Thermodynamic Critical Field Research Articles

Origin of Hysteretic Field Splitting of the Zero Bias Conductance Peak in (100) and (110) Oriented Y1Ba2Cu3O7−x Films

We have studied the evolution of the Zero-Bias Conductance Peak (ZBCP) splitting under applied magnetic fields in tunneling experiments on Y1Ba2Cu3O7-x(YBCO), and particular its hysteresis. We have been able to distinguish between two possible contributions to the splitting. One of them is connected to Meissner screening currents whose variation in increasing fields is governed by the Bean-Livingston barrier that delays flux entry well above the lower thermodynamical critical field Hc1, up to the fields of the order of the thermodynamical critical field Hc. The other contribution, dominant in (110) oriented films, is seen in decreasing fields where there are no Meissner screening currents, since there is no barrier to flux exit and it may be connected to the magnetic induction in the sample as proposed by Laughlin.

Magnetic characterization of superconducting MgB 2

The critical current density J c of pressed polycrystalline MgB 2 specimen was measured using a DC magnetization and Campbell’s method. It was found that the two J cs are coincident and this result confirms that the intergrain J c is not deteriorated by grain boundaries. The upper critical field, lower critical field, thermodynamic critical field and Ginzburg–Landau parameter were estimated to characterize the magnetic properties. Observed J c and irreversibility field could be approximately explained by the flux creep-flow model. To foresee the potential of application of this material, J c was calculated when strong pins could be introduced.

Intrinsic parameters of aT*-phaseSmLa0.8Sr0.2CuO4−δsingle crystal and the fluctuation effects deduced from magnetization data

We report the result of a detailed study on the equilibrium thermodynamic properties from the reversible magnetization data of a ${T}^{*}$-phase ${\mathrm{SmLa}}_{0.8}{\mathrm{Sr}}_{0.2}{\mathrm{CuO}}_{4}$ single crystal ${(T}_{c}^{\mathrm{on}}\ensuremath{\approx}24 \mathrm{K}).$ The analysis of those data outside the critical fluctuation region was performed according to the Hao-Clem model, while the data in the critical region were analyzed on the basis of the nonperturbative two-dimensional Ginzburg-Landau lowest Landau level scaling theory developed by Te\ifmmode \check{s}\else \v{s}\fi{}anovi\ifmmode \acute{c}\else \'{c}\fi{} et al. The analysis outside the critical region yields a complete set of intrinsic parameters of this system consisting of the Ginzburg-Landau parameter $\ensuremath{\kappa},$ the thermodynamic critical field ${H}_{c},$ the magnetic field penetration depth $\ensuremath{\lambda},$ the Cooper pairs coherence length $\ensuremath{\xi},$ and the upper critical field ${H}_{c2}.$ We found that the values of ${H}_{c}(T)$ derived from the Hao-Clem model were generally smaller than those obtained from scaling analysis in the critical region. According to the result of analysis in the critical region, these differences are suggested to have their origin in the thermal fluctuation effect evidenced by the existence of a crossing point in the magnetization data at ${T}^{*}=23.25 \mathrm{K},$ right below the onset critical temperature.

Superconducting properties of lead nanowires arrays

Mesoscopic superconducting lead nanowires with high aspect ratio and diameter ranging from 40 to 270 nm have been grown by electrodeposition inside nanoporous polycarbonate membranes. Nanowires with a diameter less than 50 nm were insulators due to a poor crystal structure. The others are shown to be type II superconductors because of their small electronic mean free path, instead of being type I which is usual for the bulk form of lead. An increase in the thermodynamic critical field H c is observed and is attributed to the small transversal dimension leading to an incomplete Meissner effect. Finally, it is demonstrated that this enhancement agrees with numerical simulations based on the Ginzburg–Landau theory.

Electronic density of states derived from thermodynamic critical field curves for underdopedLa2−xSrxCuO4+δ

Thermodynamic critical field curves have been measured for $La_{2-x}Sr_{x}CuO_{4+\delta}$ over the full range of carrier concentrations where superconductivity occurs in order to determine changes in the normal state density of states with carrier concentration. There is a substantial window in the $H-T$ plane where the measurements are possible because the samples are both thermodynamically reversible and the temperature is low enough that vortex fluctuations are not important. In this window, the data fit Hao-Clem rather well, so this model is used to determine $H_c$ and $\kappa_c$ for each temperature and carrier concentration. Using N(0) and the ratio of the energy gap to transition temperature, $\Delta (0)/k_BT_c$, as fitting parameters, the $H_c vs T$ curves give $\Delta (0)/k_BT_c \sim 2.0$ over the whole range of $x$. Values of N(0) remain rather constant in the optimum-doped and overdoped regime, but drops quickly toward zero in the underdoped regime. .

THERMODYNAMIC CRITICAL FIELD OF La2-xSrxCuO4

Thermodynamic critical fields, Hc, have been measured for the La2-xSrxCuO4 family of superconductors in order to determine the changes in free energy of the system as the number of carriers is reduced. Magnetization vs. magnetic field curves are thermodynamically reversible over large portions of the H-T plane, so the free energy is well defined in these regions. Magnetization vs. field data are then fit to theoretical models to determine the thermodynamic critical fields. As the Sr concentration is changed from x=0.10 to 0.23, the values of Hc(T=0) goes through a maximum at optimum doping in a manner similar to the Tc vs x curve. The ratio of Hc(T = 0)/Tc also peaks in the region of x somewhat larger than optimum doping. As the value of x increases from underdoped to optimum doping, the cross-over temperature in the Msc vs. T curve, T*, approaches the transition temperature. In the overdoped regime there is no crossing in these Msc vs. T curves.

Specific heat in the superconducting and normal state (2–300 K, 0–16 T), and magnetic susceptibility of the 38 K superconductor MgB 2: evidence for a multicomponent gap

The specific heat C of a sintered polycrystalline sample of MgB 2 with a bulk superconducting transition temperature T c=36.7 K is measured as a function of the temperature (2–300 K) and magnetic field (0–16 T), together with magnetic properties (normal-state susceptibility, superconducting-state magnetization, etc.). The Sommerfeld constant γ=0.89±0.05 mJ/K 2/gat (2.7 mJ/K 2/mol) is determined in the normal state above H c2. The normal- and superconducting-state entropies are equal at T c. Several moments of the PDOS are obtained from the lattice specific heat. We report bulk values for: the thermodynamic critical field, B c(0)=0.26 T; the slope of the upper critical field, (d B c2/d T) T c =0.56 T/K; the Ginzburg–Landau parameter, κ=38; the coherence length, ξ≅5 nm; the lower critical field, B c1≅0.018 T; the London penetration depth, λ(0)≅180 nm. These results characterize MgB 2 as a type-II superconductor. The nearly quadratic dependence of C( T) versus T at T≪ T c, its non-linear field dependence, and the discrepancy between the electron–phonon coupling constant λ ep as determined by the renormalization of the electron density of states ( λ ep≅0.6) and by McMillan's equation for isotropic superconductors ( λ ep≅1.1), are inconsistent with a single isotropic gap. In addition to high phonon frequencies, anisotropy or two-band gap structure may explain why the critical temperature of this superconductor is high in spite of its low condensation energy, which does not exceed 1/16 of that of YBa 2Cu 3O 7 and 1/4 of that of Nb 3Sn.

The instability point H s of the Meissner state for large-κ superconductors

The critical field Hs corresponding to the emergence of vortices in a superconductor without a threshold is found near the transition temperature and in the limit as T→0 for an arbitrary value of the depairing factor Γ. In superconductors of the second kind, this field value coincides with the absolute instability point of the Meissner state. In large-κ superconductors, the order parameter tends to zero on the surface of the super-conductor if the external magnetic field reaches the value Hs. We obtain that Hs=Hcm (where Hcm is the thermodynamic critical field) for an arbitrary value of the depairing factor Γin the temperature region near Tc and at T=0.

Static stress effects in superconducting composites: Part I. Effect of uniaxial tensile stress on resistive critical field of Cu–Nb composites

Multifilamentary Cu–Nb in situ composite wires were subjected to tensile tests in liquid helium environment to study influence of the stress σ on resistive critical field H r of the composites. External magnetic field H was parallel to wire axis and 4-probe scheme for resistive measurements was applied. The wires had various diameters, that is they differed in their overall manufacturing deformation. Our experiments evidence that values of both the critical fields H r0 of the initial composites and stress sensitivity of the fields d H r/d σ are noticeably higher than those referenced for niobium. We conclude that it is the dislocation structure of Nb filaments and its effect on Ginzburg–Landau parameter and thermodynamic critical field H c of the filaments that determine the observed dependences.

Penetration of Josephson vortices and measurement of thec-axis penetration depth inBi2Sr2CaCu2O8+δ: Interplay of Josephson coupling, surface barrier, and defects

The first penetration field H_{J}(T) of Josephson vortices is measured through the onset of microwave absorption in the locked state, in slightly overdoped $\rm{Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta}}$ single crystals (T_{c} ~ 84 K). The magnitude of H_{J}(T) is too large to be accounted for by the first thermodynamic critical field H_{c1}(T). We discuss the possibility of a Bean-Livingston barrier, also supported by irreversible behavior upon flux exit, and the role of defects, which relates H_{J}(T) to the c-axis penetration depth $\lambda_{c}(T)$. The temperature dependence of the latter, determined by a cavity perturbation technique and a theoretical estimate of the defect-limited penetration field are used to deduce from H_{J}(T) the absolute value of $\lambda_{c}(0)=(35 \pm 15) \mu m$.

Superconducting properties ofYxLu1−xNi2B2CandLa3Ni2B2N3−δ:A comparison between experiment and Eliashberg theory

Specific heat and resistivity measurements were performed on polycrystalline samples of the solid-solution ${\mathrm{Y}}_{x}{\mathrm{Lu}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ in order to determine thermodynamic properties such as the specific-heat difference $\ensuremath{\Delta}C,$ the thermodynamic critical field ${H}_{c}(T),$ as well as the upper critical field ${H}_{c2}(T).$ These properties were analyzed within the Eliashberg theory including anisotropy effects, yielding electron-phonon coupling anisotropy parameters $〈{a}_{\mathbf{k}}^{2}〉$ ranging between $0.02$ and $0.03$ for the whole series, and Fermi velocity anisotropy parameters of $〈{b}_{\mathbf{k}}^{2}〉=0.245--0.3.$ Excellent agreement between theory and experiment was achieved for these parameters, the Sommerfeld constant $\ensuremath{\gamma}$ and model phonon spectra determined from specific heat measurements. An analysis of the previously investigated boronitride ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}{\mathrm{N}}_{3\ensuremath{-}\ensuremath{\delta}}$ for comparison revealed the electron-phonon anisotropy to be of great significance in describing its thermodynamic properties and the calculations yielded $〈{a}_{\mathbf{k}}^{2}〉\ensuremath{\simeq}0.08$ and $〈{b}_{\mathbf{k}}^{2}〉\ensuremath{\simeq}0.245.$ The ${T}_{c}$ behavior within the series ${\mathrm{Y}}_{x}{\mathrm{Lu}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ is discussed in terms of the density of states at the Fermi level $N(0).$

Reversible magnetization and superconducting-state thermodynamic parameters for underdopedLa1.90Sr0.10CuO4

Magnetization studies have been made of single-crystal ${\mathrm{La}}_{1.90}{\mathrm{Sr}}_{0.10}{\mathrm{CuO}}_{4}$ with $H\ensuremath{\Vert}c$ in order to determine the magnitude of the flux expulsion and free energy in a material that has substantially less than optimal doping. Well above the superconducting transition temperature, the normal-state magnetization exhibits a two-dimensional Heisenberg antiferromagnetic behavior. Below ${T}_{c},$ there is a large portion of the $H\ensuremath{-}T$ plane where the sample shows reversible behavior so that thermodynamic variables such as the free energy and the shape of the magnetization curves can be determined. At low temperature, the vortices have a well defined Abrikosov regime that transforms to two-dimensional fluctuation behavior at higher temperatures. The magnetization vs temperature curves show a unique crossing point at 22 K where the magnetization is independent of magnetic field. From this value of the crossing point, the effective layer spacing s is derived to be 1.6 nm compared to the ${\mathrm{CuO}}_{2}$ lattice spacing of 0.66 nm. The fluctuations are found to obey two-dimensional scaling in that ${M/(\mathrm{TH})}^{1/2}$ is a universal function of $[T\ensuremath{-}{T}_{c}(H)]{/(\mathrm{TH})}^{1/2}.$ Below 12 K, the data fit the Hao-Clem theory rather well and give ${\ensuremath{\kappa}}_{c}$ values of about 175 and thermodynamic critical fields ranging from 112 mT at 12 K to 133 mT at 6 K.

First integrals of Ginzburg–Landau equations and stability criteria for vortex-free state in unconventional superconductors

The first integrals of the Ginzburg–Landau equations for a vortex-free state of superconductors with different mixed symmetries of the order parameter are found. The general boundary conditions for the order parameter at the ideal interface between the superconductor and vacuum are derived. Based on these integrals and boundary conditions, we analyze the stability criteria for vortex-free state in unconventional superconductors. The threshold field H s above which the Abrikosov vortices can enter the superconductor is found to be higher or equal to the thermodynamic critical field for all states under study.

Magnetization study in the superconducting mixed state of URu 2Si 2

Magnetization measurements of a heavy fermion compound URu 2Si 2 have been performed in the superconducting state. Broad peak structure of the irreversible magnetization was observed around 50 kOe for H‖ a. The Ginzburg–Landau parameter obtained from the equilibrium magnetization slightly decreases for H‖ c with decreasing temperature, suggesting the presence of the paramagnetic suppression of the superconductivity. However, the suppression is not so large as expected from the H c2( T) curve. Thermodynamic critical field appears to show unusual temperature dependence.

Magnetization measurements on single crystals of superconducting Ba0.6K0.4BiO3

Abstract Extensive measurements of the magnetization of superconducting single-crystal samples of Ba0.6K0.4BiO3 have been made using superconducting quantum interference device and cantilever force magnetometry at temperatures ranging between 1.3 and 350 K and in magnetic fields from near zero to 27 T. Hysteresis curves of magnetization versus field allow a determination of the thermodynamic critical field, the reversibility field and the upper critical field as functions of temperature. The lower critical field is measured separately and the Ginzburg-Landau parameter is found to be temperature dependent. AU critical fields have higher T = 0 limits than have been previously noted and none of the temperature dependences of the critical fields follows the expected power laws leading to a possible alternative interpretation of the thermodynamic nature of the superconducting transition.

Magnetization measurements on single crystals of superconducting Ba 0.6 K 0.4 BiO 3

Extensive measurements of the magnetization of superconducting single crystal samples of Ba0.6K0.4BiO3} have been made using SQUID and cantilever force magnetometry at temperatures ranging between 1.3 and 350 K and in magnetic fields from near zero to 27 T. Hysteresis curves of magnetization versus field allow a determination of the thermodynamic critical field, the reversibility field, and the upper critical field as a function of temperature. The lower critical field is measured seperately and the Ginzburg-Landau parameter is found to be temperature dependent. All critical fields have higher T = 0 limits than have been previously noted and none of the temperature dependence of the critical fields follow the expected power laws leading to possible alternate interpretation of the thermodynamic nature of the superconducting transition.

Thermodynamic functions within the van Hove BCS model: symmetry mixing effects

All the new layer perovskite superconductors seem to show a phenomenon of symmetry mixing with respect to the order parameters. An analysis of the different alternatives of mixing and how far they could be presented is carried out. For the particular case of s+ id symmetry of the gap, the temperature dependence of the specific heat ( C es) and the thermodynamic critical magnetic field ( H c) are calculated. A double peak transition is observed on C es( T) in the mixed regime while the single peak behavior is recovered for a purely symmetric state ( s or d). C es presents a quadratic law at low temperatures for a d-wave gap and the typical exponential attenuation for the s-wave. The temperature dependence of H c shows a clear phase transition of second order at temperatures where the d-wave component becomes negligible. A comparison with other results and experiments is done.

Scaling of flux pinning with the thermodynamic critical field

A systematic study of flux pinning and the thermodynamic critical field ${H}_{c}$ has been undertaken to determine whether ${H}_{c}$ is a central factor determining the critical current ${J}_{c}.$ Materials that have a fairly wide temperature interval of thermodynamic reversibility are selected so that the thermodynamic critical field can be confidently extrapolated into the irreversible regime. ${J}_{c}$ is found to scale with ${H}_{c}.$ For a given sample, the ${J}_{c}{/H}_{c}$ vs ${H/H}_{c}$ curves are close to a universal function as temperature changes. In addition, the peak in the pinning force curve also scales with ${H}_{c}^{2}$ for a wide variety of samples having quite different transition temperatures.

Possible experimentally observable effects of vertex corrections in superconductors

We calculate the effects of vertex corrections, of nonconstant density of states and of a (self-consistently determined) phonon self-energy for the Holstein model on a three-dimensional cubic lattice. We replace vertex corrections with a Coulomb pseudopotential ${\ensuremath{\mu}}_{C}^{*}$ adjusted to give the same ${T}_{c},$ and repeat the calculations, to see which effects are a distinct feature of vertex corrections. This allows us to determine directly observable effects of vertex corrections on a variety of thermodynamic properties of superconductors. To this end, we employ conserving approximations (in the local approximation) to calculate the superconducting critical temperatures, isotope coefficients, superconducting gaps, free-energy differences, and thermodynamic critical fields for a range of parameters. We find that the dressed value of $\ensuremath{\lambda}$ is significantly larger than the bare value. While vertex corrections can cause significant changes in all the above quantities (even when the bare electron-phonon coupling is small), the changes can usually be well modeled by an appropriate Coulomb pseudopotential. The isotope coefficient proves to be the quantity that most clearly shows effects of vertex corrections that can not be mimicked by a ${\ensuremath{\mu}}_{C}^{*}.$

Thermodynamic fluctuation under high pressure in Hg-1223 superconductors

Excess conductivities of polycrystalline Hg-1223 superconductor have been studied under high-pressure conditions. The critical temperature was chosen as the mean field transition temperature . Above this temperature, the normal state resistivity decreases with increasing pressure. The relative change in resistivity w.r.t. pressure, namely , is about . It is much smaller than the typical value of for most high- superconductors. As a consequence of the change in the normal state resistivity due to the applied pressure, the fluctuation-induced conductivity is also changed. The experimental results were analysed within the framework of Aslamazov-Larkin theory. The logarithmic plots of the excess conductivity versus reduced temperature reveal that there is a cross-over temperature which determines the transition from two- to three-dimensional conductivity of charge carrier transportation. With the help of the cross-over temperature , the values of the coherence length for the Hg-1223 superconductor could be estimated. The change in the fluctuation conductivity is discussed in terms of the coherence length and the thermodynamical critical field .