Conventional Metallic Superconductors Research Articles

The emergence of global phase coherence from local pairing in underdoped cuprates

In conventional metallic superconductors such as aluminium, the large number of weakly bounded Cooper pairs become phase-coherent as soon as they start to form. The cuprate high-temperature superconductors belong to a different category because, being doped Mott insulators, they are known to have low superfluid density and are therefore susceptible to phase fluctuations. It has been proposed that pairing and phase coherence may occur separately in cuprates, and that the measured critical temperature corresponds to the phase-coherence temperature controlled by the superfluid density. Here we examine the evolution of pairing and phase-ordering in underdoped cuprates, and find that a chequerboard plaquette pattern of charge order plays a crucial role, such that the global phase coherence is established once its spatial occupation exceeds a threshold. We make these observations via scanning tunnelling microscopy on underdoped Bi2LaxSr2 − xCuO6 + δ. We observe a smooth crossover from the Mott insulator to superconductor on small islands that have chequerboard order. Each chequerboard plaquette contains approximately two holes and exhibits a stripy internal structure that has a strong influence on the superconducting spectroscopic features. The local spectra remain qualitatively the same across the insulator-to-superconductor transition, and the quasiparticle interference becomes long-ranged. How the superconducting state emerges from a Mott insulator in cuprate superconductors is still not fully understood. Now, the spatial extent of a chequerboard charge order with internal stripes is shown to be crucial.

Fabrication of Superconducting Nanowires Using the Template Method.

The fabrication and characterization of superconducting nanowires fabricated by the anodic aluminium oxide (AAO) template technique has been reviewed. This templating method was applied to conventional metallic superconductors, as well as to several high-temperature superconductors (HTSc). For filling the templates with superconducting material, several different techniques have been applied in the literature, including electrodeposition, sol-gel techniques, sputtering, and melting. Here, we discuss the various superconducting materials employed and the results obtained. The arising problems in the fabrication process and the difficulties concerning the separation of the nanowires from the templates are pointed out in detail. Furthermore, we compare HTSc nanowires prepared by AAO templating and electrospinning with each other, and give an outlook to further research directions.

Ionic gating in metallic superconductors: A brief review

Ionic gating is a very popular tool to investigate and control the electric charge transport and electronic ground state in a wide variety of different materials. This is due to its capability to induce large modulations of the surface charge density by means of the electric-double-layer field-effect transistor (EDL-FET) architecture, and has been proven to be capable of tuning even the properties of metallic systems. In this short review, I summarize the main results which have been achieved so far in controlling the superconducting (SC) properties of thin films of conventional metallic superconductors by means of the ionic gating technique. I discuss how the gate-induced charge doping, despite being confined to a thin surface layer by electrostatic screening, results in a long-range ‘bulk’ modulation of the SC properties by the coherent nature of the SC condensate, as evidenced by the observation of suppressions in the critical temperature of films much thicker than the electrostatic screening length, and by the pronounced thickness-dependence of their magnitude. I review how this behavior can be modelled in terms of proximity effect between the charge-doped surface layer and the unperturbed bulk with different degrees of approximation, and how first-principles calculations have been employed to determine the origin of an anomalous increase in the electrostatic screening length at ultrahigh electric fields, thus fully confirming the validity of the proximity effect model. Finally, I discuss a general framework—based on the combination of ab-initio Density Functional Theory and the Migdal-Eliashberg theory of superconductivity—by which the properties of any gated thin film of a conventional metallic superconductor can be determined purely from first principles.

Vanadium gate-controlled Josephson half-wave nanorectifier

Recently, the possibility to tune the critical current of conventional metallic superconductors via electrostatic gating was shown in wires, Josephson weak-links, and superconductor-normal metal–superconductor junctions. Here, we exploit such a technique to demonstrate a gate-controlled vanadium-based Dayem nano-bridge operated as a half-wave rectifier at 3 K. Our devices exploit the gate-driven modulation of the critical current of the Josephson junction and the resulting steep variation of its normal-state resistance, to convert an AC signal applied to the gate electrode into a DC one across the junction. All-metallic superconducting gated rectifiers could provide the enabling technology to realize tunable photon detectors and diodes useful for superconducting electronics circuitry.

Field-effect control of metallic superconducting systems

Static electric fields have a negligible influence on the electric and transport properties of a metal because of the screening effect. This belief was extended to conventional metallic superconductors. However, recent experiments have shown that the superconductor properties can be controlled and manipulated by the application of strong electrostatic fields. Here, the authors review the experimental results obtained in the realization of field-effect metallic superconducting devices exploiting this phenomenon. The authors start by presenting the pioneering results on superconducting Bardeen–Cooper–Schrieffer wires and nanoconstriction Josephson junctions (Dayem bridges) made of different materials, such as titanium, aluminum, and vanadium. Then, the authors show the mastering of the Josephson supercurrent in superconductor-normal metal-superconductor proximity transistors, suggesting that the presence of induced superconducting correlations is enough to see this unconventional field-effect. Later, the authors present the control of the interference pattern in a superconducting quantum interference device, indicating the coupling of the electric field with the superconducting phase. The authors conclude this review by discussing some devices that may represent a breakthrough in superconducting quantum and classical computation.

Ted Geballe and HTSC

The most prominent theoretical question for high-temperature superconductors is, “Why is Tc so much higher in these materials than in conventional metallic superconductors?” My answer is that the dopants (often, but not always, oxygen vacancies or interstitials) have formed self-organized percolative networks to screen the strong ionic fields in and between tetragonal layers. This model fits very well to Geballe’s latest data with Tc = 84 K on apparently overdoped Mo-YBCO sol-gel samples, showing the effectiveness of self-organization.

Type I superconductivity in Dirac materials

Superconductivity of the second kind was observed in many 3D Weyl and Dirac semi-metals while in the PdTe2, superconductivity is clearly of the first kind. This is very rare in Dirac semi—metals, but is expected in clean conventional metallic superconductors with 3D parabolic dispersion relation. The conduction bands in this material exhibit the linear (Dirac) dispersion only along two directions, while in the third direction the dispersion is parabolic. Therefore the ‘hybrid’ Dirac-parabolic material is intermediate between the two extremes. A microscopic pairing theory is derived for arbitrary tilt parameter of the 2D cone and used to determine anisotropic coherence lengths, the penetration depths and applied to recent extensive experiments. Magnetic properties of these superconductors are then studied in the parallel to the layers magnetic field on the basis of microscopically derived Ginzburg–Landau effective theory for the order parameter.

Number theory, periodic orbits, and superconductivity in nanocubes

We study superconductivity in isolated superconducting nano-cubes and nano-squares of size $L$ in the limit of negligible disorder, $\delta/\Delta_0 \ll 1$ and $k_F L \gg 1$ for which mean-field theory and semiclassical techniques are applicable, with $k_F$ the Fermi wave vector, $\delta$ the mean level spacing and $\Delta_0$ the bulk gap. By using periodic orbit theory and number theory we find explicit analytical expressions for the size dependence of the superconducting order parameter. Our formalism takes into account contributions from both the spectral density and the interaction matrix elements in a basis of one-body eigenstates. The leading size dependence of the energy gap in three dimensions seems to be universal as it agrees with the result for chaotic grains. In the region of parameters corresponding to conventional metallic superconductors, and for sizes $L \gtrsim 10$nm, the contribution to the superconducting gap from the matrix elements is substantial ($\sim 20\%$). Deviations from the bulk limit are still clearly observed even for comparatively large grains $L \sim 50$nm. These analytical results are in excellent agreement with the numerical solution of the mean-field gap equation.

Electrodynamics of Metallic Superconductors

The theoretical and experimental aspects of the microwave, terahertz, and infrared properties of superconductors are discussed. Electrodynamics can provide information about the superconducting condensate as well as about the quasiparticles. The aim is to understand the frequency dependence of the complex conductivity, the change with temperature and time, and its dependence on material parameters. We confine ourselves to conventional metallic superconductors, in particular, Nb and related nitrides and review the seminal papers but also highlight latest developments and recent experimental achievements. The possibility to produce well-defined thin films of metallic superconductors that can be tuned in their properties allows the exploration of fundamental issues, such as the superconductor-insulator transition; furthermore it provides the basis for the development of novel and advanced applications, for instance, superconducting single-photon detectors.

Magnetic-field and temperature dependence of the energy gap in InN nanobelt

We present tunneling measurements on an InN nanobelt which shows signatures of superconductivity. Superconducting transition takes place at temperature of 1.3K and the critical magnetic field is measured to be about 5.5kGs. The energy gap extrapolated to absolute temperature is about 110μeV. As the magnetic field is decreased to cross the critical magnetic field, the device shows a huge zero-bias magnetoresistance ratio of about 400%. This is attributed to the suppression of quasiparticle subgap tunneling in the presence of superconductivity. The measured magnetic-field and temperature dependence of the superconducting gap agree well with the reported dependences for conventional metallic superconductors.

Is there a lowest upper bound for superconductive transition temperatures?

The values of superconductive transition temperatures Tc in conventional crystalline metallic superconductors are widely scattered, depend on the details of the Fermi surface (especially the density of states N(EF)), and are typically below 1 K. By far the highest Tc 's (~100 K) are found in the cuprates, and there Tc is apparently insensitive to the geometry of the Fermi surface, while it depends strongly on dopant density and configuration. For the cuprates there is a smooth master curve Tcmax(<R>) for the highest Tc's as a function of the average number <R> of Pauling resonating bonds/atom in the parent (undoped) insulator. The existence of such an <R>-dependent optimized Tc is suggested by analogies with the microscopic theory of optimized molecular glass networks (such as window glass), but it remains to derive a rigorous quantum theory of the origin of Tcmax(<R>).

Multiple-barrier and nanoscale superconducting devices

Since the pioneering studies of Josephson and Giaever, the development of electronicdevices has been a key research area in superconductivity. In conventional metallicsuperconductors, highly reliable tunnel junction fabrication techniques have enabled theapplication of superconducting devices in astronomy and metrology and have allowed thedevelopment of large scale integrated circuits for fast digital processing. These sub-micronheterostructure fabrication processes have also made possible the study of superconductingdevices containing two or more closely spaced barriers. Such structures allow theinvestigation of a wide range of novel effects and have led to the development of basicresearch areas and applications as diverse as electronic cryocoolers, coherent radiationemission and quantum computing. This paper will review the science which can beinvestigated using multiple-barrier superconducting devices and describe recent progress inthe area.

Grain boundaries in high-Tcsuperconductors

Since the first days of high-${T}_{\mathrm{c}}$ superconductivity, the materials science and the physics of grain boundaries in superconducting compounds have developed into fascinating fields of research. Unique electronic properties, different from those of the grain boundaries in conventional metallic superconductors, have made grain boundaries formed by high-${T}_{\mathrm{c}}$ cuprates important tools for basic science. They are moreover a key issue for electronic and large-scale applications of high-${T}_{\mathrm{c}}$ superconductivity. The aim of this review is to give a summary of this broad and dynamic field. Starting with an introduction to grain boundaries and a discussion of the techniques established to prepare them individually and in a well-defined manner, the authors present their structure and transport properties. These provide the basis for a survey of the theoretical models developed to describe grain-boundary behavior. Following these discussions, the enormous impact of grain boundaries on fundamental studies is reviewed, as well as high-power and electronic device applications.

Advances in Bi-Based High-Tc Superconducting Tapes and Wires

Since the discovery of high-Tc superconductors (HTSs), especially the Bi-based oxide superconductors (Bi-HTSs) in 1989, much effort has been concentrated on the fabrication of Bi-HTS wires and tapes. Bi-HTSs are interesting materials from the viewpoint of practical applications. One of the interesting applications of Bi-HTSs is the cryogen-free conduction-cooled magnet. Besides having a high transition tem- perature (Tc), Bi-HTSs have high upper critical fields (Bc2) or high irreversibility fields (Birr) at temperatures below ∼30 K. Because ∼30 K can be efficiently main- tained by a cryocooler, a Bi-HTS magnet cooled with a cryocooler has great potential in many technological applications. Another promising application of Bi-HTSs is the high-field magnet. When the temperature is reduced to ∼5 K, Bi-HTSs show a much higher Bc2 or Birr than do conventional metallic superconductors (low-temperature superconductors, LTSs) such as Nb3Sn. This indicates that Bi-HTSs also have great potential for use in a high- field superconducting magnet if the magnet is operated at low temperature.

Grain boundaries in high-Tc superconductors: insights and improyements

Abstract The properties of grain boundaries play a decisive role in the understanding and design of numerous experiments, as well as for most applications of high-T c superconductors. For basie reasons to be discussed, the physics of interfaces in high-T c superconductors and in semiconductors are surprisingly closely related. As a consequence, the behaviour of interfaces in hign-T c superconductors is considerably richer and more exciting than in conventional metallic superconductors. Based on these considerations, we developed a model to describe the electronic behaviour of grain boundaries in high-T c superconductors. Guided by this model, we were able to meet a long-standing challenge of high-T c superconductivity and to inerease the critical current densities of the grain boundaries by large factors.

Thermal conductivity of anisotropic HTS crystals YBa2Cu3O7−x and Bi2Sr2CaCu2O8+y

The results of measurements of thermal conductivity κ and resistivity ρ of some superconducting crystals of YBa2Cu3O7−x and Bi2Sr2CaCu2O8+y in the ab plane (κab and ρab) and along the c axis (κc and ρc) are presented. The magnitudes and temperature dependences of the thermal conductivity of Y- and Bi-crystals are found to be close and to vary less significantly than the resistance of samples of the same composition. In contrast to the predictions of the electron heat transport theory in HTS cuprate crystals, the relative height of the peaks in κab(T)/κab(Tc) curves becomes equal to two in highly anisotropic Bi-samples, and the peak is displaced toward lower temperatures Tm&amp;lt;0.4Tc with increasing value of this ratio, as well as in Y-crystals which have a lower anisotropy. All these facts indicate that in theoretical calculations of the thermal conductivity of layered HTS crystals in the ab plane at temperatures below Tc, the possibility of an increase in the electron and the phonon components of thermal conductivity must be taken into consideration, as in calculations of thermal conductivity of perfect crystals of conventional metallic superconductors. In the direction perpendicular to the layers, the thermal conductivity κc≪κab and decreases monotonically with temperature. The contribution from the electron component to κc can be disregarded.

Magnetic-field penetration depth in TI2Ba2CuO6+δ in the overdoped regime

THE magnetic field penetration depth λ is a basic parameter of superconductivity, related to ns/m* (superconducting carrier density/effective mass) as λ-2 ∝ ns/m* in the limit where the coherence length ζ is much shorter than the mean free path l (the 'clean limit'). Muon spin relaxation (µSR) measurements1,2 of λ in high-transition-temperature (high-Tc ) copper oxide superconductors have revealed remarkable correlations between Tc and ns/m*: Tc increases linearly with ns/m* in the underdoped region, followed by a saturation with increasing carrier doping. Here we report µSR measurements of λ in ceramic specimens of of the superconductor TI-2Ba2CuO6+δ (TI-2201) in the 'overdoped' region where Tc decreases with increasing hole doping. Recent measurements of upper critical field and resistivity3confirm that overdoped TI-2201 lies well in the clean limit with a ζ<<l. We find that the muon spin relaxation rate σ(T → 0) ∝ λ −2 ∝ ns/m* in TI-2201 decreases with increasing hole doping, implying that either ns no longer scales with the normal-state carrier density nn , and/or m* for a superconducting pair becomes much larger than the value expected from the normal-state effective mass m*n . This behaviour of overdoped TI-2201 is in marked contrast to conventional metallic superconductors having a retarded interaction, in which the normal-state properties (nn , m*n , l)directly represent the corresponding values in the superconducting state.

Femtosecond thermomodulation studies of low and high-T/sub c/ superconductors

The authors report femtosecond pump-probe measurements of electronic energy relaxation in conventional metallic and high-T/sub c/ oxide superconductors. In conventional metallic superconductors, the energy relaxation rate of electrons is used to determine the electron-phonon coupling constant lambda . The agreement between the lambda values measured and those obtained by other techniques is excellent, confirming the theoretical predictions of P.B. Allen (1987). A novel Cu overlayer technique was developed in order to measure certain metals which do not have a strong optical transition to states near the Fermi level at a laser energy, of 1.98 eV. The effect of different Cu overlayer thicknesses has been studied. In the new copper-oxide high-T/sub c/ superconducting materials, electronic energy relaxation is monitored by measuring changes epsilon /sub 2/. The observed changes in epsilon /sub 2/ are related to the dynamics of the Cu d to O p band charge transfer excitation occurring in the CuO/sub 2/ planes. By depleting a YBa/sub 2/Cu/sub 3/O/sub 7- delta / sample of oxygen, one can simultaneously vary the Fermi level and the T/sub c/ and make dramatic changes in the pump-probe signal. An estimate of lambda , in several high-T/sub c/ materials, is also made using Allen's theory to fit the relaxation behavior of epsilon /sub 2/.

Relaxation time of the order parameter in a high-temperature superconductor.

We present femtosecond time-resolved measurements on the high-${\mathit{T}}_{\mathit{c}}$ superconductor ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10}$. At temperatures below ${\mathit{T}}_{\mathit{c}}$, we observe a relaxation process which is distinct from the equilibration of hot carriers in the normal state. Our results demonstrate an increasing relaxation rate as the superconducting gap opens. This is consistent with the behavior of conventional metallic superconductors.

Bi(Pb)-Sr-Ca-Cu-O superconducting composite tapes prepared by the powder method using an Ag sheath

The Bi-based oxide superconducting tapes containing high-Tc (Tc=110 K) and low-Tc(Tc=85 K) phases were prepared by the powder metallurgy method using an Ag sheath, and Jc was measured at 77 and 4.2 K in magnetic fields up to 30 T. A grain-oriented microstructure with the c axes perpendicular to the tape surface was obtained for the tapes with a high-Tc phase by applying a combination of cold rolling and sintering. Jc of the high-Tc tape was significantly improved by this grain orientation. However, large anisotropy in Jc with respect to the magnetic field direction was observed for these textured tapes. For the low-Tc tapes, it was difficult to obtain a grain-oriented microstructure by the cold rolling and sintering process. However, Jc at 4.2 K of the nontextured low-Tc tape is as high as that of the grain-oriented high-Tc tape. Typical Jc values at 4.2 K were above 104A/cm2 at 12 T for both high- and low-Tc tapes. Jc at 4.2 K of the Bi-based tapes is much less sensitive to the magnetic field than the conventional metallic superconductors, which indicates that the Bi-based oxide is a good candidate for the high-field superconducting magnet.