Ginzburg Number Research Articles

Effect of thermal fluctuations on the flux motion and vortex dynamic in (Li0.8Fe0.2)OHFeSe single crystals

We present a qualitatively investigation on the influence of thermal fluctuation on flux motion and vortex dynamic of (Li0.8Fe0.2)OHFeSe single crystals. The importance of thermal fluctuations has been assessed through the Ginzburg number Gi. The resistivity in the mixed state for (Li0.8Fe0.2)OHFeSe exhibits a thermally activated behavior investigated by TAFF theory. The field-dependent activation energy follows the relation U0 (H) ∼ H-α. The appearance of crossover at 2 T is related to the different pinning mechanisms. Single-vortex pinning occurs in the low fields range at H < 2 T, and collective pinning dominates in the region of field higher than 2 T. The vortex phase diagram from glass state to liquid state has been discussed based on the vortex-glass theory. Due to the influence of thermal fluctuations, there is a broad vortex liquid regime in the vortex phase diagram.

Vortex Phase Dynamics in Yttrium Superhydride YH6 at Megabar Pressures.

A comprehensive study of vortex phases and vortex dynamics is presented for a recently discovered high-temperature superconductor YH6 with Tc(onset) of 215 K under a pressure of 200 GPa. The thermal activation energy (U0) is derived within the framework of the thermally activated flux flow (TAFF) theory. The activation energy yields a power law dependence U0 ∝ Hα on magnetic field with a possible crossover at a field around 8-10 T. Furthermore, we have depicted the vortex phase transition from the vortex-glass to vortex-liquid state according to the vortex-glass theory. Finally, vortex phase diagram is constructed for the first time for superhydrides. Very high estimated values of flux flow barriers U0(H) = (1.5-7) × 104 K together with high crossover fields make YH6 a rather outstanding superconductor as compared to most cuprates and iron-based systems. The Ginzburg number for YH6 Gi = (3-7) × 10-3 indicates that thermal fluctuations are not so strong and cannot broaden superconducting transitions in weak magnetic fields.

Anomalously small magnetic relaxation rate of Ca10(Pt3As8)(Fe2−x Pt x As2)5 superconductor

Large critical current density and low magnetic relaxation are the main challenges for practical applications of high-temperature superconductors (HTSs). Magnetic relaxation refers to the decay of superconducting current density caused by thermal activation and/or quantum fluctuations. This process involves the motion of vortices, particularly vortex creep, which leads to energy dissipation. HTSs typically exhibit strong superconducting fluctuations and magnetic relaxation due to their short coherence length and large anisotropy. These characteristics are usually manifested by the large Ginzburg number Gi and high magnetic relaxation rate S. The correlation between the relaxation rate S and Gi is informative to understand the interplay between vortex dynamics and relevant parameters. Recently, Eley et al (2017 Nat. Mater. 16 409) proposed that almost all the HTSs follow a universal lower limit S∼ Gi 1/2(T/T c), providing new clues to design HTSs with small relaxation rate and evaluate their application potential. Here, we systematically studied the vortex dynamics in the Ca10(Pt3As8)(Fe2−x Pt x As2)5 superconductor with a large Gi∼ 0.16. Strikingly, this material exhibits a small relaxation rate (S ∼0.02 at T c/4 under 1 T), approaching the proposed lower limit of S∼ Gi 1/2(T/T c). We propose that such a small value of S in Ca10(Pt3As8)(Fe2−x Pt x As2)5 may originate from its unique structure with metallic skutterudite blocking layers. Our results suggest a promising new avenue for the search and design of HTSs with low magnetic relaxation.

A Scenario for the Critical Fluctuations near the Transition of Few-Bilayer Films of High-Temperature Cuprate Superconductors.

We study the critical fluctuations near the resistive transition of very thin films of high-temperature cuprate superconductors composed of a number N of only a few unit cells of superconducting bilayers. For that, we solve the fluctuation spectrum of a Gaussian-Ginzburg-Landau model for few-bilayers superconductors considering two alternating Josephson interlayer interaction strengths, and we obtain the corresponding paraconductivity above the transition. Then, we extend these calculations to temperatures below the transition through expressions for the Ginzburg number and Kosterlitz-Thouless-like critical region. When compared with previously available data in YBa2Cu3O7-δ few-bilayers systems, with N = 1 to 4, our results seem to provide a plausible scenario for their critical regime.

Dynamic crossover across the peak effect in BaK x Fe2As2 superconductor for H-axis and H-plane

The vortex matter properties of a BaK x Fe2As2 single crystal ( K) were studied, by employing both isofield and isothermal ac-susceptibility measurements, , in a wide range of frequencies and amplitudes of the applied ac magnetic field. The irreversibility line (), formally defined by the onset of the third harmonic, is recorded for both -axis and -plane. It can be reproduced from the empirical equation, , with and Tesla, Tesla. The isofield measurements of the first harmonic revealed a narrow diamagnetic peak, related to a local peak of the critical current below the irreversibility line for both -axis and -plane. The local peak for Tesla is transformed to a sudden drop before it completely disappears. Detailed ac-susceptibility measurements were conducted for frequencies ranging within f = 0.1–10 kHz. From these data, the pinning potential, U, is deduced both as function of temperature and dc magnetic field. These results revealed that the ac response of vortex matter exhibits three distinct dynamic behaviors. By employing a model proposed by Mikitik and Brandt (2001 Phys. Rev. B 64 184514), that is based on a Lindemann type criterion and the collective pinning theory, we reproduced the experimentally recorded vortex matter phase diagram by taking into account both thermal fluctuations and random point disorder. To this effect, we adopted a pinning mechanism, , = 1.1–1.5 and a Ginzburg number .

Wide Critical Fluctuations of the Field-Induced Phase Transition in Graphite.

In the immediate vicinity of the critical temperature (T_{c}) of a phase transition, there are fluctuations of the order parameter that reside beyond the mean-field approximation. Such critical fluctuations usually occur in a very narrow temperature window in contrast to Gaussian fluctuations. Here, we report on a study of specific heat in graphite subject to a high magnetic field when all carriers are confined in the lowest Landau levels. The observation of a BCS-like specific heat jump in both temperature and field sweeps establishes that the phase transition discovered decades ago in graphite is of the second order. The jump is preceded by a steady field-induced enhancement of the electronic specific heat. A modest (20%) reduction in the amplitude of the magnetic field (from 33 to 27T) leads to a threefold decrease of T_{c} and a drastic widening of the specific heat anomaly, which acquires a tail spreading to two times T_{c}. We argue that the steady departure from the mean-field BCS behavior is the consequence of an exceptionally large Ginzburg number in this dilute metal, which grows steadily as the field lowers. Our fit of the critical fluctuations indicates that they belong to the 3DXY universality class as in the case of the ^{4}He superfluid transition.

Fluctuation, Diamagnetic Transition, and FTIR Spectra of La Substituting Ca in (Bi,Pb):2223 Superconductor

We report here fluctuation, diamagnetic transition, and FTIR spectra in Bi1.7Pb0.30 Sr2Ca2-xLaxCu3Oy superconductor with various x values (0.00 < x < 0.30). It is found that the magnetic moment is negative for the samples below the onset of diamagnetism in both field cooling (FC) and zero-field cooling (ZFC). Although the magnetic moments are shifted to lower values close to zero as La increases up to 0.30, they are higher for Fc than for ZFC. Furthermore, the onset temperature of diamagnetic transition (TcM) for La = 0.30 sample is 83 K, which is about 30 K higher than that obtained from resistivity data (TcR = 53 K). On the other hand, the logarithmic plots of excess conductivity ∆σ and reduced temperature e for the samples reveal three different exponents corresponding to two crossover temperatures in the slope of each plot. The first exponent occurs in the normal field region (NFR) and its values are 0.30 (3D), 0.50 (3D), 0.20 (3D), and 2.04 (0D). The second exponent occurs in the mean field region (MFR) and its values are 0.75(2D), 0.44 (3D), 0.65 (2D), and 0.36 (3D). The third exponent occurs in the critical field region (CFR) and its values are 0.51 (3D), 0.99 (2D), 0.38 (3D), and 0.65 (2D). Interestingly, the Ginzburg-Landau parameter, critical magnetic fields, and critical current density are gradually increased as La increases up to 0.30, while the interlayer coupling, coherence lengths, anisotropy, and Ginzburg number are decreased. Finally, the FTIR absorption spectra of the samples show nine successive peaks due to O-H, Bi(Pb):2223, residual carbon, SrCo, CaCo3 and CuO, and M-O, respectively. These results are discussed in terms of the correlation between hole carriers/Cu ions and excess oxygen which are introduced by La through CuO2 planes of BSCCO superconductors. PACS: 74.25.Bt74.62.Dh74.62.En74.72.gh

Excess Conductivity, Diamagnetic Transition and FTIR Spectra of Ca Substituted by La in (Bi,Pb):2212 Superconducting System

We report here measurements of the excess conductivity, the diamagnetic transition and the FTIR spectra of Bi1.7Pb0.30 Sr2Ca1−xLaxCu2Oy superconductor with various x values (0.00 ≤ x ≤ 0.30). It is found that the magnetic moment is negative below the diamagnetic transition in both field cooling (FC) and zero-field cooling (ZFC) for all samples. Furthermore, the magnetic moment is gradually shifted to lower values close to zero as the La concentration increases up to 0.30, but their values for FC are higher than that of ZFC. Moreover, the onset of diamagnetism (TcM) for the La = 0.30 sample is 80 K, which is about 29 K higher than that obtained from resistivity (TcR= 51 K). On the other hand, the logarithmic plots of excess conductivity ∆σ and reduced temperature Є reveal three different exponents corresponding to two crossover temperatures in the slope of each plot for all samples. The first exponent occurs in the normal field region (NFR) and its values are 0.90 (2D), 0.67 (2D), 0.23 (3D) and 0.77 (2D). The second exponent occurs in the mean field region (MFR) and its values are 0.51(3D), 0.23 (3D), 1.05 (2D) and 0.17 (3D). The third exponent occurs in the critical field region (CFR) and its values are 0.90 (2D), 0.78 (2D), 0.70 (2D) and 0.35 (3D). Interestingly, The Ginzburg-Landau parameter, critical magnetic fields and critical current density are gradually increased with La concentration up to 0.30, while the interlayer coupling, coherence lengths, anisotropy and Ginzburg number are decreased. Finally, the FTIR absorption spectra of the samples show nine successive peaks due to O–H, Bi(Pb):2223, residual carbon, SrCO, CaCO3 and CuO, and M–O, respectively. These results are discussed in terms of the correlation between hole carriers/Cu ions and excess oxygen which are introduced by La through CuO2 planes of BSCCO superconductors.

Surface tension in bulk and bounded liquids

The paper is aimed at theoretical studying the following problems and its relation to the available experimental data: 1) the coefficient of surface tension and capillary constant in bulk and spatially bounded liquids in a wide range of thermodynamic parameters (temperature, density, pressure, etc.), including the critical region; 2) influence of size effects on surface tension and capillary constant in liquids with a varying spatial dimensionality, namely from the “surface” 2D-state to the “bulk” 3D-state, and then to regular 4D-state where the fluctuation effects may be neglected in liquids like water with the Ginzburg number, Gi < 1; 3) comparison the obtained results and empirical approach to the water surface tension in a wide intervals of thermodynamic variables, including confined supercooled water; 4) medical application of results for surface tension, using similarity between processes of carcinogenesis and nucleation.The theoretical formulas are proposed for dependence of surface tension and capillary constant in bulk and confined liquids on temperature, density, pressure, and size variables in a wide vicinity of the critical region. The agreement of theoretical and experimental data for the temperature dependence of surface tension and capillary constant appears to be quite satisfactory. The 2D↔3D dimensional crossover for surface tension and capillary constant is analyzed. The surface tension of liquids with a relatively small Ginzburg number, including bulk water, is studied with taking into account the dimensionality crossover from 3D-systems to 4D-systems, where the Landau mean-field theory is valid. The empirical formula for surface tension of pure water is discussed together with the Tolman correction and the fluctuation theory of phase transitions. The consequences of the similarity hypothesis of nucleation and carcinogenesis are discussed.

Fluctuating specific heat in two-band superconductors**Project supported by the National Natural Science Foundation of China (Grant No. 11674007).

Theory of thermal fluctuations in two-band superconductors under an essentially homogeneous magnetic field is developed within the framework of the two-band Ginzburg–Landau theory. The fluctuating specific heat is calculated by using the optimized self-consistent perturbation approach and the results are applied to analyze the thermodynamic data of the iron-based superconductors Ba1−xKxFe2As2 with x ∼ 0.4, which have been suggested to have a two-band structure by recent experiments. We estimate the fluctuation strength in this material and find that the specific heat is described well with the Ginzburg number Gi = 4·10−4. The influence of interband coupling strength is investigated and the result of the two-band Gaussian approximation approach is compared.

BCS-like critical fluctuations with limited overlap of Cooper pairs in FeSe

In conventional superconductors, very narrow superconducting fluctuation regions are observed above $T_c$ because of the strong overlapping of Cooper pairs in a coherence volume. In the bulk form of iron chalcogenide superconductor FeSe, it is argued that the system may locate in the crossover region of BCS to BEC, indicating a strong superconducting fluctuation. In this respect, we have carried out measurements of magnetization, specific heat and Nernst effect on FeSe single crystals in order to investigate the superconducting fluctuation effect near $T_c$. The region of diamagnetization induced by superconducting fluctuation seems very narrow above $T_c$. The crossing point of temperature dependent magnetization curves measured at different magnetic fields, which appears in many systems of cuprate superconductors and is regarded as indication of strong critical fluctuation, is however absent. The magnetization data can be scaled based on the Ginzburg-Landau fluctuation theory for a quasi-two-dimensional system, but the scaling result cannot be described by the theoretical function of the fluctuation theory because of the limited fluctuation regions. The specific heat jump near $T_c$ is rather sharp without the trace of strong superconducting fluctuation. This is also supported by the Nernst effect measurements which indicate a very limited region for vortex motion above $T_c$. Associated with very small value of Ginzburg number and further analyses, we conclude that the superconducting fluctuation is very weak above $T_c$ in this material. Our results are strongly against the picture of significant phase fluctuation in FeSe single crystals, although the system has a very limited overlapping of Cooper pairs in the coherence volume. This dichotomy provides new insights into the superconducting mechanism when the system is with a dilute superfluid density.

Universal lower limit on vortex creep in superconductors.

Superconductors are excellent testbeds for studying vortices, topological excitations that also appear in superfluids, liquid crystals and Bose-Einstein condensates. Vortex motion can be disruptive; it can cause phase transitions, glitches in pulsars, and losses in superconducting microwave circuits, and it limits the current-carrying capacity of superconductors. Understanding vortex dynamics is fundamentally and technologically important, and the competition between thermal energy and energy barriers defined by material disorder is not completely understood. Specifically, early measurements of thermally activated vortex motion (creep) in iron-based superconductors unveiled fast rates (S) comparable to measurements of YBa 2Cu3O7-δ (refs,,,,,). This was puzzling because S is thought to somehow correlate with the Ginzburg number (Gi), and Gi is significantly lower in most iron-based superconductors than in YBa 2Cu3O7-δ. Here, we report very slow creep in BaFe 2(As0.67P0.33)2 films, and propose the existence of a universal minimum realizable S ∼ Gi1/2(T/Tc) (Tc is the superconducting transition temperature) that has been achieved in our films and few other materials, and is violated by none. This limitation provides new clues about designing materials with slow creep and the interplay between material parameters and vortex dynamics.

Superconducting parameter determination for (Co0.5Zn0.5Fe2O4) x /Cu0.5Tl0.5-1223 composite

Abstract The addition of magnetic Co0.5Zn0.5Fe2O4 nanoparticles to the superconducting Cu0.5Tl0.5-1223 phase has been used to investigate the electrical resistivity behavior of the composite above the superconducting transition temperature T c. This was studied according to the opening of spin gap and fluctuation conductivity. The results indicated that the pseudogap temperature (T*) and superconducting fluctuation temperature (T scf) change by increasing the addition of Co0.5Zn0.5Fe2O4 nanoparticles. It was found that T* is related to hole carrier concentration P and it also depends on the antiferromagnetic fluctuation affected by magnetic nanoparticles. The excess-conductivity analysis showed four different fluctuation regions started from high temperature up to T c, and they were denoted by short wave (sw), two-dimensional (2D), three-dimensional (3D), and critical (cr) fluctuations. The crossover temperature between 3D and 2D (T 3D–2D) in the mean field region was decreased by increasing the addition of Co0.5Zn0.5Fe2O4 nanoparticles, in accordance with the decrease in T scf with x. The coherence length at 0 K along c-axis ξ c(0), effective layer thickness of the 2D system d, and inter-layer coupling strength J were estimated as a function of Co0.5Zn0.5Fe2O4 nanoparticle addition. Moreover, the thermodynamics, lower and upper critical magnetic fields, as well as critical current density have been calculated from the Ginzburg number N G. It was found that the low concentration of Co0.5Zn0.5Fe2O4 nanoparticles up to x = 0.08 wt% improves the superconducting parameters of Cu0.5Tl0.5-1223 phase. On the contrary, these parameters were deteriorated for (Co0.5Zn0.5Fe2O4) x /Cu0.5Tl0.5-1223 composite with x &gt; 0.08 wt%.

Multiband superconductivity in Lu3Os4Ge13

Intermetallic R3T4X13 series consist of a cage-like structure and have attracted attention due to their unconventional electronic ground states. In this work, we report the normal and superconducting state properties of a high-quality single crystal of Lu3Os4Ge13. Lu3Os4Ge13 belongs to the above-mentioned series and crystallizes in a cubic crystal structure with the space group Using electrical transport, magnetization and heat capacity measurements, we show that Lu3Os4Ge13 is a type-II multi-band superconductor (Tc = 3.1 K) with unusual superconducting properties. The analysis of the low-temperature heat capacity data suggests that Lu3Os4Ge13 is a moderately coupled multi-band BCS superconductor with two gaps () in the superconducting state. The dc-magnetization (M−H) shows a large reversible region in the superconducting state similar to the vortex liquid phase observed in high-Tc superconductors. The value of the Ginzburg number Gi suggests that the thermal fluctuations, though small compared to those in high-Tc cuprates, may play an important role in the unpinning of the vortices in this compound. The electronic band structure calculations show that three bands cross the Fermi level and constitute a complex Fermi surface in Lu3Os4Ge13.

Quasi-two-dimensional superconductivity in FeSe0.3Te0.7 thin films and electric-field modulation of superconducting transition.

We report the structural and superconducting properties of FeSe0.3Te0.7 (FST) thin films with different thicknesses grown on ferroelectric Pb(Mg1/3Nb2/3)0.7Ti0.3O3 substrates. It was shown that the FST films undergo biaxial tensile strains which are fully relaxed for films with thicknesses above 200 nm. Electrical transport measurements reveal that the ultrathin films exhibit an insulating behavior and superconductivity appears for thicker films with Tc saturated above 200 nm. The current-voltage curves around the superconducting transition follow the Berezinskii-Kosterlitz-Thouless (BKT) transition behavior and the resistance-temperature curves can be described by the Halperin–Nelson relation, revealing quasi-two-dimensional phase fluctuation in FST thin films. The Ginzburg number decreases with increasing film thickness indicating the decrease of the strength of thermal fluctuations. Upon applying electric field to the heterostructure, Tc of FST thin film increases due to the reduction of the tensile strain in FST. This work sheds light on the superconductivity, strain effect as well as electric-field modulation of superconductivity in FST films.

TAFF and vortex glass state in a niobium oxy-nitride Nb(N0.98O0.02)

Resistivity broadening of niobium oxy-nitride [Nb(N0.98O0.02)] is analyzed in terms of fluctuation conductivity, thermally activated flux flow (TAFF) and vortex glass study in magnetic fields up to 14 T. Zero field fluctuation analysis of excess conductivity using the Aslamzov-Larkin theory shows an indication of a 3D character that is further supported by the lowest Landau level (LLL) scaling. We could obtain a clear vortex glass region from an extended analysis of the resistivity data. Different regions of interest are estimated that include vortex glass and vortex liquids of the phase diagram. The TAFF has been analyzed using conventional Arrhenius relation, as well as its modified version that includes a temperature- and field-dependent pre-factor. While the conventional TAFF scaling is well suited for the present system, the modified version yields deeper insight into the material parameters of interest. Ginzburg number, coherence length, critical exponents related to the vortex glass transition, etc, are estimated and discussed.

Excess conductivity and Berezinskii–Kosterlitz–Thouless transition in superconducting FeSe thin films

Temperature-dependent electronic transport in the vicinity of the superconducting transition is reported for quasi-two-dimensional textured FeSe thin films. The conspicuous rounding of the resistive transitions and large transition widths are indications of excess conductivity due to thermal Cooper-pair fluctuations, which can be well-described by the two-dimensional Aslamazov–Larkin theory. The Halperin–Nelson form of the sheet resistance between the phase-ordering temperature TBKT and the mean-field temperature TMF, and the power-law behaviour of the voltage–current characteristics, with a distinctive jump of the exponent at TBKT, are indicative of a Berezinskii–Kosterlitz–Thouless transition. The complementary results suggest a two-dimensional character of superconductivity in the FeSe films and allow a quantitative estimate of the Ginzburg number Gi.

Shrinking of the fluctuation region in a two-band superconductor

In a two-band superconductor, two qualitatively different fluctuation modes related to the gap modules contribute to the free energy and heat capacity, together with the phase fluctuations. The first mode has divergent temperature behaviour since it accounts for critical fluctuations around the phase transition point, , along with pseudo-critical ones associated with the former instability of the weaker superconductivity component. The involvement of these two factors, competing under interband interaction, results in a Ginzburg number that varies with non-monotonically, allowing a reduction of up to 75%. This makes the fluctuations effective in revealing additional superconducting components in the system. The second mode does not diverge, but has a jump at , defined uniquely by the strength of the interband interaction. This mode contributes fundamentally beyond the critical domain.

Scaling for level statistics from self-consistent theory of localization

Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the relations of finite-size scaling for different parameters characterizing the level statistics. The obtained results are compared with the extensive numerical material for space dimensions d=2,3,4. On the level of raw data, the results of numerical experiments are compatible with the self-consistent theory, while the opposite statements of the original papers are related with ambiguity of interpretation and existence of small parameters of the Ginzburg number type.

Static replica approach to critical correlations in glassy systems

We discuss the slow relaxation phenomenon in glassy systems by means of replicas by constructing a static field theory approach to the problem. At the mean field level we study how criticality in the four point correlation functions arises because of the presence of soft modes and we derive an effective replica field theory for these critical fluctuations. By using this at the gaussian level we obtain many physical quantities: the correlation length, the exponent parameter that controls the mode-coupling dynamical exponents for the two-point correlation functions, and the prefactor of the critical part of the four point correlation functions. Moreover, we perform a one-loop computation in order to identify the region in which the mean field gaussian approximation is valid. The result is a Ginzburg criterion for the glass transition. We define and compute in this way a proper Ginzburg number. Finally, we present numerical values of all these quantities obtained from the hypernetted chain approximation for the replicated liquid theory.