Anisotropic<Emphasis Type="Italic">s</Emphasis>-wave or<Emphasis Type="Italic">d</Emphasis>-wave pairing? Analysis of experiments on ion irradiation of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-x</Subscript> films

The effect of ion irradiation on the superconducting transition temperatureT _c and resistivityρ _ab (T) of YBa₂Cu₃O_7-x films with different oxygen content (initial temperatureT _c0≈90 K and 60 K) is studied experimentally. The dependenciesT _c /T _c0 on residual resistivityρ _o are obtained in very wide range 0.2<T _c /T _c0 <1 andρ _o μΩ·cm. The critical values ofρ _o , corresponding to the vanishing of superconductivity, are found to be an order of magnitude larger then those predicted by theory ford-wave pairing. At 0.5÷0.6<T _c /T _c0<1 the experimental data are in close agreement with theoretical dependencies, obtained for the anisotropics-wave superconductor within the BCS-framework.     

Einfluß von Gitterstörungen auf die Supraleiteigenschaften von Blei

The transition temperatureT _c and the critical fieldH _c of lead were measured as a function of the concentration of lattice defects. The defects were generated by plastic deformation at liquid Helium temperatures and reduced by annealing. T _c is rather insensitive to defects. With increasing residual resistance ratio ρ the transition temperature increases and finally reaches a constant value with onlyΔT _c ≈4.5 · 10^?3 °K. On the other hand a deformation of the same amount increasesH _c more than twice as much as the starting value. Annealing to room-temperature reducesρ, T _c andH _c to their initial values. During the annealing process,T _c shows a distinct maximum and ρ a marked step. Contrary to this behaviourH _c decreases linearly during the whole region of annealing. Taking into account the strong influence of ρ uponH _c a picture is given about the mechanism of deformation, which allows to understand the results qualitatively. The changes ofT _c produced by elastic strain were also measured. The results are in quantitative agreement with those of pressure experiments.     

Pion condensation in heavy ion collisions

We calculate the pion spectrum in dense nuclear matter for finite temperatures. The critical temperatureT _c(ρ) that marks the beginning of a second order phase transition due to pion condensation is given in a phase diagram. We show that in heavy ion collisions, pion condensation should occur, leading to an enhancement in the formation of nuclear shock waves.     

Enhancement of the superconducting critical temperature Tc of niobium by radiation damage

5 μm niobium foils were irradiated with 25 MeV oxygen ions at 20 K, 33 K and 145 K up to fluences of 1.3 × 10¹⁶cm^-2 corresponding to a damage rate decrease of 99%. T_c versusresistivity shows a minimum depending on the irradiation temperature. At high fluences and subsequent annealing T_c is enhanced compared to the unirradiated value and the transition is broadened by a factor of about 30.     

Lattice thermal conductivity of compounds with inhomogeneous intermediate rare-earth ion valence

The thermal conductivity κ (within the range 4–300 K) and electrical conductivity σ (from 80 to 300 K) of polycrystalline Sm₃S₄ with the lattice parameter a=8.505 Å (with a slight off-stoichiometry toward Sm₂S₃) are measured. For T>95 K, charge transfer is shown to occur, as in stoichiometric Sm₃S₄ samples, by the hopping mechanism (σ ～ exp(?ΔE/kT) with ΔE ～ 0.13 eV). At low temperatures [up to the maximum in the lattice thermal conductivity κ_ph(T)], κ_ph ～ T ^2.6; in the range 20–50 K, κ_ph ～ T ^?1.2; and for T>95 K, where the hopping charge-transfer mechanism sets in, κ_ph ～ T ^?0.3 and a noticeable residual thermal resistivity is observed. It is concluded that in compounds with inhomogeneous intermediate rare-earthion valence, to which Sm₃S₄ belongs, electron hopping from Sm²⁺ (ion with a larger radius) to Sm³⁺ (ion with a smaller radius) and back generates local stresses in the crystal lattice which bring about a change in the thermal conductivity scaling of κ_ph from T ^?1.2 to T ^?0.3 and the formation of an appreciable residual thermal resistivity.     

Superconductivity of quench-condensed beryllium and beryllium-germanium films

Tunneling experiments on Be films condensed onto helium cooled substrates show that these films are homogeneously disordered with a uniform transition temperatureT _c when Ge is codeposited, whereas thick films of pure Be do not grow homogeneously. For films of Be+10 at.% Ge a ratio 2Δ/k _B T _c =3.7 is found. Phonon induced structure in the tunneling density of states is not observed. The metastable phase obtained by quench-condensation is considered to be a disordered high-temperature phase of Be which transforms to the room temperature phase at about 60 K.     

Suppression of superconductivity in YNi2B2C at the atomic disordering

The behavior of the electrical resistivity ρ(T), the superconducting transition temperature T _c , and the upper critical field H _c2(T) of a polycrystalline sample of YNi₂B₂C irradiated by thermal neutrons with the subsequent high-temperature isochronous annealing in the temperature interval T _ann = 100–1000°C has been studied. It has been found that the irradiation of YNi₂B₂C with a fluence of 10¹⁹cm^?2 leads to the suppression of the superconductivity. The final disordered state is reversible; i.e., the initial ρ(T), T _c , and H _c2(T) values are almost completely recovered upon annealing at up to T _ann = 1000°C. The quadratic dependence ρ(T) = ρ₀ + a ₂ T ² is observed for the sample in the superconducting state (T _c = 5.5?14.5 K). The coefficient a ₂ (proportional to the square of the electron mass m*) hardly changes. The form of the dependence of T _c on ρ₀ can be interpreted as the suppression of the two superconducting gaps, Δ₁ and Δ₂ (Δ₁ ～ 2Δ₂). The degradation rate of Δ₁ is about three times higher than that of Δ₂. The dependences dH _c2/dT on ρ₀ and T _c may be described by the relations for a superconductor in the intermediate limit (the coherence length ζ₀ is on the order of the electron mean free path l _tr) under the assumption of a nearly constant electron density of states on the Fermi level N(E _F). The observed behavior of T _c obviously does not agree with the widespread opinion about the purely electron-phonon mechanism of superconductivity in the compounds of this type supposing the anomalous type of superconducting pairing.     

Formation of high-T c phases of the system Bi-Pb-Sr-Ca-Cu-O in a fluxed KCl melt

The influence of the conditions of synthesis and annealing on the ratio of the volumes and the temperature T _c ⁿ at which transition to the superconducting state begins is investigated on the basis of diamagnetic susceptibility measurements and x-ray phase analysis for bismuth 2212 and 2223 phases obtained from solution in a KCl melt. It is found that the value of T _c ⁿ for the 2212 phase decreases as the temperature and the holding time are increased in synthesis. The 2212–2223 transition in the fluxed KCl melt takes place in the presence of an oxygen deficiency, and the width of the transition interval to the superconducting state of the 2223 phase depends on the cooling rate of the fluxed melt after isothermal holding and also on subsequent annealing in air. Temperatures T _c ⁿ =107 K, 90 K, and 20 K are observed for unannealed crystals of the 2223 phase with average dimensions 50×50 μm. Air annealing leads to oxygen saturation of their lattice, and T _c ⁿ =107 K throughout the entire structure of the crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1761–1763 (October 1997)     

Variation of electronic properties and evidence for a reversible defect induced metal to semiconductor transition in PbMo6S8 observed by ion irradiation and subsequent annealing of thin films

The influence of lattice disorder varied by low temperature irradiation with 20 MeV³²S-ions and subsequent isochronal thermal annealing on Hall-effectR _H (T), resistivityp(T) and superconducting critical temperatureT _c of thin films of the Chevrel-phase PbMo₆S₈ is reported. It is found that the well known, unusual sensitivity ofT _c is correlated with drastic changes of normal state transport properties e.g.R _H (T) andp(T). In the low fluence regime (6·10¹³ cm^–2,T _c 2 K) annealing leads to a monotonous restoration of the initial properties with the main recovery occurring at temperatures as low as 500 K. Contrary to this, annealing of highly disordered samples (10¹⁵ cm^–2) creates semiconductor-like conduction behavior. This manifests itself by a strong increase of the electrical resistivity with decreasing temperature which becomes more pronounced at higher annealing temperaturesT _A . AfterT _A =800 K the resistivityp(15K) is enhanced by more than a factor of 1000 withp(15K)/p(280 K)=210 compared to as irradiated. Further annealing at 900 K and 1000K results in the reappearance of metallicp(T)-behavior and superconductivity (T _c >10K). The observed effects can be understood by systematic changes of the electronic density of states consistent with an earlier proposed defect model.     

On the chiral phase transition in hadronic matter

A qualitative analysis of the chiral phase transition in QCD with two massless quarks and nonzero baryon density is performed. It is assumed that, at zero baryonic density, ρ=0, the temperature phase transition is of the second order. Due to a specific power dependence of baryon masses on the chiral condensate, the phase transition becomes of the first order at the temperature T=T_ph(ρ) for ρ>0. At temperatures T_cont(ρ)> _T>_Tph(ρ), there is a mixed phase consisting of the quark phase (stable) and the hadron phase (unstable). At the temperature T=T_cont(ρ), the system experiences a continuous transition to the pure chirally symmetric phase.     

Structural instability and superconductivity in niobium-titanium alloys

Niobium-titanium is the most widely used technical superconductor. Titaniumrich transition metal alloys, quenched from high temperatures, can generally be retained in the bccβ phase. This phase is metastable and the instability is relieved by a variety of low temperature structural transformations. This aspect has been investigated using x-ray, TEM, low temperature resistivity,T _c and dH _c2/dT studies, in a series of Nb-Ti alloys. The instability has been characterized by the normal state resistivityρ _n and dρ/dT. The commercially used Nb-Ti alloys are Ti rich per atom-wise. This stems basically from the anomalous increase in the normal state resistivityρ _n as the Ti concentration is increased. This is a consequence of a dynamical process through which theβ phase instability tends to be relieved leading to athermal ω precipitation. The resulting anomalous resistivity behaviour can be understood in terms of a ‘two-level system’ model generally invoked for amorphous materials. It has also been possible to induce instability towards athermal ω precipitation in a system spontaneously undergoing a martensitic transformation to become stable. Thus in an alloy of Nb-83 at % Ti, addition of 1% nitrogen has suppressed the martensitic transformation, giving a three-fold increase inρ _n (about 150µΘ cm), the highest known in Nb-Ti so far. The increase in the normal state resistivity has beneficial effects on the upper critical field. From studies on several Nb-Ti alloys, it is inferred that a peak inH _c2(0) occurs at 17–18 tesla at aρ _n value of 100µΘ cm. It is pointed out that in the present commercial alloys, the sequence of thermo-mechanical treatments given to optimizeJ _c, restrictsρ _n, perhaps owing to the partial relieving of the metastability of theβ phase. They are therefore non-optimized with respect toH _c2.     

Thermal expansion and kinetic coefficients of crystals

Electrical (ρ) and thermal (W) resistivities and thermal expansion coefficient (β) of Cu, Zn, Al, Pb, Ni, β-brass, Al₂O₃, NaCl, Si, SiO₂(∥), and SiO₂(⊥) were simultaneously measured with standard four-probe, absolute steady-state, and quartz dilatometer techniques. Measurements of Ni and β-brass were performed at temperatures from 300 to 1100 K and measurements of all other samples were made between 90 and 500 K. This temperature range includes the range below and above the Debye temperature (T_D). The total uncertainties of the specific electrical and thermal resistivities and thermal expansion coefficient (TEC) measurements are 0.5%, 3.0%, and (1.5-4.0%), respectively. The universal linear relationship between the electrical and thermal resistivities and βΤ over the wide temperature range was found experimentally. Using the Landau criterion for convection development for ideal phonon and electron gases in the solids, the universal relations, ρ^ph/ρ^*≡βT and W^ph/W^*≡βT (where ρ^ph is the phonon electrical resistivity, is the characteristic electrical resistivity, W^ph is the phonon thermal resistivity, and W^*=k_BG/qc_p is the characteristic thermal resistivity) between relative phonon electrical and phonon thermal resistivities and βΤ were derived. The derived universal relations provide a new method for estimating the kinetic coefficients (electrical and thermal resistivities) from TEC measurements.     

Zum Kondo-Effekt in Zink-Mangan: Der Einfluß der Manganverteilung auf den elektrischen Widerstand im Temperaturbereich bis 0,4 °K

The electrical resistivity of dilute Zn-Mn alloys (c=0–0.6 at% Mn) has been measured in a temperature range from room temperature (RT) down to 0.4 °K. Three different series of samples are investigated: 1. annealed 72 h, 400 °C, 2. annealed and aged 1 year atRT, 3. coldworked atRT. All samples show a minimum in the residual resistance atT _min∝c ^1/5 followed by an increase of the resistivityρ∝k _s · lnT (Kondo-effect). For some alloys the resistivity minimum is followed by a resistivity maximum atT _max.T _max mainly depends on the distribution of the Mnatoms in the Zn-matrix. The coefficientk _s is also strongly influenced by changes of the Mn-distribution. For alloys withc>0.02 at% (max. solubility of Mn in Zn atRT) the slopek _s =?ρ/? lnT decreases with increasing degree of precipitation of the manganese. Samples withc<0.02 at% however, show the opposite effect, increasingk _s with increasing Mn-precipitation. Moreover, during the aging process, we observe an increase in the “residual resistance” (resistance ratioR _T/R ₂₉₃ atT _min) for these alloys. The effect can be explained by assuming that the precipitation leads to the formation of superparamagnetic clusters.     

Temperature dependence of the upper critical field as an indicator of boson effects in superconductivity in Nd2−x CexCuO4−y

The temperature dependence of the upper critical field B _c 2 was determined from the shift of the resistive transition ΔT(B) in nearly optimally doped Nd_2?x Ce_xCuO_4?y single crystals. Within the experimental accuracy, the weak-field data are described by the power function B _c 2∝(ΔT)^3/2. This result is compared with the data on heat capacity and analyzed in the context of possible manifestations of boson effects in superconductivity. The T dependence of B _c 2 persists down to the lowest temperatures, but the numerical values of B _c 2 below 1 K are different for different samples.     

Effect of annealing on the magnetic and superconducting properties of single-crystalline UCoGe

Single-crystals of the new ferromagnetic superconductor UCoGe have been grown. The quality of as-grown samples can be significantly improved by a heat-treatment procedure, which increases the residual resistance ratio (RRR) from ∼5 to ∼30. Magnetization M(T) and resistivity ρ(T) measurements show the annealed samples have a sharp ferromagnetic transition with a Curie temperature T_C is 2.8 K. The ordered moment of 0.06 μ_B is directed along the orthorhombic c-axis. Superconductivity is found below a resistive transition temperature T_s=0.65 K.     

Influence of irradiation induced atomic disorder on Hc2 of Nb3Sn

A significant monotonous decrease of H_c2(0) almost proportional to T_c has been observed after heavy ion irradiation of the A15 superconductor Nb₃Sn at low temperature < 30 K and isochronal annealing up to 300 K has been measured. The effects are discussed in connection with the Goodman—Gorkov-relation.     

Superconducting properties of the atomically disordered MgB2 compound

The effect of disorder induced by neutron irradiation in a nuclear reactor (thermal neutron fluence 1×10¹⁹cm^?2) on the superconducting transition temperature T _c and the upper critical field H _c2 of polycrystalline MgB₂ samples was investigated. Despite the appreciable radiation-induced distortions (more than ten displacements per atom), the initial crystal structure (C32) was retained. The temperature T _c decreased from 38 to 5 K upon irradiation and was practically completely restored after the subsequent annealing at a temperature of 70°C. A weak change in the dH _c2/dT derivative upon irradiation is explained by the fact that the irradiated samples are described by the “pure” limit of the theory of disordered superconductors. The suppression of T _c upon disordering may be due to the isotropization of the originally anisotropic (or multicomponent) superconducting gap or to a decrease in the density of electronic states at the Fermi level.     

Scaling of the temperature-dependent resistivity in SrFe2−xNixAs2

We show that the zero-field normal-state resistivity of temperature-dependent resistivity ρ(T) of SrFe_2?xNi_xAs₂ can be reproduced by the expression ρ(T) = ρ₀ + c T exp(?2Δ/T). ρ(T) can be scaled using both this expression where the energy scale Δ, c and the residual resistivity ρ₀ are scaling parameters and a recently proposed model-independent scaling method (H.G. Luo, Y.H. Su, T. Xiang, Phys. Rev. B 77 (2008) 014529). The scaling parameters have been calculated and the compositional variation of 2Δ(x) has been determined. This dependence show almost a linear decreasing in the underdoped regime similar to that reported for cuprates. The existence of a universal metallic ρ(T) curve in a wide temperature range which, however, is restricted for the underdoped compounds to temperatures above a structural and anitiferromagnetic transition is interpreted as an indication of a single mechanism which dominates the scattering of the charge carriers in SrFe_2?xNi_xAs₂ (x = 0–0.3).     

Decoupling of the order-disorder and displacive contributions to the phase transition in NH4H(ClH2CCOO)2

The effects of hydrostatic pressure and substitution of Rb⁺for the ammonium cations on the ferroelectric phase transition temperature in NH₄H(ClH₂CCOO)₂ have been studied by electric permittivity measurements. The transition temperature (T_c) decreases with increasing pressure up to 800 MPa and the pressure coefficient dT_c/dp=−1.4×10⁻² [K/MPa] has been experimentally determined. The substitution of Rb⁺ for the ammonium cations has been shown to considerably lower the ferroelectric phase transition temperature T_c. In mixed crystals, additional electric permittivity anomaly has been clearly evidenced. The results are discussed assuming a model, which combines polarizability effects, related to the heavy ion units, with the pseudo-spin tunnelling.     

Exact quantum partition function of the BCS model

The exact calculation of the reduced BCS model quantum partition function (QPF) in the thermodynamic limit is carried out by the path integration method. The expression for the QPF and the phase transition temperatureT _c in the regular phase coincide with the results of Bogolyubov. In the nonregular phase a temperature singularity appears in the expression for the QPF: the QPF diverges in the region of temperaturesT _c which are smaller than some critical temperatureT _c ^* , and it turns out that in all casesT _c ^* > T _c and the differenceT _c ^* –T _c is not small. The interpretation of the temperatureT _c ^* is given.