently removed and the circuit is stabilized with sub-mK precision. Unfortunately, the circuit has significant magnetic field dependence, and therefore, most of the precision TDR measurements at low-temperatures were conducted in zero magnetic field. In this work, we describe the design of a setup for precision TDR measurements in a dilution refrigerator down to ∼40 mK with a 14 T superconducting magnet. The key features of our design are the separated electronics components and the placement of the most field sensitive parts in the field-compensated zone far from the center of solenoid as well as the heat-sinking at a higher temperature stage. The performance of the working setup is demonstrated using several superconductors.

Multi-band effects in in-plane resistivity anisotropy of strain-detwinned disordered Ba(Fe1-xRux)2As2

In-plane resistivity anisotropy was measured in strain-detwinned as-grown and partially annealed samples of isovalently-substituted [Formula: see text] ([Formula: see text]) and the results were contrasted with previous reports on anneal samples with low residual resistivity. In samples with high residual resistivity, detwinned with application of strain, the difference of the two components of in-plane resistivity in the orthorhombic phase, [Formula: see text], was found to obey Matthiessen rule irrespective of sample composition, which is in stark contrast with observations on annealed samples. Our findings are consistent with two-band transport model in which contribution from high mobility carriers of small pockets of the Fermi surface has negligible anisotropy of residual resistivity and is eliminated by disorder. Our finding suggests that magnetic/nematic order has dramatically different effect on different parts of the Fermi surface. It predominantly affects inelastic scattering for small pocket high mobility carriers and elastic impurity scattering for larger sheets of the Fermi surface.

Universal doping evolution of the superconducting gap anisotropy in single crystals of electron-doped Ba(Fe1-x Rh x )2As2 from London penetration depth measurements

Doping evolution of the superconducting gap anisotropy was studied in single crystals of 4d-electron doped Ba(Fe_1-x Rh _x )₂As₂ using tunnel diode resonator measurements of the temperature variation of the London penetration depth [Formula: see text]. Single crystals with doping levels representative of an underdoped regime x  =  0.039 ([Formula: see text] K), close to optimal doping x  =  0.057 ([Formula: see text] K) and overdoped x  =  0.079 ([Formula: see text] K) and x  =  0.131([Formula: see text] K) were studied. Superconducting energy gap anisotropy was characterized by the exponent, n, by fitting the data to the power-law, [Formula: see text]. The exponent n varies non-monotonically with x, increasing to a maximum n  =  2.5 for x  =  0.079 and rapidly decreasing towards overdoped compositions to 1.6 for x  =  0.131. This behavior is qualitatively similar to the doping evolution of the superconducting gap anisotropy in other iron pnictides, including hole-doped (Ba,K)Fe₂As₂ and 3d-electron-doped Ba(Fe,Co)₂As₂ superconductors, finding a full gap near optimal doping and strong anisotropy toward the ends of the superconducting dome in the T-x phase diagram. The normalized superfluid density in an optimally Rh-doped sample is almost identical to the temperature-dependence in the optimally doped Ba(Fe,Co)₂As₂ samples. Our study supports the universal superconducting gap variation with doping and [Formula: see text] pairing at least in iron based superconductors of the BaFe₂As₂ family.

Beyond triplet: Unconventional superconductivity in a spin-3/2 topological semimetal

In all known fermionic superfluids, Cooper pairs are composed of spin-1/2 quasi-particles that pair to form either spin-singlet or spin-triplet bound states. The "spin" of a Bloch electron, however, is fixed by the symmetries of the crystal and the atomic orbitals from which it is derived and, in some cases, can behave as if it were a spin-3/2 particle. The superconducting state of such a system allows pairing beyond spin-triplet, with higher spin quasi-particles combining to form quintet or septet pairs. We report evidence of unconventional superconductivity emerging from a spin-3/2 quasi-particle electronic structure in the half-Heusler semimetal YPtBi, a low-carrier density noncentrosymmetric cubic material with a high symmetry that preserves the p-like j = 3/2 manifold in the Bi-based Γ₈ band in the presence of strong spin-orbit coupling. With a striking linear temperature dependence of the London penetration depth, the existence of line nodes in the superconducting order parameter Δ is directly explained by a mixed-parity Cooper pairing model with high total angular momentum, consistent with a high-spin fermionic superfluid state. We propose a k ⋅ p model of the j = 3/2 fermions to explain how a dominant J = 3 septet pairing state is the simplest solution that naturally produces nodes in the mixed even-odd parity gap. Together with the underlying topologically nontrivial band structure, the unconventional pairing in this system represents a truly novel form of superfluidity that has strong potential for leading the development of a new series of topological superconductors.

Uniaxial strain control of spin-polarization in multicomponent nematic order of BaFe2As2

The iron-based high temperature superconductors exhibit a rich phase diagram reflecting a complex interplay between spin, lattice, and orbital degrees of freedom. The nematic state observed in these compounds epitomizes this complexity, by entangling a real-space anisotropy in the spin fluctuation spectrum with ferro-orbital order and an orthorhombic lattice distortion. A subtle and less-explored facet of the interplay between these degrees of freedom arises from the sizable spin-orbit coupling present in these systems, which translates anisotropies in real space into anisotropies in spin space. We present nuclear magnetic resonance studies, which reveal that the magnetic fluctuation spectrum in the paramagnetic phase of BaFe₂As₂ acquires an anisotropic response in spin-space upon application of a tetragonal symmetry-breaking strain field. Our results unveil an internal spin structure of the nematic order parameter, indicating that electronic nematic materials may offer a route to magneto-mechanical control.

A fundamental understanding of nematic order is one of the most important issues to explore in the high temperature superconductors. Here, the authors unveil an internal spin structure of the nematic order in BaFe₂As₂ by using nuclear magnetic resonance under precisely controlled tunable strain.

Modular portable unit for thermal conductivity measurements in multiple cryogenic/magnetic field environments

A modular design for a miniature thermal conductivity cell suitable for a dilution refrigerator and other sample-in-vacuum cryogenic environments with different magnet options is described. The sample is mounted once and the contacts remain in place when the unit is repositioned or transported between different magnets and cryostats. This mobility enables comprehensive measurements with access to specific options, such as vector magnet in one lab and ultra-high field in another. This design enables significant expansion of the temperature range by using not only dilution refrigerators but also ³He, ⁴He cryostats and even ubiquitous Quantum Design Physical Property Measurement System.

Origin of the Resistivity Anisotropy in the Nematic Phase of FeSe

The in-plane resistivity anisotropy is studied in strain-detwinned single crystals of FeSe. In contrast to other iron-based superconductors, FeSe does not develop long-range magnetic order below the tetragonal-to-orthorhombic transition at T_{s}≈90  K. This allows for the disentanglement of the contributions to the resistivity anisotropy due to nematic and magnetic orders. Comparing direct transport and elastoresistivity measurements, we extract the intrinsic resistivity anisotropy of strain-free samples. The anisotropy peaks slightly below T_{s} and decreases to nearly zero on cooling down to the superconducting transition. This behavior is consistent with a scenario in which the in-plane resistivity anisotropy is dominated by inelastic scattering by anisotropic spin fluctuations.

Energy gap evolution across the superconductivity dome in single crystals of (Ba1-x K x )Fe2As2

The mechanism of unconventional superconductivity in iron-based superconductors (IBSs) is one of the most intriguing questions in current materials research. Among non-oxide IBSs, (Ba_1-x K _x )Fe₂As₂ has been intensively studied because of its high superconducting transition temperature and fascinating evolution of the superconducting gap structure from being fully isotropic at optimal doping (x ≈ 0.4) to becoming nodal at x > 0.8. Although this marked evolution was identified in several independent experiments, there are no details of the gap evolution to date because of the lack of high-quality single crystals covering the entire K-doping range of the superconducting dome. We conducted a systematic study of the London penetration depth, λ(T), across the full phase diagram for different concentrations of point-like defects introduced by 2.5-MeV electron irradiation. Fitting the low-temperature variation with the power law, Δλ ~ Tⁿ , we find that the exponent n is the highest and the T_c suppression rate with disorder is the smallest at optimal doping, and they evolve with doping being away from optimal, which is consistent with increasing gap anisotropy, including an abrupt change around x ≃ 0.8, indicating the onset of nodal behavior. Our analysis using a self-consistent t-matrix approach suggests the ubiquitous and robust nature of s_± pairing in IBSs and argues against a previously suggested transition to a d-wave state near x = 1 in this system.

Quantum Critical Quasiparticle Scattering within the Superconducting State of CeCoIn_{5}

The thermal conductivity κ of the heavy-fermion metal CeCoIn_{5} was measured in the normal and superconducting states as a function of temperature T and magnetic field H, for a current and field parallel to the [100] direction. Inside the superconducting state, when the field is lower than the upper critical field H_{c2}, κ/T is found to increase as T→0, just as in a metal and in contrast to the behavior of all known superconductors. This is due to unpaired electrons on part of the Fermi surface, which dominate the transport above a certain field. The evolution of κ/T with field reveals that the electron-electron scattering (or transport mass m^{⋆}) of those unpaired electrons diverges as H→H_{c2} from below, in the same way that it does in the normal state as H→H_{c2} from above. This shows that the unpaired electrons sense the proximity of the field-tuned quantum critical point of CeCoIn_{5} at H^{⋆}=H_{c2} even from inside the superconducting state. The fact that the quantum critical scattering of the unpaired electrons is much weaker than the average scattering of all electrons in the normal state reveals a k-space correlation between the strength of pairing and the strength of scattering, pointing to a common mechanism, presumably antiferromagnetic fluctuations.

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.

Superconductivity and physical properties of CaPd2Ge2 single crystals

We present the superconducting and normal state properties of CaPd(2)Ge(2) single crystals investigated by magnetic susceptibility χ, isothermal magnetization M, heat capacity Cp, in-plane electrical resistivity ρ and London penetration depth λ versus temperature T and magnetic field H measurements. Bulk superconductivity is inferred from the ρ(T) and Cp(T) data. The ρ(T) data exhibit metallic behavior and a superconducting transition with T(c onset) = 1.98 K and zero resistivity at T(c 0) = 1.67 K. The χ(T) reveals the onset of superconductivity at 2.0 K. For T > 2.0 K, the χ(T) and M(H) are weakly anisotropic paramagnetic with χ(ab) > χ(c). The Cp(T) data confirm the bulk superconductivity below T(c) = 1.69(3) K. The superconducting state electronic heat capacity is analyzed within the framework of a single-band α-model of BCS superconductivity and various normal and superconducting state parameters are estimated. Within the α-model, the Cp(T) data and the ab plane λ(T) data consistently indicate a moderately anisotropic s-wave gap with Δ(0)/k(B)T(c) ≈ 1.6, somewhat smaller than the BCS value of 1.764. The relationship of the heat capacity jump at Tc and the penetration depth measurement to the anisotropy in the s-wave gap is discussed.

Intrinsic nanostructure in Zr2-xFe4Si16-y(x = 0.81, y = 6.06)

We present a study of the crystal structure and physical properties of single crystals of a new Fe-based ternary compound, Zr2-xFe4Si16-y(x = 0.81, y = 6.06). Zr1.19Fe4Si9.94 is a layered compound, where stoichiometric β-FeSi2-derived slabs are separated by Zr-Si planes with substantial numbers of vacancies. High resolution transmission electron microscopy (HRTEM) experiments show that these Zr-Si layers consist of 3.5 nm domains where the Zr and Si vacancies are ordered within a supercell sixteen times the volume of the stoichiometric cell. Within these domains, the occupancies of the Zr and Si sites obey symmetry rules that permit only certain compositions, none of which by themselves reproduce the average composition found in x-ray diffraction experiments. Magnetic susceptibility and magnetization measurements reveal a small but appreciable number of magnetic moments that remain freely fluctuating to 1.8 K, while neutron diffraction confirms the absence of bulk magnetic order with a moment of 0.2μB or larger down to 1.5 K. Electrical resistivity measurements find that Zr1.19Fe4Si9.94 is metallic, and the modest value of the Sommerfeld coefficient of the specific heat γ = C/T suggests that quasi-particle masses are not particularly strongly enhanced. The onset of superconductivity at Tc ≃ 6 K results in a partial resistive transition and a small Meissner signal, although a bulk-like transition is found in the specific heat. Sharp peaks in the ac susceptibility signal the interplay of the normal skin depth and the London penetration depth, typical of a system in which nano-sized superconducting grains are separated by a non-superconducting host. Ultra low field differential magnetic susceptibility measurements reveal the presence of a surprisingly large number of trace magnetic and superconducting phases, suggesting that the Zr-Fe-Si ternary system could be a potentially rich source of new bulk superconductors.

Interlayer coherence and superconducting condensate in the c-axis response of optimally doped Ba(Fe(1-x)Co(x))2As2 high-T(c) superconductor using infrared spectroscopy

We report on the infrared studies of the interlayer charge dynamics of a prototypical pnictide superconductor Ba(Fe(0.926)Co(0.074))(2)As(2). We succeeded in probing the intrinsic interlayer response by performing infrared experiments on the crystals with a cleaved ac surface. Our experiments identify the coexistence of the suppression of the electronic spectral weight and the development of a coherent Drude-like response in the normal state. The formation of the interlayer condensate is clearly observed in the superconducting state and appears to be linked to coherent contribution to the normal-state conductivity.

Universal heat conduction in the iron arsenide superconductor KFe2As2: evidence of a d-wave state

The thermal conductivity κ of the iron arsenide superconductor KFe2As2 was measured down to 50 mK for a heat current parallel and perpendicular to the tetragonal c axis. A residual linear term at T→0, κ(0)/T is observed for both current directions, confirming the presence of nodes in the superconducting gap. Our value of κ(0)/T in the plane is equal to that reported by Dong et al. [Phys. Rev. Lett. 104, 087005 (2010)] for a sample whose residual resistivity ρ(0) was 10 times larger. This independence of κ(0)/T on impurity scattering is the signature of universal heat transport, a property of superconducting states with symmetry-imposed line nodes. This argues against an s-wave state with accidental nodes. It favors instead a d-wave state, an assignment consistent with five additional properties: the magnitude of the critical scattering rate Γ(c) for suppressing T(c) to zero; the magnitude of κ(0)/T, and its dependence on current direction and on magnetic field; the temperature dependence of κ(T).

A sharp peak of the zero-temperature penetration depth at optimal composition in BaFe2(As(1-x)P(x))2

In a superconductor, the ratio of the carrier density, n, to its effective mass, m*, is a fundamental property directly reflecting the length scale of the superfluid flow, the London penetration depth, λ(L). In two-dimensional systems, this ratio n/m* (~1/λ(L)(2)) determines the effective Fermi temperature, T(F). We report a sharp peak in the x-dependence of λ(L) at zero temperature in clean samples of BaFe(2)(As(1)(-x)P(x))(2) at the optimum composition x = 0.30, where the superconducting transition temperature T(c) reaches a maximum of 30 kelvin. This structure may arise from quantum fluctuations associated with a quantum critical point. The ratio of T(c)/T(F) at x = 0.30 is enhanced, implying a possible crossover toward the Bose-Einstein condensate limit driven by quantum criticality.

Infrared measurement of the pseudogap of P-doped and Co-doped high-temperature BaFe2As2 superconductors

We report on infrared studies of charge dynamics in a prototypical pnictide system: the BaFe2As2 family. Our experiments have identified hallmarks of the pseudogap state in the BaFe2As2 system that mirror the spectroscopic manifestations of the pseudogap in the cuprates. The magnitude of the infrared pseudogap is in accord with that of the spin-density-wave gap of the parent compound. By monitoring the superconducting gap of both P- and Co-doped compounds, we find that the infrared pseudogap is unrelated to superconductivity. The appearance of the pseudogap is found to correlate with the evolution of the antiferromagnetic fluctuations associated with the spin-density-wave instability. The strong-coupling analysis of infrared data further reveals the interdependence between the magnetism and the pseudogap in the iron pnictides.

Doping dependence of heat transport in the iron-arsenide superconductor Ba(Fe(1-x)Co(x))2As2: from isotropic to a strongly k-dependent gap structure

The temperature and magnetic field dependence of the in-plane thermal conductivity kappa of the iron-arsenide superconductor Ba(Fe(1-x)Co(x))2As2 was measured down to T approximately 50 mK and up to H = 15 T as a function of Co concentration x in the range 0.048 < or = x < or = 0.114. At H = 0, a negligible residual linear term in kappa/T as T-->0 at all x shows that the superconducting gap has no nodes in the ab plane anywhere in the phase diagram. However, while the slow H dependence of kappa(H) at T-->0 in the underdoped regime is consistent with a superconducting gap that is large everywhere on the Fermi surface, the rapid increase in kappa(H) observed in the overdoped regime shows that the gap acquires a deep minimum somewhere on the Fermi surface. Outside the antiferromagnetic-orthorhombic phase, the superconducting gap structure has a strongly k-dependent amplitude.

Nonexponential London penetration depth of FeAs-based superconducting RFeAsO(0.9)F(0.1) (R = La, Nd) single crystals

The superconducting penetration depth lambda(T) has been measured in RFeAsO(0.9)F(0.1) (R = La, Nd) single crystals (R-1111). In Nd-1111, we find an upturn in lambda(T) upon cooling and attribute it to the paramagnetism of the Nd ions, similar to the case of the electron-doped cuprate Nd-Ce-Cu-O. After the correction for paramagnetism, the London penetration depth variation is found to follow a power-law behavior, Deltalambda_{L}(T) proportional, variantT;{2} at low temperatures. The same T2 variation of lambda(T) was found in nonmagnetic La-1111 crystals. Analysis of the superfluid density and of penetration depth anisotropy over the full temperature range is consistent with two-gap superconductivity. Based on this and on our previous work, we conclude that both the RFeAsO (1111) and BaFe(2)As(2) (122) families of pnictide superconductors exhibit unconventional two-gap superconductivity.

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.

Momentum dependence of the superconducting gap in NdFeAsO0.9F0.1 single crystals measured by angle resolved photoemission spectroscopy

We use angle resolved photoemission spectroscopy to study the momentum dependence of the superconducting gap in NdFeAsO0.9F0.1 single crystals. We find that the Gamma hole pocket is fully gapped below the superconducting transition temperature. The value of the superconducting gap is 15+/-1.5 meV and its anisotropy around the hole pocket is smaller than 20% of this value-consistent with an isotropic or anisotropic s-wave symmetry of the order parameter. This is a significant departure from the situation in the cuprates, pointing to the possibility that the superconductivity in the iron arsenic based system arises from a different mechanism.

Hybrid gap structure of the heavy-fermion superconductor CeIrIn5

The thermal conductivity kappa of the heavy-fermion superconductor CeIrIn5 was measured as a function of temperature down to T(c)/8, for current directions parallel (J parallel c) and perpendicular (J parallel a) to the tetragonal c axis. For J parallel a, a sizable residual linear term kappa(0)/T is observed, as previously, which confirms the presence of line nodes in the superconducting gap. For J parallel c, on the other hand, kappa/T-->0 as T-->0. The resulting precipitous decline in the anisotropy ratio kappa(c)/kappa(a) at low temperature rules out a gap structure with line nodes running along the c axis, such as the d-wave state favored for CeCoIn5, and instead points to a hybrid gap of E(g) symmetry.

Anisotropic Violation of the Wiedemann-Franz Law at a Quantum Critical Point

A quantum critical point transforms the behavior of electrons so strongly that new phases of matter can emerge. The interactions at play are known to fall outside the scope of the standard model of metals, but a fundamental question remains: Is the basic concept of a quasiparticle-a fermion with renormalized mass-still valid in such systems? The Wiedemann-Franz law, which states that the ratio of heat and charge conductivities in a metal is a universal constant in the limit of zero temperature, is a robust consequence of Fermi-Dirac statistics. We report a violation of this law in the heavy-fermion metal CeCoIn5 when tuned to its quantum critical point, depending on the direction of electron motion relative to the crystal lattice, which points to an anisotropic destruction of the Fermi surface.

Nonvanishing energy scales at the quantum critical point of CeCoIn5

Heat and charge transport were used to probe the magnetic field-tuned quantum critical point in the heavy-fermion metal CeCoIn5. A comparison of electrical and thermal resistivities reveals three characteristic energy scales. A Fermi-liquid regime is observed below T(FL), with both transport coefficients diverging in parallel and T(FL) -->0 as H --> Hc, the critical field. The characteristic temperature of antiferromagnetic spin fluctuations, T(SF), is tuned to a minimum but finite value at Hc, which coincides with the end of the T-linear regime in the electrical resistivity. A third temperature scale, T(QP), signals the formation of quasiparticles, as fermions of charge e obeying the Wiedemann-Franz law. Unlike T(FL), it remains finite at Hc, so that the integrity of quasiparticles is preserved, even though the standard signature of Fermi-liquid theory fails.

Thermal conductivity in the vicinity of the quantum critical end point in Sr3Ru2O7

Thermal conductivity of Sr3Ru2O7 was measured down to 40 mK and at magnetic fields through the quantum critical end point at Hc=7.85 T. A peak in the electrical resistivity as a function of the field was mimicked by the thermal resistivity. In the limit as T-->0 K, we find that the Wiedemann-Franz law is satisfied to within 5% at all fields, implying that there is no breakdown of the electron despite the destruction of the Fermi liquid state at quantum criticality. A significant change in disorder [from rho0(H=0 T)=2.1 to 0.5 microOmega cm] does not influence our conclusions. At finite temperatures, the temperature dependence of the Lorenz number is consistent with ferromagnetic fluctuations causing the non-Fermi liquid behavior as one would expect at a metamagnetic quantum critical end point.

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.

Heat transport as a probe of electron scattering by spin fluctuations: the case of antiferromagnetic CeRhIn(5)

Heat and charge conduction were measured in the heavy-fermion metal CeRhIn(5), an antiferromagnet with T(N)=3.8 K. The thermal resistivity is found to be proportional to the magnetic entropy, revealing that spin fluctuations are as effective in scattering electrons as they are in disordering local moments. The electrical resistivity, governed by a q(2) weighting of fluctuations, increases monotonically with temperature. In contrast, the difference between thermal and electrical resistivities, characterized by a omega(2) weighting, peaks sharply at T(N) and eventually goes to zero at a temperature T(*) approximately = 8 K. T(*) thus emerges as a measure of the characteristic energy of magnetic fluctuations.

Delocalized fermions in underdoped cuprate superconductors

Low-temperature heat transport was used to investigate the ground state of high-purity single crystals of the lightly doped cuprate YBa2Cu3O6.33. Samples were measured with doping concentrations on either side of the superconducting phase boundary. We report the observation of delocalized fermionic excitations at zero energy in the nonsuperconducting state, which shows that the ground state of underdoped cuprates is a thermal metal. Its low-energy spectrum appears to be similar to that of the d-wave superconductor, i.e., nodal. The insulating ground state observed in underdoped La2-xSrxCuO4 is attributed to the competing spin-density-wave order.

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

Point-contact spectroscopy was performed on single crystals of the heavy-fermion superconductor CeCoIn(5) between 150 mK and 2.5 K. A pulsed measurement technique ensured minimal Joule heating over a wide voltage range. The spectra show Andreev-reflection characteristics with multiple structures which depend on junction impedance. Spectral analysis using the generalized Blonder-Tinkham-Klapwijk formalism for d-wave pairing revealed two coexisting order parameter components with amplitudes Delta(1) = 0.95 +/- 0.15 meV and Delta(2) = 2.4 +/- 0.3 meV, which evolve differently with temperature. Our observations indicate a highly unconventional pairing mechanism, possibly involving multiple bands.

Giant electron-electron scattering in the Fermi-liquid state of Na0.7CoO2

The in-plane resistivity rho and thermal conductivity kappa of single crystal Na0.7CoO2 were measured down to 40 mK. Verification of the Wiedemann-Franz law, kappa/T=L(0)/rho as T-->0, and observation of a T2 dependence of rho at low temperature establish the existence of a well-defined Fermi-liquid state. The measured value of coefficient A reveals enormous electron-electron scattering, characterized by the largest Kadowaki-Woods ratio A/gamma(2) encountered in any material. The rapid suppression of A with magnetic field suggests a possible proximity to a magnetic quantum critical point. We also speculate on the possible role of magnetic frustration and proximity to a Mott insulator.

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.

Field-induced thermal metal-to-insulator transition in underdoped La(2-x)Sr(x)CuO(4+delta)

The transport of heat and charge in cuprates was measured in single crystals of La(2-x)Sr(x)CuO(4+delta) (LSCO) across the doping phase diagram at low temperatures. In underdoped LSCO, the thermal conductivity is found to decrease with increasing magnetic field in the T-->0 limit, in striking contrast to the increase observed in all superconductors, including cuprates at higher doping. In heavily underdoped LSCO, where superconductivity can be entirely suppressed with an applied magnetic field, we show that a novel thermal metal-to-insulator transition takes place upon going from the superconducting state to the field-induced normal state.

Heat conduction in the vortex state of NbSe2: evidence for multiband superconductivity

The thermal conductivity kappa of the layered s-wave superconductor NbSe2 was measured down to T(c)/100 throughout the vortex state. With increasing field, we identify two regimes: one with localized states at fields very near H(c1) and one with highly delocalized quasiparticle excitations at higher fields. The two associated length scales are naturally explained as multiband superconductivity, with distinct small and large superconducting gaps on different sheets of the Fermi surface. This behavior is compared to that of the multiband superconductor MgB2 and the conventional superconductor V3Si.

Universal heat transport in Sr2RuO4

We present the temperature dependence of the thermal conductivity kappa(T) of the unconventional superconductor Sr2RuO4 down to low temperatures ( approximately 100 mK). In the T-->0 K limit we found a finite residual term in kappa/T, providing clear evidence for the superconducting state with an unconventional pairing. The residual term remains unchanged for samples with different T(c), demonstrating the universal character of heat transport in this spin-triplet superconductor. The low-temperature behavior of kappa suggests the strong impurity scattering with a phase shift close to pi/2. A criterion for the observation of universality is experimentally deduced.

Anisotropy of magnetothermal conductivity in Sr2RuO4

The dependence of in-plane and interplane thermal conductivities of Sr2RuO4 on temperature, as well as magnetic field strength and orientation, is reported. We found no notable anisotropy in the thermal conductivity for the magnetic field rotation parallel to the conducting plane in the whole range of experimental temperatures and fields, except in the vicinity of the upper critical field H(c2), where the anisotropy of the H(c2) itself plays a dominant role. This finding imposes strong constraints on the possible models of superconductivity in Sr2RuO4 and supports the existence of a superconducting gap with a line of nodes running orthogonal to the Fermi surface cylinder.