Ginzburg-Landau Coherence Length Research Articles

Quasi-two-dimensional fluctuations in the magnetization of La1.9Ca1.1Cu2O6+δ superconductors

We report the results of magnetization measurements with the magnetic field applied along the $c$ axis on superconducting $\mathrm{L}{\mathrm{a}}_{1.9}\mathrm{C}{\mathrm{a}}_{1.1}\mathrm{C}{\mathrm{u}}_{2}{\mathrm{O}}_{6+\ensuremath{\delta}}$ single crystals processed under ultrahigh oxygen pressure. Strong fluctuation effects were found in both low- and high-field regimes. Scaling analysis of the high-field magnetization data near the critical temperature $({T}_{c}=53.5\phantom{\rule{0.16em}{0ex}}\mathrm{K})$ region reveals the characteristics of critical fluctuation behavior of quasi-two-dimensional (2D) superconductivity, described by Ginzburg-Landau theory using the lowest Landau level approximation. Low-field magnetic susceptibility data can be successfully explained by the Lawrence-Doniach model for a quasi-2D superconductor, from which we obtained the $ab$ plane Ginzburg-Landau coherence length of this system, ${\ensuremath{\xi}}_{ab}(0)=11.8\ifmmode\pm\else\textpm\fi{}0.9\phantom{\rule{0.16em}{0ex}}\AA{}$. The coherence length along the $c$ axis, ${\ensuremath{\xi}}_{c}(0)$, is estimated to be about 1.65 \AA{}, which is in between those of 2D cuprate systems, such as $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{r}}_{2}\mathrm{C}{\mathrm{a}}_{2}\mathrm{C}{\mathrm{u}}_{3}{\mathrm{O}}_{10}$ and $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{r}}_{2}\mathrm{CaC}{\mathrm{u}}_{2}{\mathrm{O}}_{8}$, and quasi-three-dimensional (3D) cuprate systems, such as overdoped $\mathrm{L}{\mathrm{a}}_{2\ensuremath{-}x}\mathrm{S}{\mathrm{r}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ and $\mathrm{YB}{\mathrm{a}}_{2}\mathrm{C}{\mathrm{u}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$. Our studies suggest a strong interplay among the fluctuation effects, dimensionalities, and the ratios of the interlayer Cu-O plane spacing, $s$, to the c-axis coherence lengths. A high $s/{\ensuremath{\xi}}_{c}(0)$ was observed in the high-pressure oxygenated $\mathrm{L}{\mathrm{a}}_{1.9}\mathrm{C}{\mathrm{a}}_{1.1}\mathrm{C}{\mathrm{u}}_{2}{\mathrm{O}}_{6+\ensuremath{\delta}}$, and that apparently drives this system to behave more like a quasi-2D superconductor.

Numerical Solution of Maxwell Equations for S-Wave Superconductors

The present paper is a sequel to the paper by Karchev (Condensed Matter 20 February 2017). We report the numerical solutions of the system of equations, which describes the electrodynamics of s-wave superconductors without normal quasi-particles for time-independent fields and half-plane superconductor geometry. The results are: (i) the applied magnetic field increases the Ginzburg–Landau (GL) coherence length and suppresses the superconductivity; (ii) the applied electric field decreases GL coherence length and supports the superconductivity; (iii) if the applied magnetic field is fixed and the applied electric field increases, the London penetration depth of the magnetic field decreases. The main conclusion is that by applying electric field at very low temperature where there are no normal quasi-particles one increases the critical magnetic field. This result is experimentally testable.

Flux pinning properties of YBa2Cu3O7–δ thin films containing a high density of nanoprecipitates: A comparative study to reveal size effects

Temperature dependence of critical current density Jc(H, T) was measured in moderate magnetic fields (H ⊥ film) in two thermally co-evaporated YBa2Cu3O7–δ (YBCO) thin films (A, B) and two YBCO films (C, D) deposited using a pulsed-laser deposition method. All sample films were grown epitaxially with the c-axis perpendicular to the surface of a single-crystalline substrate. Transmission electron microscopy observation revealed that these four films contained a high density of nanoprecipitates with typical sizes of 3.6 – 5.0 nm (A), 5.0 – 7.1 nm (B), 7.0 – 10.1 nm (C) and 8.7 – 14.3 nm (D). Films A and B contained very fine nanoprecipitates, whose typical diameters Dtyp are smaller than double the estimated Ginzburg-Landau coherence length 2ξab at T = 77 K, and exhibited a steep increase of Jc with decreasing temperature. Whereas, film D, which contained relatively large nanoprecipitates (Dtyp > 2ξab at T ≤ 70 K), exhibited a gradual increase in Jc. This led to a remarkable crossing of the Jc(T) curves. The temperature dependence of Jc(H//c) under a fixed magnetic field is approximated by Jc ∼ (1 – T/Tc)m(1 + T/Tc)2 where the index m is larger for films containing finer precipitates; that is, m(A) > m(B) > m(C) > m(D). This means that finer nanoprecipitates generally cause steeper Jc increase at low temperatures, which is the origin of the observed crossing phenomenon. The experimental results are reasonably explained by several theoretical models based on the direct summation of elementary pinning forces fp calculated by core pinning interactions.

Superconductivity in LaBi3 with AuCu3-type structure

We succeeded in synthesizing a new intermetallic compound with a AuCu3-type structure, LaBi3, by utilizing a high-pressure technique. Reacting Bi and LaBi at 450 °C under a pressure of 3.4 GPa resulted in the crystallization of LaBi3 with an a-axis lattice parameter of Sharp superconducting transitions were observed in both its magnetic susceptibility and electrical resistivity at 7.3–7.4 K. The upper critical field and Ginzburg–Landau coherence length ξ0 were estimated to be 1.70 T and 139 Å, respectively. The superconducting transition temperature Tc was found to decrease linearly with increasing applied pressure with a slope of −0.26 K GPa−1. Band structure calculations indicated that this compound has a multiband nature and that its Fermi energy is located exactly at one of the peak density of states.

Improved superconducting properties of La3Co4Sn13 with indium substitution

We report two fold increase in superconducting transition temperature of La3Co4Sn13 by substituting indium at the tin site. The transition temperature of this skutterudite related compound is observed to increase from 2.5 K to 5.1 K for 10% indium substituted sample. The band structure and density of states calculations also indicate such a possibility. The compounds exhibit type-II superconductivity and the values of lower critical field (Hc1), upper critical field (Hc2), Ginzburg–Landau coherence length (ξ), penetration depth (λ) and GL parameter (κ) are estimated to be 0.0028 T, 0.68 T, 21.6 nm, 33.2 nm and 1.53 respectively for La3Co4Sn11.7In1.3. Hydrostatic external pressure leads to decrease in transition temperature and the calculated pressure coefficient is −0.311 K/GPa. Flux pinning and vortex activation energies also improved with indium addition. Only positive frequencies are observed in phonon dispersion curve that relate to the absence of charge density wave or structural instability in the normal state.

Theoretical Study of Upper Critical Magnetic Field (HC2) in Multiband Iron Based Superconductors

This research work focuses on the theoretical investigation of the upper critical magnetic field,HC2; Ginzburg-Landau coherence length,ξGL(T); and Ginzburg-Landau penetration depth,λGL(T), for the two-band iron based superconductorsBaFe2(As1-xPx)2,NdO1-xFxFeAs, and LiFeAs. By employing the phenomenological Ginzburg-Landau (GL) equation for the two-band superconductorsBaFe2(As1-xPx)2,NdO1-xFxFeAs, and LiFeAs, we obtained expressions for the upper critical magnetic field,HC2; GL coherence length,ξGL; and GL penetration depth,λGL, as a function of temperature and the angular dependency of upper critical magnetic field. By using the experimental values in the obtained expressions, phase diagrams of the upper critical magnetic field parallel,HC2∥c, and perpendicular,HC2⊥c, to the symmetry axis (c-direction) versus temperature are plotted. We also plotted the phase diagrams of the upper critical magnetic field,HC2versus the angleθ. Similarly, the phase diagrams of the GL coherence length,ξGL, and GL penetration depth,λGL, parallel and perpendicular to the symmetry axis versus temperature are drawn for the superconductors mentioned above. Our findings are in agreement with experimental observations.

Stripe-like nanoscale structural phase separation in superconducting BaPb(1-x)Bi(x)O3.

The phase diagram of BaPb1−xBixO3 exhibits a superconducting dome in the proximity of a charge density wave phase. For the superconducting compositions, the material coexists as two structural polymorphs. Here we show, via high-resolution transmission electron microscopy, that the structural dimorphism is accommodated in the form of partially disordered nanoscale stripes. Identification of the morphology of the nanoscale structural phase separation enables determination of the associated length scales, which we compare with the Ginzburg–Landau coherence length. We find that the maximum Tc occurs when the superconducting coherence length matches the width of the partially disordered stripes, implying a connection between the structural phase separation and the shape of the superconducting dome.

Superconducting fluctuations in isovalently substitutedBaFe2(As1−xPx)2: Possible observation of multiband effects

The nature of superconducting fluctuation effects in the isovalently-substituted iron pnictide BaFe$_2$(As$_{1-x}$P$_x$)$_2$ (x=0.35) is probed through measurements of the magnetization and magnetoconductivity around the superconducting transition. The results, obtained with magnetic fields up to 9 T applied in the two main crystal directions, are consistent with anisotropic Ginzburg-Landau (GL) approaches for finite applied magnetic fields. The analysis allowed to determine with accuracy the out-of-plane, $\xi_c(0)$, and in-plane, $\xi_{ab}(0)$, GL coherence lengths. Significant differences are found between the $\xi_c(0)$ values resulting from electrical transport and magnetization data. According to recent theoretical approaches, these differences could be interpreted in terms of the multiband nature of this material. The analysis of data in the low field region around the transition temperature also suggests that phase fluctuations, although possibly relevant in other Fe-based superconductors, may play a negligible role in this compound.

Superconductivity by Sr intercalation in the layered topological insulatorBi2Se3

Strontium intercalation between van der Waals bonded layers of the topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is found to induce superconductivity with a maximum ${T}_{c}$ of 2.9 K. Transport measurement on a single crystal of the optimally doped sample ${\mathrm{Sr}}_{0.1}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ shows weak anisotropy $(\mathrm{\ensuremath{\Gamma}}\ensuremath{\sim}1.5)$ and an upper critical field ${H}_{c2}(0)$ equal to 2.1 T for a magnetic field applied perpendicular to the $c$ axis of the sample. The Ginzburg-Landau coherence lengths are found to be ${\ensuremath{\xi}}_{ab}=15.3$ nm and ${\ensuremath{\xi}}_{c}=10.2$ nm. The lower critical field ${H}_{c1,ab}(0)$ and zero temperature penetration depth ${\ensuremath{\lambda}}_{ab}(0)$ are estimated to be $0.39\ifmmode\pm\else\textpm\fi{}0.02$ mT and $1221\ifmmode\pm\else\textpm\fi{}36$ nm, respectively. Hall and Seebeck measurements confirm the dominance of electronic conduction, and the carrier concentration is surprisingly low $(n=1.85\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$ at 10 K, indicating the possibility of unconventional superconductivity.

Study of Upper Critical Magnetic Field of Superconducting HoMo<sub>6</sub>Se<sub>8</sub>

This work focuses on the study of mathematical aspects of upper critical magnetic field of superconducting HoMo6Se8. At zero external magnetic field, HoMo6Se8 was found to undergo a transition from the normal state to the superconducting state at 5.6 K and returned to a normal but magnetically ordered state between the temperature range of 0.3 K and 0.53 K. The main objective of this work is to show the temperature dependence of the upper critical magnetic field of superconducting HoMo6Se8 by using the Ginzburg-Landau (GL) phenomenological Equation. We found the direct relationship between the GL coherence length (ξGL) and penetration depth (λGL) with temperature. From the GL Equations and the results obtained for the GL coherence length, the expression for upper critical magnetic field (Hc2) is obtained for the superconducting HoMo6Se8. The result is plotted as a function of temperature. The graph shows the linear dependence of upper critical magnetic field (Hc2) with temperature (T) and our finding is in agreement with experimental observations.

Field dependence of the superconducting gap in YPd2Sn: A μSR and NMR study

We have performed muon spin rotation/relaxation and 119Sn nuclear magnetic resonance (NMR) measurements to study the vortex state of polycrystalline samples of YPd2Sn (Tc = 5.4 K), over a wide range of applied magnetic fields up to Bc2(T). Measurements in the vortex state provide the temperature dependence of the effective magnetic penetration depth λ(T) and the field dependence of the superconducting gap Δ(0). The results are consistent with a very dirty s-wave BCS superconductor with λ(0) = 212(1) nm, a gap Δ(0) = 0.85(3) meV, and a Ginzburg-Landau coherence length ξGL(0) ≊ 23 nm. The μSR data in a broad range of applied fields are well reproduced by taking into account a field-related reduction of the effective superconducting gap. Interestingly, the ratio 2Δ(0)/(kBTc) appears to a good approximation to be field-independent, with a value at low field of 3.85(9), implying a field dependence of the gap . We discuss the significance of this result.

Hard domain walls in superfluidHe3−B

We study theoretically planar interfaces between two domains of superfluid $^{3}\mathrm{He}$-B. The structure of the B-B walls is determined on the scale of the superfluid condensation energy, and thus the domain walls have thickness on the order of the Ginzburg-Landau coherence length ${\ensuremath{\xi}}_{\mathrm{GL}}$. We study the stability and decay schemes of five inequivalent structures of such domain walls using a one-dimensional Ginzburg-Landau simulation. We find that only one of the structures is stable against small perturbations. We also argue that B-B interfaces could result from the adiabatic $A\ensuremath{\rightarrow}B$ transition and study textures at B-B interfaces. The B-B interface has a strong orienting effect on the spin-orbit rotation axis $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{n}}$ producing textures similar to those caused by external walls. We study the B-B interface in a parallel-plate geometry and find that the conservation of spin current sets an essential condition on the structure. The stable B-B interface gives rise to half-quantum circulation. The energies of bound quasiparticle excitations are studied in a simple model.

Oscillations of critical superconducting current in thin doubly-connected Sn films in an external perpendicular magnetic field

We report the results of experimental and theoretical studies of critical current oscillations in thin doubly-connected Sn films in an external perpendicular magnetic field. The experiments were performed on samples that consisted of two wide electrodes joined together by two narrow channels. The length of the channels l satisfied the condition l ≫ ξ (ξ is the Ginzburg–Landau coherence length). At temperatures close to the critical temperature Tc, the dependence of the critical current Ic on average external magnetic flux Φ¯e has the form of a piecewise linear function, periodic with respect to the flux quantum Φ0. The amplitude of the Ic oscillation at a given temperature is proportional to the factor ξ/l. Moreover, the dependence Ic=Ic(Φ¯e) is found to be multivalued, hence indicating the presence of metastable states. Based on the Ginzburg–Landau approximation, a theory was constructed that explains the above features of the oscillation phenomenon taking a perfectly symmetric system as an example. Further, the experiments displayed the effects related to the critical currents imbalance between the superconducting channels, i.e., shift of the maxima of the dependence Ic=Ic(Φ¯e) accompanied by an asymmetry with respect to the transport current direction.

Vortex core properties in iron pnictides

The mechanism of unconventional superconductivity in recently discovered Fe-based superconductors has been intensively discussed. A plausible candidate is the superconducting (SC) pairing mediated by antiferromagnetic (AFM) interactions. There are two different approaches predicting the s ± pairing state, in which the SC gap shows an s -wave symmetry that changes sign between different Fermi-surface (FS) sheets. The first one is based on the itinerant spin fluctuations promoted by FS nesting, and the second is based on the local AFM exchange couplings. We apply quasiclassical Eilenberger approach to the vortex state to calculate the cutoff parameter, ξh , at different levels of impurity scattering rates and to compare results with experimental data for iron pnictides. The s ± -wave pairing symmetry is considered as a presumable state for these materials. Magnetic field dependence of ξh /ξ c 2 is found to be nonuniversal for s ± pairing: depending on the chosen parameter set it can reside both below and above analytical Ginzburg-Landau curve. It is also found that normalized ξ 2 /ξ c 2 (B/B c 2 ) dependence is increasing with pair-breaking (interband) impurity scattering, and the intraband scattering results in decreasing of the ξ 2 /ξ c 2 value. Here, ξ 2 is the vortex core size and ξ c 2 is the Ginzburg-Landau coherence length determined from the upper critical field. The ξ 2 /ξ c 2 (B/B c 2 ) curve has a minimum at low temperatures and small scattering evolving into monotonously decreasing function at strong scattering and high temperatures.

Characterization of the spontaneous symmetry breaking due to quenching of a one-dimensional superconducting loop

We study the final distribution of the winding numbers in a 1D superconducting ring that is quenched through its critical temperature in the absence of magnetic flux. The study is conducted using the stochastic time-dependent Ginzburg–Landau model, and the results are compared with the Kibble–Zurek mechanism (KZM). The assumptions of the KZM are formulated and checked as three separate propositions. We find characteristic lengths and characteristic times for the processes we study. Besides the case of uniform rings, we examined the case of rings with several weak links. For temperatures close to or below Tc, the Ginzburg–Landau coherence length ξ(0)|T/Tc−1|−1/2 does not play the role of the correlation length. In order to regard the winding number as a conserved quantity, it is necessary to allow for a short lapse of time during which unstable configurations decay. We found criteria for the validity of the 1D treatment. There is no lower bound for the final temperatures that permit 1D treatment. For moderate quenching times τQ, the variance of the winding number obeys the scaling , as predicted by the KZM in the case of mean field models; for τQ ≲ 105ħ/kBTc, the dependence is weaker. We also studied the behavior of the system when fluctuations of the gauge field are suppressed, and obtained that the scaling is obeyed over a wider range.

μSR and NMR study of the superconducting Heusler compound YPd2Sn

We report on muon-spin rotation and relaxation ($\ensuremath{\mu}$SR) and ${}^{119}$Sn nuclear magnetic resonance (NMR) measurements to study the microscopic superconducting and magnetic properties of the Heusler compound with the highest superconducting transition temperature, YPd${}_{2}$Sn (${T}_{c}=5.4$ K). Measurements in the vortex state provide the temperature dependence of the effective magnetic penetration depth $\ensuremath{\lambda}(T)$ and the field dependence of the superconducting gap $\ensuremath{\Delta}(0)$. The results are consistent with a very dirty $s$-wave BCS superconductor with a gap $\ensuremath{\Delta}(0)=0.85(3)$ meV, $\ensuremath{\lambda}(0)=212(1)$ nm, and a Ginzburg-Landau coherence length ${\ensuremath{\xi}}_{\mathrm{GL}}(0)\ensuremath{\cong}23$ nm. In spite of its very dirty character, the effective density of condensed charge carriers is high compared to that in the normal state. The $\ensuremath{\mu}$SR data in a broad range of applied fields are well reproduced by taking into account a field-related reduction of the effective superconducting gap. Zero-field $\ensuremath{\mu}$SR measurements, sensitive to the possible presence of very small magnetic moments, do not show any indications of magnetism in this compound.

Annealing Time Effect Fluctuation Induced Excess Conductivity in Bi (Pb):2223 Superconductors

We report here on the effect of annealing time, in air and at 800°C for time periods of (6-30 h), on the fluctuation induced excess conductivity ∆σ in Bi2-xPbx: 2223 superconductors with various x values. The logarithmic plots of ∆σ and the reduced temperature e reveal three different exponents corresponding to two different crossover temperatures in the slope of each plot. The first exponent in the normal region is at a temperature of (Tc^(mf) ＜＜ T ＜ 2Tc ^(mf) ) and its values are close 2.5, in which the order parameter dimensionality (OPD) is not 0D. The second exponent is at a temperature of T ＞ Tc^(mf) , and its values are close to 1, in which the OPD is 2D. The third exponent is in the critical-field region at a temperature of (Tc ＜ T ≤ Tc^(mf)), and its values are close to 0.5, in which the OPD is 3D. Furthermore, the interlayer coupling J, Ginzburg-Landau coherence length ζc(0), temperature width (To-T^c(mf)), and resistivity slope (dp/dT) are also calculated for the two examined samples, and their values are affected by changing both the annealing time and Pb content. Our results are discussed in terms of the correlation between the carrier concentration and volume fraction of the high Tc phase for the considered samples.

Magnetoresistance measurements of a superconducting surface state of in-induced and Pb-induced structures on Si(111).

In situ micro-four-point-probe conductivity measurements in ultrahigh vacuum revealed that the Si(111)-striped incommensurate-Pb surface showed the superconductivity transition at 1.1 K. Both of the hexagonal and rectangular phases of Si(111)√[7]×√[3]-In surface showed superconductivity at 2.4 and 2.8 K, respectively. By applying magnetic field perpendicular to the surface, the upper critical field was deduced to be 0.1-1 T. The derived Ginzburg-Landau coherence length of the Cooper pairs was several tens of nm, which was much smaller than the Pippard's coherence length estimated from the band structures. The short coherence length is determined by the carrier mean free path.

Mo/Au Bilayer Superconducting Transition Edge Sensor Tuning With Surface Modification Structures

We have conducted an experimental study tuning the critical temperature, transition width, normal resistance, and critical current of Mo/Au bilayer transition edge sensors (TES) using Nb stripes on the TES surface. The Nb stripes modify the TES parameters through the lateral proximity effect. We summarize the dependence of the shift in transition temperature and the broadening of the transition width on the separation length between the Nb stripes and leads. We calculate the Ginzburg-Landau coherence length of the TES in two methods. One takes advantage of the dependence of the TES normal resistance on the number of the TES and Nb contacts. Another utilizes the temperature dependence of the TES critical current. The two methods are in good agreement with a coherence length ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ≈ 0.4 μm.

Unusual quantum magnetic-resistive oscillations in a superconducting structure of two circular asymmetric loops in series

We measured both quantum oscillations of a rectified time-averaged direct voltage Vrec(B) and a dc voltage Vdc(B) as a function of normal magnetic field B, in a thin-film aluminum structure of two asymmetric circular loops in series at temperatures below the superconducting critical temperature Tc. The Vrec(B) and Vdc(B) voltages were observed in the structure biased only with an alternating current (without a dc component) and only with a direct current (without an ac component), respectively. The aim of the measurements was to find whether interaction (nonlinear coupling) exists between quantum magnetic-resistive states of two loops at a large distance from each other. The distance between the loop centers was by an order of magnitude longer than the Ginzburg–Landau coherence length ξ(T). At such distance, one would not expect to detect any interaction between the quantum states of the loops. But we did find such an interaction. Moreover, we found that Vdc(B) functions (like Vrec(B) ones) can be used to describe the quantum states of the loops.