Critical Field Hc2 Research Articles

The transition-metal-dichalcogenide family as a superconductor tuned by charge density wave strength

In metallic transition metal dichalcogenides (TMDs), which remain superconducting down to single-layer thickness, the critical temperature Tc decreases for Nb-based, and increases for Ta-based materials. This contradicting trend is puzzling, impeding the development of a unified theory. Here we study the thickness-evolution of superconducting tunneling spectra in TaS2 heterostructures. The upper critical field Hc2 is strongly enhanced towards the single-layer limit – following Hc2∝Tc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${H}_{c2}\\propto {T}_{c}^{2}$$\\end{document}. The same ratio holds for the entire family of intrinsically metallic 2H-TMDs, covering 4 orders of magnitude in Hc2. Using Gor’kov’s theory, we calculate the suppression of Tc by the competing charge density wave (CDW) order, which affects the quasiparticle density of states and the resulting Tc and Hc2. The latter is found to be universally enhanced by two orders of magnitude. Our results substantiate CDW as the key determinant factor limiting Tc across the TMD family.

Improved flux pinning properties of Mg exceed MgB2 ceramics with B4C and Dy2O3 additions

In this study, MgB2 polycrystals were synthesized via the addition of B4C and Dy2O3. X-ray diffraction confirmed that MgB2 was the predominant phase in all the samples. The superconducting properties of the samples were characterized by in-field temperature-dependent resistivity and magnetization measurements. The upper critical field (Hc2) and the critical current density (Jc) of each sample were estimated. The results indicate significant enhancements in Hc2 and Jc with the optimal addition levels of B4C and Dy2O3. According to collective pinning theory, δl pinning was identified as the dominant pinning type in the fabricated samples. The dominant pinning mechanism was determined to be core surface pinning induced by grain boundaries, which is consistent with predictions made by the Dew–Hughes model.

Flux dynamics, anisotropy in Jc and vortex phase diagram of H+-intercalated FeSe single crystal

This paper investigates the superconductivity, pinning, and vortex dynamics of FeSe before and after protonation. The study shows that, after being protonated, FeSe's superconducting critical temperature Tc has been increased to more than 40 K and the critical current density Jc has also been increased from 2.1 × 104 A/cm2 to 1.2 × 106 A/cm2, with significantly larger magnetic relaxation rates (Q). Meanwhile, the critical current density anisotropy (γ) decreases substantially while the upper critical field Hc2 increases from 13 T to 91 T after protonation. In addition, the reasons for the absence of the second peak effect in Hx-FeSe were explored. This investigation also reveals the existence of the vortex phase transition associated with the pinning behavior in protonated FeSe, demonstrated by the foot-like characteristics of resistivity. Based on these results, the vortex phase diagrams of FeSe before and after protonation were established. These findings provide important insights for exploring new high-temperature superconductors and their magnetic flux dynamics through protonation.

Experimental investigation on the crystal structure and superconductivity of germanium-intercalated 2H–NbSe2 system

We report the structural and superconducting properties of Ge-intercalated 2H–NbSe2 polycrystals. GexNbSe2 samples with nominal 0 ≤ x ≤ 0.1 crystallize in the space group P63/mmc with Ge disorderedly occupying the interlayer Se6 octahedral interstices. Superconducting critical temperature Tc monotonically decreases from 7.2 K in NbSe2 to 4.9 K in Ge0.1NbSe2. Studies on resistivity, magnetization and specific heat derive the superconducting- and normal-state parameters, indicating that the suppression of the two-gap superconductivity is mostly caused by the lowered electron-phonon coupling parameter λe-p and density of states at the Fermi level N(EF). Surprisingly, the upper critical field Hc2 and irreversible field Hirr of the low Ge-level samples are enhanced compared with those of the undoped one, which may ascribe to the electron scattering and vortex pinning by nonmagnetic Ge. This study suggests the feasibility for improving high-field performance by slight impurity doping and advances the understanding of superconductivity in transition-metal dichalcogenides.

Evidence for vertical line nodes in Sr2RuO4 from nonlocal electrodynamics

By determining the superconducting lower and upper critical fields Hc1(T) and Hc2(T), respectively, in a high-purity spherical Sr2RuO4 sample via ac-susceptibility measurements, we obtain the temperature dependence of the coherence length ξ and the penetration depth λ down to 0.04Tc. Given the high sample quality, the observed T2 dependence of λ at low temperatures cannot be explained in terms of impurity effects. Instead, we argue that the weak type-II superconductor Sr2RuO4 has to be treated in the nonlocal limit. By comparing our data with existing theory in that limit, the penetration depth in Sr2RuO4 agrees with a gap structure having vertical line nodes, while horizontal line nodes cannot account for the observation. The work highlights the potential benefits of purifying other unconventional superconductors in order to access the fascinating nonlocal regime in more materials and to determine their Cooper pair wave functions. Published by the American Physical Society 2024

Superconductivity, antiferromagnetism, and charge density waves in ZrTe3 intercalated with Terbium

The uniaxial compound ZrTe3 displays a complex charge density wave (CDW) ground state below ≈ 63 K. Here we report that Tb intercalated ZrTe3 single crystals display superconductivity with Tc ≈ 5.4 K. The effect of the Tb additions to the superconducting properties, magnetism, and CDW are probed by means of measurements of electrical resistivity (ρ), thermoelectric potential (S), and Hall effect. The temperature dependence of the upper critical field (Hc2) could be fit with a two-band model. The magnetic susceptibility measurements suggest that upon the addition of Tb an antiferromagnetic order is developed with ordering temperature of TN ≈ 4.0 K. Tb doping's enhancing effect on Tc suggests promising paths for future research involving lanthanide dopants in transition metal tellurides.

A pulsed current set-up for use in magnetic fields above 30 T; application to high-temperature superconductors

Physical measurements of the normal state of an unconventional or high-temperature superconductor in the zero-temperature limit can provide vital information on the nature of the electronic ground state from which the superconductivity emerges. Viable routes to fully suppress the superconductivity include the application of magnetic fields stronger than the upper critical field Hc 2 or current densities larger than the critical current density Jc . In high-Tc superconductors, Hc 2 is typically higher than the available field strengths, while high currents can often create large heating effects that cause irreparable damage to the sample. Here, we present a technique that combines intense current pulses with high magnetic fields to fully suppress the superconductivity of a candidate high-Tc superconductor while keeping both J and μ 0 H below their critical values. Two adaptable circuit designs are presented with negligible stray field or self-heating effects (below a critical current value). As a proof of principle, we apply the technique to a high-Tc cuprate with nominal μ 0 Hc 2 ∼ 36 T and demonstrate the suppression of superconductivity down to T/Tc ≤ 0.1 in a field strength of just 24 T. Further applications of this dual technique are also discussed.

Type-II superconductivity at 9K in Pb–Bi alloy

In the present work, we report the synthesis of Pb–Bi alloy with enhanced Tc of up to 9K, which is higher than that of Pb. The alloy is synthesized via a solid-state reaction route in the vacuum-encapsulated quartz tube at 700°C in an automated furnace. The synthesized sample is characterized by X-ray Diffraction(XRD) and Energy dispersive X-ray analysis(EDAX) for its phase purity and elemental composition. Rietveld refinement of XRD reveals that the end product is a majority hexagonal Pb7Bi3, with minor rhombohedral Bi. The electronic transport measurement shows metallic behavior with the Debye temperature of 108K and a superconductivity transition temperature (Tc) below 9K, which is the maximum to date for any reported Pb–Bi alloy, Pb or Bi at ambient pressure. Partial substitution of Bi at the Pb site may modify the free density of electronic states within the BCS model to attain the optimum Tc, which is higher by around 2K from the reported Tc of Pb. The superconductor phase diagram derived from magneto-transport measurements reveals that the synthesized alloy is a conventional superconductor with an upper critical field (Hc2) of 3.9 T, which lies well within the Pauli paramagnetic limit. The magnetization measurements carried out following ZFC(Zero Field Cool) protocols infer that the synthesized alloy is a bulk superconductor below 9K. The isothermal M-H(Magnetization vs. Field) measurements performed below Tc establish it as a type-II superconductor. The specific heat capacity measurements show that the Pb–Bi alloy is a strongly coupled bulk superconductor below around 9K with possibly two superconducting gaps.

On the Thermodynamic Properties of FexSe0.5Te0.5 Superconducting Single Crystals: An Experimental Study

The variation of the thermodynamic critical fields (Hc) with temperature has been obtained from the equilibrium magnetization of FexSe0.5Te0.5 superconducting single-crystal with (0.95 ≤ × ≤ 1.1). Based on the BCS theory, we used the Hc values to obtain the variations in the energy gap Δ(T), the cooper pair coupling, the energy gap ratio 2Δ(0)/kBTc, and the specific heat jump ΔCBCS/Tc with varying Fe content. We found that the Cooper pairs coupling strength decreases with increasing Fe content within the range (∼3.1 to 2.6) for 1.0 ≤ × ≤ 1.1, which is consistent with the BCS-weak coupling limit for all samples. Moreover, the value of the energy gap is nearly constant at about 3.5 meV for all samples, while the Hc(0)/Tc ratio reaches a maximum near x ∼ 1.05. The obtained values of the energy gap, the coupling strength, and the specific heat ratio are consistent with recently published results using various experimental techniques.

Crystal orientation-dependent superconductivity in titanium nitride films

High-quality titanium nitride (TiN) films with different crystal orientations (001, 110, and 111) obtained under the same growth conditions are systematically investigated by both ultra-low temperature scanning tunneling microscope/spectroscopy and transport experiments. Our results reveal that all of them are conventional type-II superconductors, which exhibit spatially homogeneous superconducting properties. The superconductivity is uniform between surface and bulk. Intriguingly, the TiN (111) film has the highest transition temperature (Tc) but the lowest upper critical field (Hc2). This crystal orientation-dependent superconductivity could be explained by the fact that TiN (001) and TiN (110) films are dirtier than TiN (111). Our results suggest that (111)-oriented TiN is superior to design certain superconducting devices, including Josephson junction devices. The crystallographic orientation could offer an effective controlling parameter for designing TiN-based superconducting devices.

Unconventional superconductivity in Cr-based compound Pr3Cr10−xN11

We report results of specific heat and muon spin relaxation (μSR) measurements on a polycrystalline sample of Pr3Cr10−xN11, which shows superconducting state below Tc = 5.25 K, a large upper critical field Hc2 ~ 20 T and a residual Sommerfeld coefficient γ0. The field dependence of γ0(H) resembles γ of the U-based superconductors UTe2 and URhGe at low temperatures. The temperature-dependent superfluid density measured by transverse-field μSR experiments is consistent with a p-wave pairing symmetry. ZF-μSR experiment suggests a time-reversal symmetry broken superconducting transition, and temperature-independent spin fluctuations at low temperatures are revealed by LF-μSR experiments. These results indicate that Pr3Cr10−xN11 is a candidate of p-wave superconductor which breaks time-reversal symmetry.

Nodal superconductivity in miassite Rh17S15

Solid state chemistry has produced a plethora of materials with properties not found in nature. For example, high-temperature superconductivity in cuprates is drastically different from the superconductivity of naturally occurring metals and alloys and is frequently referred to as unconventional. Unconventional superconductivity is also found in other synthetic compounds, such as iron-based and heavy-fermion superconductors. Here, we report compelling evidence of unconventional nodal superconductivity in synthetic samples of Rh17S15 (Tc = 5.4 K), which is also found in nature as the mineral miassite. We investigated the temperature-dependent variation of the London penetration depth Δλ(T) and the disorder evolution of the critical superconducting temperature Tc and the upper critical field Hc2(T) in single crystalline Rh17S15. We found a T − linear temperature variation of Δλ(T) below 0.3Tc, which is consistent with the presence of nodal lines in the superconducting gap of Rh17S15. The nodal character of the superconducting state is supported by the observed suppression of Tc and Hc2(T) in samples with a controlled level of non-magnetic disorder introduced by 2.5 MeV electron irradiation. We propose a nodal sign-changing superconducting gap in the A1g irreducible representation, which preserves the cubic symmetry of the crystal and is in excellent agreement with the derived superfluid density. To the best of our knowledge, this establishes miassite as the only mineral known so far that reveals unconventional superconductivity in its clean synthetic form, though it is unlikely that it is present in natural crystals because of unavoidable impurities that quickly destroy nodal superconductivity.

Magnetization spiral structure and high domain wall velocity induced by inertial effect

In ultrafast magnetism, i.e., the short time scales such as picosecond and femtosecond, we report that the spiral structure of magnetization can be formed by the inertial effect. Comparing with the case of fast magnetism in nanosecond time scale, we can obtain a higher velocity of domain wall in ultrafast magnetism due to the driving of inertial moment. There is a critical value τc of angular momentum relaxation time τ for the inertial breakdown in uniaxial ferromagnet. Under the action of the inertial effect the domain wall width shows the characteristics of increases firstly as τ<τc, and then decreasing as τ>τc. It directly leads to the positive or negative mobility for the domain wall velocity as the inertia is less than or exceeds the critical value, respectively. In the high frequency mode (i.e., high field mode), we obtain the limit domain wall velocity, i.e., V→1/ατ. The smaller the inertia or damping, the faster the domain wall moves. For the case of biaxial anisotropic ferromagnets, the domain wall width and velocity decreases with the increasing inertia term, respectively. In the presence of inertia effect, there is an another critical magnetic field hc. The domain wall width decreases with the increase of the magnetic field as h<hc, while increases as h>hc. However, the domain wall velocity shows a nearly linear increase with the magnetic field. These results indicate that the ultrafast magnetism has more advantages than fast magnetism. It also provides a good control technique for rapid information processing in the future.

Thermal-driven gigantic enhancement in critical current density of high-entropy alloy superconductors

The high-entropy alloy (HEA) superconductor, Ta1/6Nb2/6Hf1/6Zr1/6Ti1/6 (Ta–Nb–Hf–Zr–Ti), is systematically studied to examine changes in superconducting critical properties, critical temperature (Tc), critical current density (Jc), and upper critical field (Hc2), concerning thermal treatment conditions. Annealing condition affects Jc more significantly than Tc and Hc2, with a large improvement of flux pinning force density (Fp). The Jc of bare sample is reduced to 10 A cm–2 at an applied magnetic field of approximately 1.5 T, whereas the sample annealed at 550 °C for 12 h exhibits Jc > 100 kA cm–2 up to around 4 T. Furthermore, the Vickers hardness (HVIT) of the Ta–Nb–Hf–Zr–Ti HEA superconductor notably increases from ∼384 to 528 HVIT following a 24-h annealing at 500 °C. These results demonstrate that thermal annealing is a powerful process to optimize both the superconducting and mechanical properties of high-entropy alloy superconductors.

Effects of gamma-irradiation on the superconducting properties of FeTe0.55Se0.45 single crystals grown by self-flux method

We have investigated the effect of gamma (γ)-irradiation on the structural and superconducting properties of FeTe0.55Se0.45 single crystals grown by the self-flux method. The impact of γ-irradiation on the superconducting transition temperature (TC), critical current density (JC), and vortex pinning mechanism has been systematically studied. The x-ray diffraction study reveals the growth of single crystals along the c-axis. The superconductivity has been confirmed in pristine and γ-irradiated samples through temperature-dependent resistivity (ρ(T)) and magnetization [M(T)] measurements. After irradiation, a slight improvement is observed in the upper critical field Hc2(0) values. The values of thermally activated energy have been calculated and a crossover from a single to collective vortex pinning regime is observed. Additionally, we have analyzed the vortex phase diagrams, revealing a transition from vortex liquid to vortex glass state. Furthermore, the presence of second magnetization peak (SMP) or fishtail effect has been noticed in the M(H) loops, and with increasing temperature, the position of SMP (Hsp) shifts toward lower magnetic field regions. The critical current density has been estimated by Bean's critical state model at different magnetic fields [JC(H)] and temperatures [JC(T)]. The defects through gamma-irradiation lead to a significant threefold increase in JC compared to pristine samples in self-field and at 2 K. The pinning mechanisms have been explained using collective pinning theory and the Dew-Hughes model by analyzing the normalized pinning force density. Our analysis indicates that δl-pinning is dominant and point defects are present in all the samples.

Anomalous field-temperature phase diagram of superconductivity in Sn–Pb solder

Sn–Pb solders are superconducting materials whose Sn and Pb are perfectly phase-separated. Recently, anomalous magnetic-flux trapping in a Sn45–Pb55 solder has been revealed, where the magnetic fluxes are selectively trapped in the Sn regions due to the supercurrents in the surrounding Pb regions. Here, we report on the observation of the anomalous critical field (Hc)-temperature (T) phase diagram of superconductivity in the Sn45–Pb55 solder. Although the Hc(T) for the Pb regions decreases with increasing field as in normal type-I superconductors and is consistent with the conventional trend with Hc(0) ∼ 800 Oe, the Hc(T) for the Sn regions exhibits anomalous behaviors. The most noticeable trend was observed in the field-cooled (under 1500 Oe) solder. The Hc-T phase diagram for the Sn regions largely varies when the applied external field is reversed, and Tc increases with increasing field amplitude when H &amp;lt; 0 Oe is applied. On the basis of the flux trapping and the observed anomalous Hc-T phase diagrams, we propose that the field-robust superconductivity in the Sn regions is related to the ferromagnetically aligned magnetic fluxes (or formation of vortices) in the Sn regions of the Sn45–Pb55 solder.

Competing length scales and 2D versus 3D dimensionality in relatively thick superconducting NbN films

Magneto-transport characteristics of 2D and 3D superconducting layers, in particular, temperature and angular dependences of the upper critical field Hc2, are usually considered to be fundamentally different. In the work, using non-local resistance measurements at temperatures near the normal-to-superconducting transition, we probed an effective dimensionality of nm-thick NbN films. It was found that in relatively thick NbN layers, the thicknesses of which varied from 50 to 100 nm, the temperature effect on Hc2 certainly pointed to the three-dimensionality of the samples, while the angular dependence of Hc2 revealed behavior typical for 2D samples. The seeming contradiction is explained by an intriguing interplay of three length scales in the dimensionally confined superconducting films: the thickness, the Ginzburg–Landau coherence length, and the magnetic-field penetration depth. Our results provide new insights into the physics of superconducting films with an extremely large ratio of the London penetration depth to the Ginzburg–Landau coherence length exhibiting simultaneously 3D isotropic superconducting properties and the 2D transport regime.

Magnetization Plateaus of a Double Fullerene Core/Shell Like-Nanostructure in an External Magnetic Field: Monte Carlo Study

Abstract: This paper concerns the investigation of the critical (HC) and the saturation (HS) magnetic fields behavior of the studied system as a function of different physical parameters. The Monte Carlo method is used to study the magnetic properties of the ferrimagnetic behavior of a double fullerene X60 core/shell-like nanostructure. Based on the Ising model, we focus our study on a system formed by a double sphere core/shell. The two spheres contain the spins  = ± 1/2 in the core surrounded by the spin S = ± 1, 0 in the shell. Various types of magnetization curves have been established, depending on the competition among the exchange couplings, the crystal fields, and the temperature. The study reveals that the saturation magnetic field (Hs) is significantly influenced by variations in all exchange coupling parameters, whereas the critical magnetic field (Hc) is only mildly affected by these parameter variations. Moreover, the crystal field and temperature both influence the critical and saturation magnetic fields. Keywords: Double fullerene core/shell-like structure, Magnetization plateaus, Monte Carlo simulations, Critical and saturation fields, External magnetic field.

The Depairing Current Density of a Fe(Se,Te) Crystal Evaluated in Presence of Demagnetizing Factors

The effect of the demagnetizing factor, regarding the determination of the de-pairing current density Jdep, has been studied in the case of a Fe(Se,Te) crystal, using DC magnetic measurements as a function of a magnetic field (H) at different temperatures (T). First, the lower critical field Hc1(T) values were obtained, and the demagnetization effects acting on them were investigated after calculating the demagnetizing factor. The temperature behaviors of both the original Hc1 values and the ones obtained after considering the demagnetization effects (Hc1demag) were analyzed, and the temperature dependence of the London penetration depth λL(T) was obtained in both cases. In particular, the λL(T) curves were fitted with a power law dependence, indicating the presence of low-energy quasiparticle excitations. Furthermore, by plotting λL−2 as a function of T, we found that our sample behaves as a multigap superconductor, which is similar to other Fe-11 family iron-based compounds. After that, the coherence length ξ values were extracted, starting with the Hc2(T) curve. The knowledge of λL and ξ allowed us to determine the Jdep values and to observe how they are influenced by the demagnetizing factor.

THE STUDY ON TEMPERATURE-DEPENDENT SURFACE CRITICAL MAGNETIC FIELD OF IRON-BASED SUPERCONDUCTORS

The upper critical magnetic field (Hc2) is one of the important properties of superconductors in external magnetic field. The higher magnetic field strength, the more superconductivity is maintained. However, the surface critical magnetic field (Hc3) is larger than upper critical magnetic field which the ratio of Hc3 to Hc2 is constant. In this study, we investigated the surface critical magnetic field of the iron-based superconductor using Ginzburg-Landau’s anisotropic two-band method. The surface critical magnetic field was calculated with four temperature-dependent models. Our analytical formula of the surface critical magnetic field obtains the temperature parameters. Finally, the numerical calculation was applied to the experimental data of iron-based superconductors