Temperature Dependence Of Hc2 Research Articles

Upper Critical Field of a Two-Band SrFe2 − xNixAs2 Superconductor

The upper critical field of an iron-based SrFe2 − xNixAs2 superconductor single crystal is measured for the first time in longitudinal and transverse magnetic fields up to 16 T in the basal ab plane and to it along the c axis. The Hc2(0) values are 18 and 25 T for H ∥ c and H ∥ ab, respectively. The anisotropy of the upper critical field γ(T) = Hc2 / Hc2 decreases monotonically to 1.4 with decreasing temperature. The temperature dependence of Hc2 is not described fully by the Werthamer–Helfand–Hohenberg model taking into account the influence of orbital and spin paramagnetic effects. However, an effective two-band model reproduces well the measured temperature dependence. This indicates the two-band nature of this superconductor, where one of the bands is almost isotropic. According to the two-band model approximation, the contribution from the anisotropic band dominates near Tc, whereas the main contribution at low temperatures comes from the isotropic band with a lower diffusion coefficient.

Different behavior of upper critical field in Fe1−xSe single crystals**Project supported by the National Natural Science Foundation of China (Grant Nos. 11888101 and 11834016), the National Key Research and Development Program of China (Grant Nos. 2017YFA0303003 and 2016YFA0300300), and the Strategic Priority Research Program and Key Research Program of Frontier Sciences of the Chinese Academy of Sciences (Grant Nos. QYZDY-SSW-SLH001

The temperature dependences of upper critical field (Hc2) for a series of iron-deficient Fe1−xSe single crystals are obtained from the measurements of in-plane resistivity in magnetic fields up to 9 T and perpendicular to the ab plane. For the samples with lower superconducting transition temperature Tc (<7.2 K), the temperature dependence of Hc2 is appropriately described by an effective two-band model. For the samples with higher Tc (≳ 7.2 K), the temperature dependence can also be fitted by a single-band Werthamer–Helfand–Hohenberg formula, besides the two-band model. Such a Tc-dependent change in Hc2(T) behavior is discussed in connection with recent related experimental results, showing an inherent link between the changes of intrinsic superconducting and normal state properties in the FeSe system.

Single Crystal Growth and Superconductivity in La7Ni3 without Inversion Symmetry in the Crystal Structure

We succeeded in growing single crystals of La7Ni3 with the non-centrosymmetric hexagonal structure by the Bridgman method, and measured the electrical resistivity and specific heat under magnetic fields. The superconducting transition temperature Tsc is 2.4 K. The electronic specific heat coefficient γ is 44 mJ/(K2-f.u.-mol). Correspondingly, the upper critical field Hc2(0) in superconductivity is large, Hc2 = 27 kOe. The electronic specific heat shows the jump at Tsc = 2.4 K, indicating the bulk superconductivity with ΔCe/γTc = 1.2, which is close to the weak coupling BCS value of 1.43. Although the temperature dependence of specific heat and some parameters of superconductivity are well explained by the conventional BCS model, the temperature dependence of Hc2 is not consistent with the simple BCS model.

Effect of Sb and Si doping on the superconducting properties of FeSe0.9

In the present work, we have studied the effect of doping Sb and Si at the Se-site of FeSe0.9 on the superconducting properties, such as transition temperature (Tc), upper critical field (Hc2) and irreversibility field (Hirr). The polycrystalline samples have been synthesized via two step solid state reaction route with nominal compositions Fe[Se1−x(Sb/Si)x]0.9 (x=0.0, 0.05, 0.10, 0.15 and 0.20). The X-ray diffraction results show the presence of tetragonal α-FeSe phase with the P4/nmm space group symmetry in all the samples. The highest superconducting onset temperatures, Tconset∼9.42Kand9.20K, respectively, for Si and Sb doped samples have been found for x=0.05. The temperature dependence of Hc2(T) and Hirr(T) have been calculated from the magnetoresistance data using the criteria of 90% and 10% of normal state resistivity (ρn) values, respectively. The values of Hc2(0) estimated from Werthamer–Helfand–Hohenberg (WHH) and Ginzburg–Landau (GL) theories are found to follow the same trends and maximum Hc2(0) is found for the composition x=0.10 for both the Si and Sb doped samples. The irreversibility field, Hirr and activation energy, U0 have also been calculated to study the vortex motion behavior of the samples. A clear cut correlation between Hirr and U0 has been found.

Effect of Fe composition on the superconducting properties (Tc, Hc2 and Hirr) of FexSe1/2Te1/2 (x = 0.95, 1.00, 1.05 and 1.10)

In the present work, we have studied the effect of Fe composition on the superconducting properties, such as transition temperature (Tc), upper critical field (Hc2), and irreversibility field (Hirr) of FeSe1/2Te1/2. The polycrystalline samples have been prepared via solid state reaction route with nominal compositions FexSe1/2Te1/2 (x = 0.95, 1.00, 1.05 and 1.10). The x-ray diffraction results show the presence of tetragonal α-FeSe phase with the p4/nmm space group symmetry in all the samples. The zero resistance temperatures, Tczero, measured in zero magnetic field, have been found to be 10.0, 12.4, 12.3, and 11.7 K for x = 0.95, 1.00, 1.05, and 1.10, respectively. The temperature dependence of Hc2(T) and Hirr(T) have been calculated from the magnetoresistance data using the criteria of 90% and 10% of normal state resistivity (ρn) values, respectively. The values of Hc2(0) are 121.3 T, 142.8 T, 82.7 T, and 79.3 T for x = 0.95, 1.00, 1.05, and 1.10, respectively. The possible reasons for the variation of superconducting properties with Fe composition (x) have been described and discussed in this paper.

TRANSPORT ANISOTROPY IN ErNi2B2C ALONG c-AXIS

The resistivities along c-axis ρc(H, T) of ErNi 2 B 2 C have been measured with H⊥ and H‖c-axis for 2 &lt; T &lt; 300 K and the superconducting upper critical field Hc2(T) curves of ErNi 2 B 2 C were constructed for each magnetic fields. Our Hc2(T) curves have been compared and discussed with those from ρab(H, T) measurements which explain the anisotropy and its temperature dependence of Hc2(T) are thought to arise from magnetic pair breaking and the anisotropic field dependence of Néel temperature TN originated from Er +3 sublattice.

The Superconducting Transition in Boron Doped Silicon Films

We report on a detailed analysis of the superconducting properties of boron-doped silicon films grown along the 001 direction by gas immersion laser doping. This technique is proved to be a powerful technique to dope silicon in the alloying range 2-10 at.% where superconductivity occurs. The superconducting transitions are sharp and well defined both in resistivity and magnetic susceptibility. The variation of Tc on the boron concentration is in contradiction with a classical exponential dependence on superconducting parameters. Electrical measurements were performed in magnetic field on the sample with cB = 8 at.% (400 laser shots) which has the highest Tc (0.6 K). No hysteresis was found for the transitions in magnetic field, which is characteristic of a type-II superconductor. The corresponding upper critical field was on the order of 1000 G at low temperatures, much smaller than the value previously reported. The temperature dependence of Hc2 is very well reproduced by the linearized Gorkov equations neglecting spin effects in the very dirty limit. These measurements in magnetic field allow an estimation of the electronic mean-free path, the coherence length, and the London penetration depth within a simple two-band free electron model.

Specific heat of superconducting MgCNi3 single crystals

The ac microcalorimetry measurements with light emitting diode used as a heater has been performed on high quality MgCNi3 single crystals with Tc of 6.9 K. The measurements have been realized in the temperature range down to 0.7 K and magnetic fields up to 8 T. All the measurements show sharp and well defined specific heat anomaly at the transition. The low-temperature electronic specific heat in superconducting state shows a classical exponential decrease confirming an s-wave pairing. Analysis of the data in the framework of classical BCS theory points to the moderate coupling in this material. The upper critical field Hc2 has also been derived from specific heat measurements in different magnetic fields. The temperature dependence of Hc2 is discussed.

Critical magnetic field H c2 and electron scattering in MgB2

The correlation between the upper critical field Hc2 and the residual resistivity ρ of the MgB2 compound is studied in a wide range of ρ values. The slope −dHc2/dT of the temperature dependence of Hc2 near Tc is found to increase steadily with increasing residual resistivity to 100 μΩ cm. Over the range from 0 to 50 μΩ cm, the dependence of −dHc2/dT on ρ is fitted well by a linear function, which is typical of a single-band superconductor. The fit is performed using the electronic parameters of the two bands (π and σ) that form the Fermi surface. The field Hc2 is assumed to depend on the electronic parameters of the σ band only. Using this approximation, the following quantities are estimated: the relative contribution of σ electrons to the total conductivity along the boron planes (which turns out to be about 1/2), the ratio of the mean free paths of electrons in the σ and π bands lσ/lπ ≈ 1.5, and the ratios between some other parameters describing electron scattering.

Comparison of the scaling analysis of mixed-state magnetizationdata with direct measurements of the upper critical field forYBa2Cu3O7−x

By comparison of recent direct measurements of the temperature dependence of the upper critical fieldHc2 ofan YBa2Cu3O7−x high-Tc superconductor with the scaling analysis of magnetization data, collected in fields , we demonstrate that the temperature dependence of the Ginzburg–Landau parameterκ is negligible. Another conclusion is that the normalized temperature dependence ofHc2 is independent of the orientation of the magnetic field with respect to the crystallographicaxes of the sample. We also discuss the fact that isotropy of the temperature dependence ofHc2 straightforwardly follows from the Ginzburg–Landau theory ifκ does not depend on the temperature.

Microscopic theory of superconductivity in MgB2-type systems in a magnetic field: A neighborhood of H c2

We calculate the upper critical magnetic field H c2 in the framework of a microscopic superconductivity theory with two energy bands of different dimensions on the Fermi surface with the cavity topology typical of the compound MgB2 taken into account (an anisotropic system). We assume an external magnetic field parallel to the crystallographic z axis. We obtain analytic formulas in the low-temperature range (T/Tc ≪ 1) and also near the critical temperature ((T-Tc)/Tc ≪ 1). We compare the temperature dependence of Hc2 for a two-band anisotropic system with that of H c2 0 corresponding to a two-band isotropic system (with Fermi-surface cavities of the same topology). We determine the role of the band-structure anisotropy, the positive curvature of the upper critical field near the critical temperature, and the important role of the ratio v1/v2 of the velocities on the Fermi surface in determining Hc2. We also obtain the values of the parameters Δ1 and Δ2 along the line of the critical magnetic field.

Dependence of the Upper Critical Field on the Defect Concentration in MgB[sub 2] and the Electronic Structure Parameters

The upper critical field Hc2 (H ‖ c) of the two-band superconductor MgB2 is studied as a function of the residual resistivity ρn. It is found that the superconductor follows the standard trend: the slope-dHc2/dT of the temperature dependence of Hc2(T) increases with the number of defects. The upper critical field in the clean limit is found, and direct estimations of the parameters of carriers in the 2D σ band (including the Fermi velocity and the coherence length) are made. The contribution of the electron scattering to the magnitude of Hc2 is determined, and the mean free path of electrons in samples with various defect concentrations is estimated. The density of states of σ electrons at the Fermi level is calculated using the dependence of the slope-dHc2/dT on ρn and a band structure model. It is impossible to estimate this density of states directly, because the upper critical field is determined by the carriers of one band, whereas the resistivity depends on the carriers in both bands.

Ullah-Dorsey Scaling of Fluctuation Conductivity Near the Superconducting Transition in (LaSe)1.14(NbSe2)

Magnetotransport measurements with the quasi two-dimensional misfit-layer compound (LaSe)1.14(NbSe2) with critical temperature Tc = 1.23 K are presented. The temperature dependence of the upper critical magnetic field Hc2 has been determined from an analysis of magnetoresistance data through the scaling procedure obtained theroretically by Ullah and Dorsey for the fluctuation conductivity. We show that in contrast to a direct determination of Hc2(T) with a positive curvature the temperature dependence of Hc2 obtained via the scaling procedure reveals a negative curvature in agreement with the Werthammer-Helfand-Hohenberg theory for conventional type-II superconductors.

Magnetic Impurities in a Metal

One can observe an unusual temperature dependence of Hc2 in the overdoped cuprates. The problem of evaluation of the average value of the impurity spin in the presence of magnetic field is discussed.

Electrical conductivity and upper critical magnetic field of the molecular superconductor a-(EDT‐TTF)[Ni(dmit)2

The ambient-pressure superconductor a-(EDT-TTF)[Ni(dmit)2], which is a charge transfer salt formed between EDT-TTF and Ni(dmit)2, exhibits a superconducting transition at 1.3 K and a phase transition around 20 K featuring a characteristic resistance hump. We estimated that the room-temperature electrical conductivity was 140–370 and 14–36 S cm−1 for the current parallel and perpendicular to the conducting plane respectively. We measured the upper critical magnetic field (Hc2) in the superconducting phase. The temperature dependence of Hc2 was estimated |d Hc2/dT| T = Te = −0.27 T K−1 (B||c-axis); |dHc2/d T| T = Tc = −3.5 T K−1 (B||ab-plane). The anisotropy of Hc2 within the ab-plane was found to be quite small, indicating a two-dimensionally isotrope character within the ab-plane in the superconducting state of the salt.

Pair breaking, ?intrinsic?T c, and the upper limit ofT c in the cuprates

The presence of magnetic impurities leads to a drastic decrease inTc in the overdoped region, gaplessness, and the usual temperature dependence ofHc2. The magnetic moments are localized on the apical oxygen site, and this allows us to explain the increase inTc with the increase in the number of Cu-O planes in the unit cell. Applied pressure can raiseTc above the usual value at optimum doping, toward the “intrinsic”Tc. The cuprates as a class of compounds have an upper limit ofTc in the rangeTc,upp=160–170 K.

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.

Upper critical field of Ba1−χKχBiO3 single crystal

We measured the upper critical field Hc2 on Ba1−χKχBiO3 (0.35<χ<0.40) single crystal down to 2 K in pulsed magnetic fields up to 35 T. Resistive transitions in the magnetic field systematically shift as the temperature decreases and the ϱ-H curves saturate for high enough magnetic field strength. The initial slope of the upper critical field (dHc2/dT)Tc is -0.5 T/K. As temperature decreases, the Hc2−T curve shows an upward curvature. At 2 K, we find Hc2=30 T, which gives a coherence length ξ=33 A. Such an Hc2 value is almost twice as large as what one can deduce by using the standard expression Hc2(0)=−0.693Tc(dHc2/ dT)Tc. From the comparison with several models, we conclude that this unusual temperature dependence of Hc2 can be due either to structural instability or to microscopic sample inhomogeneities.

Angular dependence of the upper critical field in layered superconductors

Abstract The upper critical field, Hc2(θ), in layered superconductors is investigated in an arbitrary direction θ, using a Ginzburg-Landau model proposed in a previous paper. Here, θ is the angle measured from the direction perpendicular to the layers. The angular dependence of Hc2(θ) in the region near θ=90° is correlated with the dimensionality in the temperature dependence of Hc2 (90°). We have a bell-shaped curve in the 3D regime and a curve with a cusp at θ=90° in the 2D regime in the Hc2 versus θ curve. The global angular dependence of Hc2(θ) in layered superconductors shows a clear difference from that in a 2D thin film and also from that in the anisotropic effective mass model. The behavior of Hc2(θ) in the small θ region is well understood on the basis of the proximity effect in layered superconductors. Qualitatively, the calculated result for Hc2(θ) reproduces well the angular dependence observed in Nb/Cu multilayers with various layer thicknesses.

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |Hc2(T)|,T ∼ 0 andT →Tc(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|Hc2(0)|/[-Tδ|Hc2T|δT]T{s0} for the case of a FS open inkz-direction with thekz-bandwidth, 4t3, very small compared to the Fermi energy,EF, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofTc and the temperature dependence of Hc2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa2Cu3O7 used elsewhere, we find reasonable values for the upper critical fieldHc2(0), the slope (dHc2/dT)Tc0, anisotropic coherence lengths ζi(T=0),i=x, y, z, and (dTc/d|H|)|H| → 0.