GLAG Theory Research Articles

GLAG theory for superconducting property variations with A15 composition in Nb3Sn wires

We present a model for the variation of the upper critical field Hc2 with Sn content in A15-type Nb-Sn wires, within the Ginzburg-Landau-Abrikosov-Gor’kov (GLAG) theory frame. Hc2 at the vicinity of the critical temperature Tc is related quantitatively to the electrical resistivity ρ, specific heat capacity coefficient γ and Tc. Hc2 versus tin content is theoretically formulated within the GLAG theory, and generally reproduces the experiment results. As Sn content gradually approaches the stoichiometry, A15-type Nb-Sn undergoes a transition from the dirty limit to clean limit, split by the phase transformation boundary. The H-T phase boundary and pinning force show different behaviors in the cubic and tetragonal phase. We dipict the dependence of the composition gradient on the superconducting properties variation in the A15 layer, as well as the curved tail at vicinity of Hc2 in the Kramer plot of the Nb3Sn wire. This helps understanding of the inhomogeneous-composition inducing discrepancy between the results by the state-of-art scaling laws and experiments.

Mixed-State Specific Heat of the Type-II Superconductor Nb0.77Zr0.23 in Magnetic Fields up toB c2

In order to document the behavior of the mean-field mixed-state specific heat of an isotropic. strongly type-II superconductor (i.e., with a large value of the Ginzburg parameterk), and to provide a basis for comparison with high-temperature superconductors, we measured the specific heatC of the alloy Nb0.77Zr0.23 withT c = 10.8K, B c2 (0) = 7.9T, in magnetic fieldsB = 0, 0.2, 1.0, 12, 2.0, 2.4. 3.0, 3.3. 4.0. 4.4, 4.8, 5.2, 6.0. 6.6, 7.2 and 10 T. The values of the upper critical fieldB c2 ( T), thermodynamic critical fieldB c (T), Ginzburg parameterk(T), and coefficient γ(B) = limT0(C(T. B)/T) are derived from the specific heat data and found to be in agreement with the GLAG theory in the dirty limit. The behavior of the mixed-state specific heat is analyzed in terms ofC el /T,∂(C el /T)/∂B, and∂(C el /T)/∂T vs. Tcurves, whereC el is the electronic contribution to the specific heat.

Restoration of superconductivity at high magnetic fields in layered high- Tc and organic superconductors

An integral equation determining the upper critical field parallel to the conducting plane of a layered superconductor is derived from microscopic BCS theory. From this equation, it follows that the superconductivity-destruction mechanism due to the orbital effect becomes ineffective at magnetic fields higher than a critical field H c4 due to a quantum nature of an electron motion in a magnetic field. This leads to the appearance of reentrant superconducting phase with dT c / dH > 0 in the case of p-pairing and under certain conditions in the case of s(d)-pairing. We also show that the orbital effect cannot destroy superconductivity at T = 0 at arbitrary magnetic fields. Therefore qualitative deviations from the description of GLAG (WHH) theory have to appear for arbitrary symmetry of the order parameter at low enough temperatures. We argue that p(s)-wave superconductor Sr 2RuO 4 as well as s(d)-wave superconductors TlBa 2CaCu 2O 7, Tl 2Ba 2Ca 3Cu 4O x , β-(ET) 2AuI 2, and κ-(ET) 2I 3 are good candidates for the observation of the above mentioned phenomena.

Electronic structure parameters of Sm 1+ xBa 2− xCu 3O y solid solution of orthorhombic and tetragonal structure

Two series of Sm 1+ x Ba 2− x Cu 3O y samples were prepared, both exhibiting a change from orthorhombic to tetragonal structure. The first is a series of solid solution of increasing Sm/Ba ratio, the second is a series of exact “123” cation stoichiometry with lowering oxygen content. Several quantities, such as electrical resistivity in magnetic field up to 8T (ϱ), Hall carrier concentration ( n H) and thermopower ( S), were measured. Despite the different chemical nature of the deviation from the initial SmBa 2Cu 3O 6.85 composition in the two series, the transport properties of the normal state change in an analogous manner. No significant differences in the Hall mobility at room temperature were revealed between 90 K superconducting and non-metallic samples; however, a wide maximum was observed for both series for samples with intermediate T c values. The critical temperature ( T c) is depressed with increasing deviation from the initial composition in both series; however, for the solid solution there is no clear 60 K plateau as for the stoichiometric series. The electronic density of states ( g( E F)) was assessed from in-field T c measurements on the basis of the GLAG theory and, independently, from analysis of S and n H values at room temperature. Both methods revealed no significant differences in the behavior of the g( E F) between the solid solution and stoichiometric series. However, the g( E F) calculated by the first method decreases fast with deviation from the initial composition, whereas the results of the second method remain nearly constant over a wide range of composition factors. The value of the g( E F) obtained for the initial SmBa 2Cu 3O 6.85 sample from the jump of the specific heat at T c based on BCS theory also agrees well with the values calculated from transport measurements.

Upper critical field and resistive data of high-T c films irradiated by He ++ ions

He ++ ion irradiation effect on resistive characteristics and upper critical field H c2(T) of YBa 2Cu 3O 7 and HoBa 2Cu 3O 7 c-axis oriented films has been studied. Analyzing the normal states resistivity modification and T c degradation with influence F, we estimated the H c2(T) change in GLAG theory. The -dH c2/dT rise with F has been found. The measured resistive transition midpoint shift T cH-T c in magnetic field proves higher, then one found from the estimated H c2(T). So, the transition broadening has been found to be the main effect, determining the T cH-T c, at least for high fluences.

Direct determination of electronic density of states N★(EF) for Nb3Sn from upper critical field HC2 and resistivity ϱ

The electronic density of states at the Fermi level N ★ (E F ) is extracted from the experimental upper critical field H C2 and resistivity ϱ Nb 3 Sn in terms of anisotropic GLAG theory. The proposed consideration is not confined by dirty superconductor limit and does not require the electronic specific heat coefficient γ or the plasma frequency ω p data, which were used earlier to estimate the N ★ (E F ) of Nb 3 Sn from H C2 . We show, that the anomaly in the −dH C2 /dT dependency on ϱ is connected with the N ★ (E F ) change.

A study of the H c2 enhancement due to the addition of Ti to the matrix of bronze-processed Nb3Sn superconductors

The measurements of ρn (the normal state resistivity), Tc, Hc2, and (dHc2/dt)T=Tc have been made for bronze-processed Nb3Sn wires with addition of Ti to the Cu-Sn matrix in order to study the mechanism of Hc2 enhancement due to the addition of Ti. The coefficient of electron specific heat, γ, has been derived by two independent methods: one using the Ginzburg–Landau–Abrikosov–Gor’kov (GLAG) theory and the measured values of ρn, Tc, and (dHc2/dT)T=Tc, and the other using the Kramer pinning theory and the gradient of J1/2cH1/4 -H curves. The ratios of γ/γ0 which have been derived by these two methods are in good agreement with each other. (γ0 is the value of γ for the specimen to which Ti is not added.) The upper critical fields given by the GLAG theory, H*c2 and Hc2, at 0 K increase rapidly with Ti concentration in the Nb3Sn layer up to 2 at. % and decrease slightly above 2 at. %. The rapid increase in ρnγTc caused by the addition of Ti is sufficient to explain the enhancement in Hc2, and among ρn, γ and Tc, only ρn shows a significant increase with increasing amounts of additional Ti, indicating that the main reason for the Hc2 enhancement is the increase in ρn.

Correlation between structural relaxation enthalpy and superconducting properties of amorphous Zr70Cu30 and Zr70Ni30 alloys

The anneal-induced change in the superconducting properties together with the irrecoverable relaxation enthalpy (ΔHi,exo) and recoverable relaxation enthalpy (ΔHr,endo) of amorphous Zr70Cu30 and Zr70Ni30 alloys was examined. The increase in Δi,exo and the degradation ofTc progress logarithmically with annealing timeta in a temperature range of 373 to 523 K. The activation energy and the attempted frequency were respectively estimated to be 1.5eV and 6.6 × 1013 sec−1 for the increase in ΔHi,exo and 1.5eV and 1.9×1014 sec−1 for the degradation ofTc. The recoverable structure relaxation exerts little effect onTc. Based on the agreement between the kinetic parameters for the changes of ΔHi,exo andTc, it appears that the degradation ofTc on annealing is associated with the irrecoverable structural relaxation as a result of the annihilation of frozen-in defects and the topological and compositional atomic rearrangement. The values of the attempted frequency being of the order of Debye frequency suggest that the irrecoverable structural relaxation processes occur more or less independently from each other. The dressed density of electronic states at the Fermi level,N(Ef)(1+λ), determined from the measured values ofρn and -(dHc2/dT)Tc using GLAG (theory), was found to have a similar annealing dependence to that ofTc. The degradation ofTc by the irrecoverable relaxation was thus inferred as resulting from the decrease inλ due to the decrease inN(Ef) and the increases inM and ω. Furthermore, the irrecoverable structural relaxation resulted in a significant depression of fluxoid pinning force and was interpreted as due to an enhanced structural homogeneity on the scale of coherence length.

Origin of the B<inf>c2</inf>enhancement in ternary Nb-Sn phases

Nb-Sn-Ga alloys were chosen as a model system in order to investigate the influence of third element additions on the normal and superconducting properties of alloyed Nb 3 Sn phases. With respect to compositions formed by the bronze process (with Ga added to the Cu Sn matrix) alloys with concentrations close to the Sn-rich side of the A15 phase boundary were prepared. The analyses based on the GLAG theory shows that inspite of a decrease in the density of states at the Fermi level with increasing Ga content the upper critical field, B c2 , is increased due to a large enhancement of the residual resistivity. However, Ga destabilizes the stoichiometric composition of the A15 phase and the critical temperature decreases for higher Ga contents. Therefore, B c2 maximized at 1 to 1.5at% Ga for reaction temperatures at 700°C. High critical fields up to 31.5 T (at T = 4.2K) have been achieved for higher reaction temperatures, which shift the phase boundary of the A15 phase field towards stoichiometry.

Susceptibility and upper critical field studies on A-15 superconducting Ti 3Sb compound

Normal state susceptibility and upper critical field measurements have been made on A-15 superconducting Ti 3Sb compound. Susceptibility shows a week temperature dependence from 15 K to 300 K. The value of the susceptibility is smaller compared to those of other Ti bases A-15 systems. The value of the upper critical field at T = OK deduced from the experiment is higher than the value predicted by GLAG theory.

Effect of magnetic iron impurity on the superconducting properties of an amorphous Nb50Zr35Si15 alloy

The effect of magnetic iron impurity on the superconducting properties of amorphous Nb50Zr35−x Si15Fe x (x⩽4 at %) alloys was examined. Doping with an iron impurity resulted in a linear depression ofT c andH c2(T) and a decrease in $$(dH_{c2} /dT)_{T_c } $$ andρ n after reaching a maximum value at 0.5 to 1.0 at % iron. The observed decrease was about 35% forT c, 85% forH c2 at 2.0 K, 16% for $$(dH_{c2} /dT)_{T_c } $$ and 21% forρ n. Although the decrease in $$(dH_{c2} /dT)_{T_c } $$ occurs through the decrease inρ n as expected from the GLAG theory, the depression inT c caused by magnetic impurity could not be explained in terms of the GLAG theory which is applicable to Nb-Zr-Si amorphous alloys without magnetic impurity, but was interpreted as arising from the pair-breaking effect in the superconducting nature due to magnetic scattering. However, the pair-breaking effect was found to be smaller by about one-tenth for the present amorphous superconductors than for crystalline superconductors, indicating the high stability of the superconductivity of the Nb-Zr-Si-Fe alloys against the magnetic scattering arising from the magnetic impurity. The reduced magnetic field at which the reduced fluxoid pinning force exhibits a maximum value increased with iron concentration, indicative of an enhancement of fluxoid pinning force. The enhancement in fluxoid pinning force was interpreted as arising from the increase in compositional, electronic and/or magnetic fluctuations by the dope of iron impurity.

Comparison of amorphous melt-spun and vapor-quenched Zr-Rh alloys

Amorphous Zr-Rh alloys produced by melt spinning have a higher superconducting transition temperature T c than materials generated by r.f. cosputtering techniques. However, the temperature dependence of the upper critical field H c 2 ( T is consistent with the GLAG theory for both materials. The T c differences, as well as variations in the electronic density of states, can be partially understood in terms of slight differences in the average density, perhaps due to the inclusion of Ar gas during sputtering.

The effect of IIIB and IVB elements on the superconducting properties of zirconium-based amorphous alloys

Zr-based amorphous alloys exhibiting superconductivity have been found in ternary Zr85Si15−xMx and Zr85Ge15−xMx (M=B, Al, C, Si, Ge or Sn) systems by a melt-spinning technique. Specimens are in the form of continuous ribbons of 1 mm wide and 0,02 mm thick. The M content in the amorphous alloys is limited to less than 10at% B, 7 at% Al, 3 at% C, 9 at% Sn for the Zr-Si-M system and less than 7 at% B, 7 at % Al, 3 at % C and 9 at% Sn for the Zr-Ge-M system. The hardness and crystallization temperature increase significantly with the substitution of B, C or Al for Si or Ge, but the effect of the other elements is less significant. The superconducting transition temperature, 7~c, rises with the substitution of C, AI, Sn or B for Si, whereas the substitution by Ge causes a slight lowering ofTc. The effectiveness of element M on the rise ofTc decreases in the order C > Al >Sn > B >Si >Ge. The upper critical field gradient atTc,Tc, (dHc2/dT)Tc, and the electrical resistivity at 4.2 K, ϱn, decrease from 2.30 × 106 to 1.97 × 106 Am−1 K−1 and from 2.70 to 2.00 μΩm, respectively, with the amount of element M. The coefficient of low-temperature electronic specific heat,γ, land the dressed density of electronic states at the Fermi level,N*(Ef), were calculated from the experimentally measuredvalues of ϱn and (dHc2/dT)Tc using the strong-coupling theories. From the comparison ofTc with their calculated parameters, it was found that the rise ofTc with the substitution of Si by B, C, Al or Sn is caused by the increase inγ andN*(Ef). The GL parameter,k, estimated by using the GLAG theory, decreases from 100 to 78 by the substitution of elements M for Si and it is inferred that the decrease in the dirtiness is also attributable to the rise ofTc.

Superconductivity of Zr-Nb-Si amorphous alloys

Superconducting amorphous alloys with high strength and good ductility have been found in rapidly quenched alloys of the Zr-Nb-Si system. These alloys were produced in a continuous ribbon form of 1 to 2 mm width and 0.02 to 0.03 mm thickness using a modified single roller quenching apparatus. The amorphous alloys were formed over the whole composition range between zirconium and niobium, but the silicon content was limited to the relatively narrow range between about 12 and 24 at%. All the amorphous alloys showed a superconducting transition whose temperature, Tc, increased from 2.31 to 4.20 K with increasing niobium content or with decreasing silicon content. The upper critical magnetic field, Hc2, and the critical current density, Jc, for Zr15Nb70Si15 alloy were of the order of 4.5 Tesla(T) and 5.5×106 A m−2 at 1.5 K in the absence of applied field. The upper critical field gradient at Tc, \((dH_{c2} /dT)_{T_c } \), and the electrical resistivity at 4.2 K, ρn, decreased from 2.89 to 2.10 T K−1 and from 2.70 to 1.80μΩm, respectively, with the amount of niobium. The Debye temperature, θD, the electron-phonon coupling constant, λ, and the bare density of electronic states at the Fermi level, N(Ef) were calculated from the experimentally measured values of ρn, \((dH_{c2} /dT)_{T_c } \), Young's modulus and density by using the strong-coupling theories. From the comparison of Tc with their calculated parameters, it was found that λ is the most dominant parameter for Tc. The GL parameter, κ, and the GL coherence length, ξGL(0), were estimated to be 70 to 100 and about 7.6 nm, respectively, from the experimental values of \((dH_{c2} /dT)_{T_c } \) and ρn by using the GLAG theory and hence it is concluded that the present amorphous alloys are an extremely “dirty” type-II superconductor having a very weak flux pinning force.

Determination of microscopic parameters by macroscopic measurements in superconductors

Macroscopic magnetic measurements were performed on superconducting alloys. From the results of these experiments microscopic parameters namely the energy gap and the vortex creation energy could be calculated. Their dependence on the additive material content (or on the GL-parameter) was determined. It was shown that the BCS and the GLAG theory are applicable for small-κ superconductors in wide temperature interval.

The gap and the vortex creation energy of small-κ superconductors

Magnetic properties of different superconducting alloys with small-κ were investigated. By the help of experimental data the energy gap and the vortex creation energy are determined. The obtained results provide a new proof for the BCS and the GLAG theory.

Enhanced critical field curves of metastable superconductors

Spatial inhomogeneities on a scale of the order of the superconducting coherence length can lead to the enhancement of H c2(T). Experimental observations of critical field behavior in amorphous transition metal alloy superconductors can be explained by a phenomenological modification of GLAG theory.

Upper critical field in multifilamentary Nb<inf>3</inf>Sn conductors

The critical current of bronze processed multifilamentary Nb 3 Sn conductors was measured at 4.2 K up to 23 T. The flux pinning theory of Kramer does not fit the results at flux densities higher than about 18 T. The critical field B* c2 extrapolated from data below 18 T is smaller than the field B c2 at which superconductivity is completely suppressed. From independent measurements of the temperature dependence of B c2 on the same samples (using very small current) B c2 at 4.2 K can be calculated by applying the GLAG theory. A nonvanishing resistivity at fields close to B c2 is evidence of inhomogeneities which considerably broaden the transition.

A phase transition of higher than second order in small-? superconductors

The magnetic properties of small-κ superconducting In-Bi, In-Tl, In-Pb, Sn-Bi, and Sn-Sb alloys are investigated. The evaluation of the experiments is carried out in the framework of BCS and GLAG theory. At a critical alloy concentration a phase transition occurs, at which type I superconductivity goes over into type II. Comparing the results with Lifshitz's theory, it is found that the phase transition is of higher than second order. The contribution from the nonanalytical part of the concentration dependence of the electronic specific heat coefficient is 0.63–0.77, and thus the order of the phase transition increases by this amount.

Anisotropy of the generalized Ginzburg-Landau parameters x 1 and x 2 in clean, cubic, type II superconductors

From the nonlocal GLAG theory expressions are derived for chi/sub 1/ and chi/sub 2/ of a clean, cubic crystal with a general Fermi surface. In the region of weak nonlocality near T/sub c/ the correction terms in H/sub c/2, chi/sub 1/, and chi/sub 2/ due to the nonspherical Fermi surface are expressed by two dimensionless Fermi surface averages. For highly purified Nb single crystals and polycrystalline Nb samples, chi/sub 1/ and chi/sub 2/ were determined from magnetization measurements in the temperature range (0.3--0.95) T/sub c/. The experimental data show that the orientation dependence in chi/sub 2/ is twice as large as in chi/sub 1/, in agreement with the theoretical result near T/sub c/. The two Fermi surface averages that characterize the anisotropy of H/sub c/2, chi/sub 1/, and chi/sub 2/ near T/sub c/ are estimated from experimental data for Nb and V.