Quantum oscillations in the high-Tc cuprates

We review recent progress in the study of quantum oscillations as a tool for uniquely probing low-energy electronic excitations in high-T(c) cuprate superconductors. Quantum oscillations in the underdoped cuprates reveal that a close correspondence with Landau Fermi-liquid behaviour persists in the accessed regions of the phase diagram, where small pockets are observed. Quantum oscillation results are viewed in the context of momentum-resolved probes such as photoemission, and evidence examined from complementary experiments for potential explanations for the transformation from a large Fermi surface into small sections. Indications from quantum oscillation measurements of a low-energy Fermi surface instability at low dopings under the superconducting dome at the metal-insulator transition are reviewed, and potential implications for enhanced superconducting temperatures are discussed.     

RF impedance of high-Tc cuprates

Surface impedance of a high-T_c superconductor (HTS) is described in terms of equivalent lumped-circuit elements, i.e. resistance and inductance, based on the concept of the complex conductivity of a hard type II superconductor containing weak links (WLs), modelled as a parallel combination of a pure superconducting branch and a branch containing WLs.     

Magnetic field dependence of the critical current density for the bismuth-based bulk high-Tc superconductors

Three types of bismuth-based bulk samples were prepared through uniaxial pressing at room temperature, hot isostatic pressing (HIP) and drawing and rolling. Transport current properties were characterized in a steady field up to 1.12 T at 77 K (T/T _c=0.75). The Josephson weak-link decoupling fields have been found to be 5 mT for the cold-pressed pellet and 30 mT for the HIPed pellet and the rolled tape. At the decoupling field the transport critical current density,J _c, drops 80% from 124 (OT) to 29 A cm^–2 (5 mT) for the cold-pressed pellet, 80% from 582 (OT) to 126 A cm^–2 (30 mT) for the HIPed sample and 50% from6500 (0 T) to 2850 A cm^–2 (30 mT) for the rolled tape. In the flux flow regime, whereB is perpendicular to thec-axis a modified Kim's modelJ _c=(/B ₀)/[(1+B/B ₀)] ⁿ can be used to describe the field dependence of the critical current density, J_c, in the field range 0.2–1.12 T. The effective upper critical fields were estimated to be 0.98, 1.54 and 1.94 T for the three types of samples, respectively. An adjustable range ofB _c2 for bismuth-based bulk highT _c superconductors is given. Flux shear may operate in these materials. The prediction of this pinning mechanism is yielded from fitting the equation qualitatively. WhenB is parallel to thec-axis, the absence of strongly intragranular flux-pinning is emphasized by the poor flux flow regime for the rolled tape sample.     

The upper critical field of layered superconductors

The results of a theoretical study of the upper critical fields of layered superconducting compounds are presented. It is found that for sufficiently decoupled layers the parallel critical fieldsH _c2,‖ can be quite large compared to those expected with ordinary type II superconductors and essentially determined by the destruction of the superconductivity in the individual superconducting layers. It is found thatH _c2,‖ can be calculated from standard pair breaking theory in terms of a pair breaking parameter appropriate for layered compounds. The pair breaking parameter includes both orbital effects and the effects of Pauli paramagnetism and spin-orbit scattering.     

A theory of the upper critical field in antiferromagnetic superconductors

A generalized Ginzburg-Landau approach is used to study the nonmonotonic temperature dependence of the upper critical field H _c 2(T) in antiferromagnetic superconductors RE(Mo)₆S₈; RE = Dy, Tb, Gd. It is found that electrodynamic effects incorporated through screening and indirect coupling between the staggered magnetization M _Q (T) and superconducting order parameter cannot explain the observed nonmonotonicity. This suggests that the direct coupling between the two order parameters should be considered to understand the experimental results, a finding which is consistent with recent microscopic calculations.     

The anisotropy of the upper critical field in lead-indium alloys

The anisotropy of the upper critical field H_{c 2} has been investigated for six Pb-In alloys with indium concentration ranging from 1 to 20 at%. This concentration range corresponds to 2<<4 for the impurity parameter . The measured anisotropy curves were analyzed by fitting to an expansion in cubic harmonics and it is shown that the dependence of the coefficient for the leading anisotropy term on the impurity parameter at a fixed reduced temperature and on temperature at a fixed value of the impurity parameter can be described well by theory based on nonlocality assuming nearly local conditions, provided the Fermi surface properties do not change appreciably with alloying.     

A theory of the upper critical field in quasi-zero-dimensional superconductors

A microscopic theory describing the upper critical field in quasi-zero-dimensional superconductors is presented. The model is applicable to materials in which the superconducting electrons form clusters which are spatially separated from each other. It is argued that in quasi-zero-dimensional superconductors the orbital upper critical field is apt to be very high, and it is predicted that in highly zero-dimensional superconductors the Hinc2 (T) curve will exhibit structure not yet seen experimentally.This work was supported by the U.S. Department of Energy, contract No. W-7405-Eng-82, Division of Materials Sciences, budget code AK-01-02-02-1.     

Further investigations of the upper critical field and the high field critical current density in Nb-Ti and its alloys

The work described in this report was undertaken, within the context of the 12 Tesla program, to investigate the possibility of increasing the upper critical field, Hc2, of Nb-Ti through alloying additions. A preliminary report has previously been given by us. In the first part of this paper we report further measurements of Hc2in the Nb-Ti-Ta and Nb-Ti-Hf systems. Whilst we find only small enhacements of ∼0.3 Tesla in μoHc2(4.2K) compared to binary Nb-Ti, at 2K there is a wide composition range in the Nb-Ti-Ta system where μoHc2(2K) exceeds 15 Tesla, reaching a maximum of 15.5 Tesla. This represents an enhancements of 1.3 Tesla over unalloyed Nb-Ti. By comparison alloys in the Nb-Ti-Hf system show a maximum enhancement in μoHc2(2K) of only 0.3 Tesla. The reasons both for the enhancements in Hc2and for the differences in behavior systems shown by alloys containing Ta and Hf are briefly discussed. In part II we discuss common features in the behavior of the high field critical current density, Jc, of four commercial Nb-Ti composites and upon the basis of this behavior predict the enhancements in the high field Jcto be expected from using Nb-Ti-Ta and its alloys.     

Low-temperature magnetoresistivity and upper critical field in UBe13

The unusual field dependence of the upper critical field in UBe₁₃ can be explained by a field variation of the condensation energy which is estimated by the magnetoresistivity experiments. Another interesting feature is the occurrence of large critical fluctuations.     

Determination of pairing symmetry using phase-sensitive tunneling in tricrystal cuprates

An unambiguous determination of the pairing symmetry in cuprate superconductors is important in order to understand the origin of high-temperature superconductivity. By making use of the effects of pair tunneling and flux quantization, we have designed and implemented several tricrystal experiments for phase-sensitive determination of the order parameter symmetry in high-Tc superconductors such as YBa₂Cu₃O₇ Tl₂Ba₂CuO₆, GdBa₂Cu₃O₇, and Bi₂Sr₂CaCu₂O₈. By using a high-resolution scanning SQUID microscope, we have made the first direct observation of spontaneously generated half-flux quanta at the tricrystal point. The half-integer flux quantum effect in various specially designed tricrystal cuprate systems provides strong evidence for d-wave pairing in high-T_c cuprates. Our various tricrystal experiments have demonstrated that this effect can be used as a general probe of the microscopic phase of the pair wavefunction in unconventional superconductors.     

On the maximum reduced upper critical magnetic field in Eliashberg theory

Consideration of the functional derivative of the zero-temperature reduced upper critical magnetic fieldh _c2(0) with electron-phonon spectral density ² F() suggests that its value can be maximized, for a given areaA under ² F(), with the choice of a delta-function spectral density. We show thath _c2(0) is then independent ofA and that it increases steadily as the Einstein frequency _E of the delta function is lowered. We argue that there is a local maximum inh _c2(0) at _E=0. The value at maximum is very sensitive to impurity content and increases sharply from a clean-limit value of 1.5 atT _c /_E=1.33 to more than 3.45 in the dirty limit.     

Impurity effect on the anisotropy of the upper critical field in type II superconductors

The effect of the reduction in mean free path on the anisotropy of the upper critical fieldH _c2 has been studied in Nb by adding Ta and Mo as impurities. It is found that impurities suppress the degree of anisotropy, in qualitative accord with the theory of Hohenberg and Werthamer, which shows that in cubic materials with a nonspherical Fermi surface anisotropy arises from nonlocal corrections to the GLAG theory. The results were analyzed by fitting the observed anisotropy curves to an expansion in Kubic harmonics. It is found that the second harmonic coefficientA ₂, which depends on first nonlocal corrections, decreases initially with addition of Ta or Mo according to theory, but tends to level off to an approximately constant value in the dirty limit, where it should vanish. The value of the third harmonic coefficientA ₃, which depends on higher-order nonlocal terms, vanishes rapidly with the addition of impurity, the rate of decrease being more rapid for Mo. It is also found that the presence of an impurity does not affect the temperature dependence ofA ₂ for both Nb-Ta and Nb-Mo systems andA ₃ for the Nb-Ta system and has an approximately similar effect as for pure Nb.     

Superconducting gap function and upper critical field in the presence of inhomogeneous magnetic order

Rare earth ternary superconductors are known to exhibit oscillatory magnetic orders below their superconducting transition temperatures. The study of behaviour of superconducting electrons in an inhomogeneous magnetic field is therefore important for such systems. We report here the results of our theoretical study of superconducting gap function Δ(T) and upper critical fieldH _c2 (T). The results are applied to analyse and explain the variation of Δ(T) andH _c2 (T) in case of NdRh₄B₄.     

The upper critical field of thin superconducting films with large resistance

The influence of the electron-electron interaction on the upper critical fieldH _c2 of thin superconducting films with large resistance and of layered superconductors is investigated theoretically. The orbital effect only is taken into account. It is shown that the electron-electron interaction in the diffusion and Cooper channels influencesH _c2 in different manners. The interaction in the diffusion channel (dynamically screened Coulomb interaction) leads to essential deviations from the standard BCS dirty limitH _c2 (T) curve at low temperatures and as a result upward curvature inH _c2 (T) is possible. The interaction in the Cooper channel is significant only at temperaturesT _c–TT_c and enlarges the slopedH _c2 (T)/dt atT=T _c.     

Strong coupling effects on the upper critical field of the heavy-fermion superconductor UBe13

The upper critical fieldH _c2 (T) of a high quality single crystal of UBe₁₃ is studied with very low noise resistivity measurements. It shows a large but finite slope of —45 T/K, an unusual temperature dependence with an inflexion point atT/T _C 0.5 and a large saturated limit forT 0 ofH _c2 (0) = 14 T. The complete temperature dependence ofH _c2 (T) can be described by a simple model of strong coupling superconductor, assuming a full Pauli limitation and the occurence of a non-uniform superconducting state (FFLO state) at low temperature.     

Flux flow resistivity and upper critical field in ideal type II amorphous superconductors

Flux flow resistivity _f and upper critical fieldH _c2 of ideal type II amorphous bulk supercbnductors Zr₃Ni and Zr₃Rh on both as-quenched and thermally relaxed states have been studied. It is found that thermal annealing does not change the temperature dependence ofH _c2 in homogeneous superconductors. The temperature and field dependence of _f in all samples studied exhibits a universal scaling relation of the form _f / _n =f(h, t), where _n is the normal state resistivity, andh andt are the reduced field and reduced temperature, respectively. The results are compared with predictions of the time-dependent microscopic theories for bulk superconductors in the dirty limit. In the low-field region (HH _c2 ) the viscosity coefficient contains both the ordinary (Bardeen-Stephen, Tinkham) and anomalous (Gor'kov-Kopnin) terms. ForHH _c2 the results agree qualitatively with the theory of Imai with pair-breaking in the anomalous term. Implications of the present results are discussed.This work is sponsored by the National Science Foundation under Grant DMR-82-02624.     

The upper critical field and dimensional crossover in superconductors with anisotropic electron spectrum

The theory of superconductivity in metallic superstructures with anisotropic electron spectrum is presented. It is shown that these structures, three-dimensional in the normal state, become layered or fibrous in the superconducting state. The upper critical magnetic field changes the temperature dependence in the vicinity of the critical temperature from one (two)-dimensional to three-dimensional.     

The effect of composition and neutron irradiation on the upper critical field of Nb3Pt

The upper critical field H _c2 (T) of the A15 compound Nb_100–x Pt _x (19 x 29.1) has been measured as a function of temperature T for various compositions and levels of irradiation with fast reactor neutrons. Compositions ranging from 19 to 29 at % Pt and neutron fluences up to 16 × 10¹⁸ n/cm² (E > 1 Me V) were studied. A stoichiometric sample that had been rapidly quenched from the liquid (splat-cooled) was also investigated. For the unirradiated samples, T _cexhibits a maximum of 10.4 K at the stoichiometric composition, while both H _c2 (0) and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GaaeizaiaabIeadaWgaaWcbaGaae4yaiaabkdaaeqaaOGaaeiiaiaa% bIcacaqGubGaaeykaiaab+cacaqGKbGaaeivaiaabYhadaWgaaWcba% Gaaeivaiaab2dacaqGubaabeaakmaaBaaaleaacaqGJbaabeaaaaa!48E5!\[{\rm{dH}}_{{\rm{c2}}} {\rm{ (T)/dT|}}_{{\rm{T = T}}} _{\rm{c}} \] attain their maximum values on the Pt-rich side of stoichiometry. The irradiated samples show a decrease of H _c2 (0) with increasing neutron fluence. The results are discussed in terms of antisite disorder and a strong correlation is obtained between decreasing H _c2 (0) and increasing disorder of the Nb atomic sites.Research supported by the U.S. Department of Energy under Contract No. EY-76-S-03-0034-PA227-3 (SEL and MBM), by Research Corporation (ARS), and by the U.S. Department of Energy under Contract No. EY-76-C-02-0016 (SM).     

The effect of neutron irradiation on the upper critical magnetic field of superconducting Mo3Os

The effect of irradiation with high-energy (E>1 MeV) reactor neutrons on the upper critical magnetic fieldH _c2 (T) and the superconducting transition temperatureT _c has been determined for the A15 compound Mo₃Os. An increase ofH _c2(0) by 37% relative to its unirradiated value was observed for a neutron fluence of1.7×10¹⁹ n/cm². For the same fluence,T _c was found to decrease by 12%. The results are discussed in terms of defects in the A15 structure and their influence onH _c2(0).