type-II Superconductors Research Articles

Observation of Two-Dimensional Type-II Superconductivity in Bulk 3R-TaSe2 by Scanning Tunneling Spectroscopy.

Here we report a low-temperature and vector-magnetic-field scanning tunneling microscopy/spectroscopy (STM/S) study on 3R-TaSe2. The sample surface was obtained by exfoliating a bulk 3R-TaSe2 single crystal in an ultrahigh-vacuum (UHV) chamber and then transferred in situ to STM. It was observed that the topmost layer shows a 3 × 3 charge density wave pattern at T = 4.2 K with metallic character in STS. The electronic characterization study by variable-temperature and magnetic field STS revealed that 3R-TaSe2 behaves as a type-II superconductor. More intriguingly, such superconductivity (SC) can survive under strong in-plane magnetic fields even up to 2.5 T and out-of-plane magnetic fields up to 0.7 T, exhibiting an anisotropic superconducting property. Temperature-dependent STS showed that 3R-TaSe2 undergoes a transition above 0.58 K. Our results may be important for understanding the intriguing SC properties of the 3R-phase van der Waals materials.

Temperature Dependent Performance of a Conduction-Cooled Jc(B) Transformer- Rectifier Flux Pump

Transformer-rectifier flux pumps provide an elegant solution for high current generation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&gt;$</tex-math></inline-formula> 1 kA) in superconducting magnets. By using step-down transformers and superconducting switches they can charge magnets with minimal heat-load between the external and cryogenic components. High temperature superconductors' type-II superconductivity enables a range of different switching approaches. It was recently shown that a switching approach based on reducing the critical current with an applied DC magnetic field - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J_c(B)</i> switching - is feasible. The efficiencies of this switching method are an attractive option for a conduction-cooled system where cooling power is limited. In this work we present the first conduction-cooled transformer-rectifier driven by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J_c(B)</i> switching where we successfully charge a magnet up to its critical current of 115 A whilst monitoring various component temperatures. We explore the parameter space of applied current and switch temperature to establish the effects on the charging time and maximum current.

Expanded quantum vortex liquid regimes in the electron nematic superconductors FeSe1−xSx and FeSe1−xTex

The quantum vortex liquid (QVL) is an intriguing state of type-II superconductors in which intense quantum fluctuations of the superconducting (SC) order parameter destroy the Abrikosov lattice even at very low temperatures. Such a state has only rarely been observed, however, and remains poorly understood. One of the key questions is the precise origin of such intense quantum fluctuations and the role of nearby non-SC phases or quantum critical points in amplifying these effects. Here we report a high-field magnetotransport study of FeSe1−xSx and FeSe1−xTex which show a broad QVL regime both within and beyond their respective electron nematic phases. A clear correlation is found between the extent of the QVL and the strength of the superconductivity. This comparative study enables us to identify the essential elements that promote the QVL regime in unconventional superconductors and to demonstrate that the QVL regime itself is most extended wherever superconductivity is weakest.

Metallurgy, superconductivity, and hardness of a new high-entropy alloy superconductor Ti-Hf-Nb-Ta-Re

We explored quinary body-centered cubic (bcc) high-entropy alloy (HEA) superconductors with valence electron concentrations (VECs) ranging from 4.6 to 5.0, a domain that has received limited attention in prior research. Our search has led to the discovery of new bcc Ti-Hf-Nb-Ta-Re superconducting alloys, which exhibit an interesting phenomenon of phase segregation into two bcc phases with slightly different chemical compositions, as the VEC increases. The enthalpy of the formation of each binary compound explains the phase segregation. All the alloys investigated were categorized as type-II superconductors, with superconducting critical temperatures (Tc) ranging from 3.25 K to 4.38 K. We measured the Vickers microhardness, which positively correlated with the Debye temperature, and compared it with the hardness values of other bcc HEA superconductors. Our results indicate that Tc systematically decreases with an increase in hardness beyond a threshold of approximately 350 HV. Additionally, we plotted Tc vs. VEC for representative quinary bcc HEAs. The plot revealed the asymmetric VEC dependence. The correlation between the hardness and Tc, as well as the asymmetric dependence of Tc on VEC can be attributed to the simultaneous effects of the electronic density of states at the Fermi level and electron-phonon coupling under the uncertainty principle, especially in the higher VEC region.

Edge effects on the electromagnetic response of inhomogeneous type-II superconductors

From a macroscopic point of view, the edges of a type II superconductor are degraded non-homogeneous regions compared with the bulk of the sample. This paper presents numerical simulations of a long superconducting bar with square cross section subjected to an axial external magnetic field, the edges effect on its electromagnetic properties is studied. The edges of the sample are modeled as finite width regions with lower critical current density than the rest of the material. The simulations are based on a continuum electrodynamics model which describes the magnetic induction dynamics of partially penetrated states. Unlike a simpler homogeneous superconductor, in an inhomogeneous material rough flux fronts are formed. It was established that the stochastic profile of the current density produces jets of magnetic flux near a macrodefect.

Model of relativistic superconductivity

We propose a simplified 2D effective scalar electrodynamics model of relativistic type-II superconductivity. Within this framework, we discuss possible electromagnetic (EM) behaviors of superconductivity along the lines of the nonrelativistic Ginzburg–Landau (GL) theory. This model may be of significance to study very diverse physical phenomena such as a nonlinear version of the electron–hole conversion by a superconductor and electron-positron dynamics around neutron stars. We briefly comment on extending the model to study the 3D dynamics of vortex–vortex interactions and Abrikosov fluxonics.

Size effect of randomly distributed pinning centers on magnetic vortices motion in type-Ⅱ superconductor

We consider the size effect of randomly distributed pinning centers on magnetic vortices motion in a mesoscopic type-Ⅱ superconductor in the present of magnetic field using the time-dependent Ginzburg-Landau (TDGL) equations. The pinning centers distributed randomly in various contents in the system are characterized by a distribution function p(r) which fixes the size and positions of them. We investigate the magnetization curves and the magnetic induction as a function of the external magnetic field along the z-axis. In addition, the density of superconducting electrons and the maximum magnetization values for various sizes of the pinning centers is considered. The size of the pinning centers obviously affects the dynamics of the magnetic vortices in the superconductor. The numerical simulations show that Magnetization values and the stable vortex configuration depend on not only content but also size of the pinning centers. The smaller size R (or w) by which the shape of them is characterized results in an increase (or decrease) of both the lower critical magnetic field H1 and the maximum magnetization value. The present work will show good results into understanding and studying the size effect of pinning centers on dynamics of the magnetic vortices in a mesoscopic type-Ⅱ superconductor.

Surface Barrier of Holes Drilled in a Type-II Superconductor

Surface Barrier of Holes Drilled in a Type-II Superconductor

Superconducting vortices carrying a temperature-dependent fraction of the flux quantum.

Magnetic field penetrates type-II bulk superconductors by forming quantum vortices that enclose a magnetic flux equal to the magnetic flux quantum. The flux quantum is a universal quantity that depends only on fundamental constants. In this study, we investigated isolated vortices in the hole-overdoped Ba1-xKxFe2As2 (x = 0.77) by using scanning superconducting quantum interference device (SQUID) magnetometry. In many locations, we observed objects that carried only part of a flux quantum, with a magnitude that varied continuously with temperature. We demonstrated mobility and manipulability of these objects and interpreted them as quantum vortices with nonuniversally quantized (fractional) magnetic flux whose magnitude is determined by the temperature-dependent parameters of a multicomponent superconductor.

Microwave response of type-II superconductors at weak pinning

Theory of linear microwave response of thin films of type-II superconductors in the mixed state is developed taking into account random spatial fluctuations of the parameters of the system, such as the order parameter, diffusion coefficient, or film thickness. In the regime of collective pinning the microwave response of the system exhibits strong frequency dispersion, arising from nonequilibrium vortex core quasiparticles. The corresponding contribution to the ac conductivity is controlled by the inelastic relaxation time, and may exceed the usual Bardeen-Stephen conductivity. It is caused by the Debye-type inelastic relaxation. Debye mechanism of microwave losses may be responsible for strong effects of electromagnetic noise upon dc conductivity in the mixed state at low temperatures.

Anisotropic properties of a noncentrosymmetric NbReSi superconducting single crystal

A single crystal of NbReSi which crystallizes in the hexagonal structure with the noncentrosymmetric space group $P\overline{6}2m$ (No. 189) has been grown by the Czochralski method using a tetra-arc furnace. The anisotropic physical properties have been studied by measuring the magnetic susceptibility and electrical transport. The superconducting transition temperature $({T}_{\mathrm{c}})$ is around 6.1 K, and the measured upper critical field $({H}_{\mathrm{c}2})$ values are 8.39 T and 11.65 T for applied field parallel to [0001] and $[11\overline{2}0]$, respectively. The anisotropy ratio $\mathrm{\ensuremath{\Gamma}}={H}_{\mathrm{c}2}^{a}/{H}_{\mathrm{c}2}^{c}$ is close to 1.38. The GL parameters ${\ensuremath{\kappa}}_{c}$ and ${\ensuremath{\kappa}}_{a}$ are much larger than $1/\sqrt{2}$, indicating that NbReSi is a strong type-II superconductor. The lower critical field $({H}_{\mathrm{c}1})$ values are very small (1.65 mT for $H\phantom{\rule{0.16em}{0ex}}||\phantom{\rule{0.16em}{0ex}}[0001]$ and 1.22 mT for $H\phantom{\rule{0.16em}{0ex}}||\phantom{\rule{0.16em}{0ex}}[11\overline{2}0]$) compared to ${H}_{\mathrm{c}2}$. From the magnetization hysteresis loops, calculated critical current at low field is of the order ${10}^{4}$ $\mathrm{A}/{\mathrm{cm}}^{2}$ which indicates the presence of strong pinning in the sample.

Theory of Caroli–de Gennes–Matricon analogs in full-shell hybrid nanowires

Full-shell nanowires are hybrid nanostructures consisting of a semiconducting core encapsulated in an epitaxial superconducting shell. When subject to an external magnetic flux, they exhibit the Little-Parks (LP) phenomenon of flux-modulated superconductivity, an effect connected to the physics of Abrikosov vortex lines in type-II superconductors. We show theoretically that full-shell nanowires can host subgap states that are a variant of the Caroli-de Gennes-Matricon (CdGM) states in vortices. These CdGM analogs are shell-induced Van Hove singularities in core subbands. We elucidate their structure, parameter dependence and behavior in tunneling spectroscopy through a series of models of growing complexity. Using microscopic numerical simulations, we show that CdGM analogs exhibit a characteristic skewness towards higher flux values inside non-zero LP lobes resulting from the interplay of three ingredients. First, the orbital coupling to the field shifts the energy of the CdGM analogs proportionally to the flux and to their generalized angular momentum. Second, CdGM analogs coalesce into degeneracy points at flux values for which their corresponding radial wavefunctions are threaded by an integer multiple of the flux quantum. And third, the average radii of all CdGM-analog wavefunctions inside the core are approximately equal and are controlled by the electrostatic band bending at the core/shell interface. As the average radius moves away from the interface, the degeneracy points shift towards larger fluxes from the center of the LP lobes, causing the skewness. This analysis provides a transparent interpretation of the nanowire spectrum that allows to extract microscopic information by measuring the number and skewness of CdGM analogs. Moreover, it allows to derive an efficient Hamiltonian of the full-shell nanowire in terms of a modified hollow-core model at the average radius.

Bulk superconductivity in transition metal oxide TaO

The discovery of coexistence of bulk superconductivity and nontrivial topological bands in the compounds, such as LaO and NbC, with a rocksalt structure, motivates us to study the physical properties of TaO with the same structure. Based on preparing successfully TaO polycrystalline sample, we measured its resistivity, magnetization, and specific heat. It was first found that TaO is a type-II superconductor with the critical temperature Tc = 6.20 K and the Ginzburg–Landau parameter κGL(0) = 16.2. The estimated electron–phonon coupling constant λep (0.62) and the specific heat jump ΔCel/γnTc (0.56) demonstrate that TaO is a weak-coupling phonon-mediated superconductor. The lack of single crystal sample impedes us to study experimentally its properties related to the electronic band topology, which is the subject of endeavor in the future.

A new methodology for studying vortex dynamics based on point-contact spectroscopy

Vortex dynamics has attracted tremendous attention for both fundamental physics and applications of type-II superconductors. However, methods to detect local vortex motion or vortex jump with high sensitivity are still scarce. Here, we fabricated soft point contacts on the clean layered superconductor 2H–NbSe2, which are demonstrated to contain multiple parallel micro-constrictions by scanning electronic microscopy. Andreev reflection spectroscopy was then studied in detail for the contacts. Differential conductance taken at fixed bias voltages was discovered to vary spontaneously over time in various magnetic fields perpendicular to the sample surface. The conductance variations become invisible when the field is zero or large enough, or parallel to the sample surface, which can be identified as the immediate consequence of vortex motion across a finite number of micro-constrictions. These results demonstrate point contact Andreev reflection spectroscopy to be a new potential way with a high time resolution to study the vortex dynamics in type-II superconductors.

Two-fold anisotropic superconducting state in topological superconductor Sn4Au

Here we report the anisotropic magnetotransport properties in the superconducting state of a Sn4Au single crystal. The Sn4Au single crystal is synthesized through an easy melt growth method. Superconducting properties are evidenced from resistivity vs. temperature (ρ-T) and DC magnetization measurements. Isothermal magnetization measurements (M-H) hint toward type-II superconductivity in Sn4Au. In-plane and out-of-plane ρ-H measurements show anisotropic behavior of the upper critical field at temperatures below superconducting transition (T c = 2.3 K). The observed anisotropy is more elucidated in ρ-H measurements performed below at different tilt angles. The anisotropy parameter is found to be 1.26. The observed results show the presence of a two-fold anisotropic superconducting state in the Sn4Au single crystal, which may be induced due to the layered structure of the synthesized Sn4Au single crystal.

Direct Observation of Quantum Anomalous Vortex in Fe(Se,Te)

Vortices are topological defects of type-II superconductors in an external magnetic field. In a similar fashion to a quantum anomalous Hall insulator, quantum anomalous vortex (QAV) spontaneously nucleates due to orbital-and-spin exchange interaction between vortex core states and magnetic impurity moment, breaking time-reversal symmetry (TRS) of the vortex without an external field. Here, we used scanning superconducting quantum interference device microscopy (sSQUID) to search for its signatures in iron-chalcogenide superconductor Fe(Se,Te). Under zero magnetic field, we found a stochastic distribution of isolated anomalous vortices and antivortices with flux quanta $\Phi_0$. By applying a small local magnetic field under the coil of the nano-SQUID device, we observed hysteretic flipping of the vortices reminiscent of the switching of ferromagnetic domains, suggesting locally broken-TRS. We further showed vectorial rotation of a flux line linking a paired vortex-antivortex with the local field. These unique properties of the anomalous vortices satisfied the defining criteria of QAV. Our observation suggests a quantum vortex phase with spontaneous broken-TRS in a high-temperature superconductor.

Stability of interlinked neutron vortex and proton flux-tube arrays in a neutron star – III. Proton feedback

ABSTRACT The coupled, time-dependent Gross–Pitaevskii and Ginzburg–Landau equations are solved simultaneously in three dimensions to investigate the equilibrium state and far-from-equilibrium, spin-down dynamics of an interpenetrating neutron superfluid and proton type-II superconductor, as an idealized description of the outer core of a neutron star. The simulations generalize previous calculations without the time-dependent Ginzburg–Landau equation, where proton feedback is absent. If the angle θ between the rotation and magnetic axes does not equal zero, the equilibrium state consists of geometrically complicated neutron vortex and proton flux-tube tangles, as the topological defects pin to one another locally but align with different axes globally. During spin-down, new types of motion are observed. For θ = 0, entire vortices pair rectilinearly with flux tubes and move together while pinned. For θ ≠ 0, vortex segments pair with segments from one or more flux tubes, and the paired segments move together while pinned. The degree to which proton feedback impedes the deceleration of the crust is evaluated as a function of θ and the pinning strength, η. Key geometric properties of vortex-flux-tube tangles, such as filament length, mean curvature, and polarity are analysed. It is found that proton feedback smooths the deceleration of the crust, reduces the rotational glitch sizes, and stabilizes the vortex tangle dynamics. The dimensionless control parameters in the simulations are mutually ordered to match what is expected in a real neutron star, but their central values and dynamic ranges differ from reality by many orders of magnitude due to computational limitations.

Superconductivity in Mo4Ga20As with endohedral gallium clusters

We report the discovery and detailed investigation of superconductivity in Mo4Ga20As. Mo4Ga20As crystallizes in a space group of I4/m (No. 87), with the lattice parameters a = 12.86352 Å and c = 5.30031 Å. The resistivity, magnetization, and specific heat data reveal Mo4Ga20As to be a type-II superconductor with T c = 5.6 K. The upper and lower critical fields are estimated to be 2.78 T and 22.0 mT, respectively. In addition, electron-phonon coupling in Mo4Ga20As is possibly stronger than the BCS weak-coupling limit. First-principles calculations suggest the Fermi level being dominated by the Mo-4d and Ga-4p orbitals.

Tuning superconductivity and charge density wave order in TaSe2 through Pt intercalation

Tantalum diselenide ($\mathrm{Ta}{\mathrm{Se}}_{2}$) has emerged as a promising platform to investigate the interplay between two intriguing quantum electronic states in materials: the charge density wave order (CDW) and superconductivity. In this work, we report the ability to tune these quantum electronic states by intercalating Pt into $2H\ensuremath{-}\mathrm{Ta}{\mathrm{Se}}_{2}$. By introducing 20% of Pt into $2H\ensuremath{-}\mathrm{Ta}{\mathrm{Se}}_{2}$, we demonstrate that the structural phase changes from the $2H$ to the $4{H}_{b}$ phase of $\mathrm{Ta}{\mathrm{Se}}_{2}$ with Pt atoms intercalated within the van der Waals spacing. According to the Fermi surface of the $4{H}_{b}$ phase, a Lifshitz transition occurred, destroying the Fermi-surface nesting found in the $2H$ phase. This can be attributed to the structural phase transformation and the influence of donated electrons from Pt, thus tuning the Van Hove singularities into the Fermi-level vicinity, suppressing the CDW state, and enhancing the superconducting temperature $({T}_{c})$ to $\ensuremath{\sim}2.7$ K. The resulting superconducting properties of the $4{H}_{b}\ensuremath{-}\mathrm{P}{\mathrm{t}}_{0.2}\mathrm{Ta}{\mathrm{Se}}_{2}$ are consistent with those of a BCS type-II superconductor, with a superconducting gap of 3.0 meV. Our results provide insights into the role of electron doping and structural phase changes in fine-tuning quantum electronic-state phenomena in materials. These findings could have significant implications in designing superconducting materials with tailored properties for practical applications.

Plastic vortex creep and dimensional crossovers in the highly anisotropic superconductor HgBa2CuO4+x

In type-II superconductors exposed to magnetic fields between upper and lower critical values, ${H}_{c1}$ and ${H}_{c2}$, penetrating magnetic flux forms a lattice of vortices whose motion can induce dissipation. Consequently, the magnetization $M$ of superconductors is typically progressively weakened with increasing magnetic field $B\ensuremath{\propto}{n}_{v}$ (for vortex density ${n}_{v}$). However, some materials exhibit a nonmonotonic $M(B)$, presenting a maximum in $M$ at what is known as the second magnetization peak. This phenomenon appears in most classes of superconductors, including low-${T}_{c}$ materials, iron-based, and cuprates, complicating pinpointing its origin and garnering intense interest. Here we report on vortex dynamics in optimally doped and overdoped ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4+x}$ crystals, with a focus on a regime in which plastic deformations of the vortex lattice govern magnetic properties. Specifically, we find that both crystals exhibit conspicuous second magnetization peaks and, from measurements of the field- and temperature-dependent vortex creep rates, identify and characterize phase boundaries between elastic and plastic vortex dynamics, as well as multiple previously unreported transitions within the plastic flow regime. We find that the second magnetization peak coincides with the elastic-to-plastic crossover for a very small range of high fields and a sharp crossover within the plastic flow regime for a wider range of lower fields. Moreover, we find evidence that this transition in the plastic flow regime is due to a dimensional crossover, specifically, a transition from three to two-dimensional plastic dynamics.