Small Coherence Length Research Articles

Intrinsic Josephson effects in layered superconductors

Due to their extremely small coherence length many high temperature superconductors from natural superconducting multilayers. Adjacent superconducting layers are weakly coupled by the Josephson effect. As a result, single crystals act intrinsically as vertical stacks of hundreds of Josephson junctions. In this paper we will, after summarizing the current state of knowledge, present several recent results on intrinsic Josephson effects.

Universal scaling in BCS superconductivity in three dimensions in non-s waves

The solutions of a renormalized BCS equation are studied in three space dimensions in $s$, $p$ and $d$ waves for finite-range separable potentials in the weak to medium coupling region. In the weak-coupling limit, the present BCS model yields a small coherence length $\xi$ and a large critical temperature, $T_c$, appropriate for some high-$T_c$ materials. The BCS gap, $T_c$, $\xi$ and specific heat $C_s(T_c)$ as a function of zero-temperature condensation energy are found to exhibit potential-independent universal scalings. The entropy, specific heat, spin susceptibility and penetration depth as a function of temperature exhibit universal scaling below $T_c$ in $p$ and $d$ waves.

Progress in the first ten years of HTS film growth

Since its discovery, the quality of highcritical-temperature superconducting (HTS) thin films has continued to improve through a better understanding of how the crystalline structure affects transport properties and the development of new approaches to oxidefilm deposition. Thin-film processing plays a key role in determining the properties because of the extremely small coherence length in all HTS materials. Issues of appropriate substrate matching and oxygen mobility still remain before YBa2Cu2O7.8 thin films can find use in digital applications.

Optical properties ofNd1.85Ce0.15CuO4

The ab-plane reflectance of a Nd{sub 1.85}Ce{sub 0.15}CuO{sub 4} single crystal (T{sub c}=23 K) has been measured from {approx}35 to 9500 cm{sup {minus}1} at temperatures above and below T{sub c}, and the optical properties calculated from a Kramers-Kronig analysis. A rich phonon spectrum is observed, and there are a number of c-axis infrared and Raman modes that are observed at low temperature which are believed to be activated by disorder; several of these modes show evidence for electron-phonon coupling. The normal-state optical conductivity may be described by a Drude-like component and an overdamped midinfrared component. The Drude-like component narrows rapidly; at 30 K the mean free path is estimated to be {approx}750 {Angstrom}. Below T{sub c} the Drude carriers collapse into the condensate; the plasma frequency of the {delta} function is determined to be {omega}{sub pS}{approx}10000 cm{sup {minus}1}. The small coherence length ({xi}{sub 0}{approx}70 {Angstrom}) places this material into the clean limit ({xi}{sub 0}/l{lt}1). The London penetration depth is determined to be {lambda}{sub ab}=1600{plus_minus}100 {Angstrom}, which places it well off the Uemura line. Estimates of the electron-phonon coupling from normal-state transport measurements of {lambda}{sub tr}{lt}0.5, and the absence of Holstein sidebands below T{sub c}, indicate that the carriers that participatemore » in superconductivity are weakly coupled to the phonons. The small values for the penetration depth and the electron-phonon coupling constant suggest that the superconductivity in this material is not due to the electron-phonon mechanism, and is different than in other hole-doped superconducting cuprates. {copyright} {ital 1997} {ital The American Physical Society}« less

White light continuum as a tunable radiation source for second-harmonic generation experiments

We have used a white light continuum generated with ultrashort laser pulses from a Ti:sapphire laser system as the radiation source for second-harmonic generation measurements. The white light continuum provides easily tuned radiation for experiments requiring a range of wavelengths. Despite the small coherence length of the radiation, parametric processes, such as second-harmonic generation, are possible with this source. In particular, surface second-harmonic generation using the white light continuum is reasonable because the extent of the interface is much smaller than the coherence length of the radiation. We demonstrate second-harmonic generation from a gold surface and show that surface second-harmonic generation using the white light continuum can be used to measure absorption spectroscopy of molecules adsorbed to surfaces via resonance enhancement of the surface second-harmonic signals.

Triple-axis diffractometry on GaN/Al2O3(001) and AlN/Al2O3(001) using a parabolically curved graded multilayer as analyzer

X-ray Bragg diffraction profiles of epitaxial layers of A1N and GaN grown onc-plane sapphire were measured with a novel triple-axis diffractometer using a parabolically curved, graded multilayer mirror in the diffracted beam instead of an analyzer crystal. In addition, the intensity of the incident beam is enhanced by a parabolically graded multilayer mirror acting as condensor for a Ge(022) channel-cut monochromator. This novel diffractometer configuration provides a clear improvement in intensity at sufficiently high resolution for the study of angular peak broadening and peak shape functions of weak reflections from samples of poor structural quality and from thin layers. For AlN and GaN, the reason for peak broadening of symmetric rocking curves was found to be small coherence lengths parallel to the substrate surface and not distinct out-of-plane misorientations. Additionally, different peak broadenings of asymmetric reflections due to edge dislocations were observed for AlN and GaN.

Lyα Absorption‐Line Systems in the Gravitational Lens Q0957+561

Far-ultraviolet spectra of the gravitational lens components Q0957+561A and B were obtained with the Hubble Space Telescope Faint Object Spectrograph (HST FOS). Two previously known absorption-line systems were detected at redshifts zdamped = 1.3911 and zLyα = 1.1249. Their prominent absorption features are superposed on intense QSO continuum emission between λλ900-1400 in the quasar rest frame. Strong O VI λ1033, Lyα λ1216, and N V λ1240 line emission found at the QSO redshift (zQSO = 1.41) accompany the absorption-line systems. Lyα through Ly associated with the damped absorption system were found in both lensed components, together with other ionic species of N I, N III, C II, C III, Si II, Si III, and O I. We tentatively identify O VI λλ1033, 1037 absorption at the damped Lyα redshift, which, if confirmed, would be the highest ionization species yet detected in such systems. The equivalent widths of the Lyman series in Q0957+561A are measurably greater compared with absorption in 0957+561B, consistent with the narrower and shallower depth of the Lyman series line profiles in image B. The differences of the damped Lyman series absorption in the lensed components are the only significant spectral characteristic that distinguishes the far-ultraviolet spectra of 0957+561A and B. These results indicate that the damped Lyα absorber is inhomogeneous over scale lengths of ~200 pc, which corresponds to the beam separation at the damped Lyα redshift. However, the equivalent widths of neutral and ionized metals in lens components A and B are correlated, which suggests these spectral features arise in an extended region. The metal line-absorption strength is consistent with lower column densities compared with the hydrogen line-forming region. Thus, the small coherence length scale indicated by the difference in hydrogen line absorption between the lensed components suggests the geometric ray paths intercept different regions of a galactic disk that is viewed pole-on, while the metal absorption occurs in the halo.

Hole localization, electronic structure and high- Tc superconductivity

It is shown that the dielectric gap in the electronic spectrum of oxide high- T c systems appears because of ordering arrays of localized (heavy) holes or the charge density waves. Dielectric-metal (DM) phase transitions in these systems are the consequence of impurity bands appearing at doping, delocalization of the ordered heavy holes located on the metal-apical ion bonds. The free carriers introduced by doping can couple through excitation of these localized holes. This leads to high- T c superconductivity with small coherence length and anomalous temperature dependence of H c2( T). These results were obtained on the basis of experimental studies of specific heat, magnetic properties, thermal expansion and other characteristics. The physical nature of the observed DM transitions and negative thermal expansion in HTSC systems are discussed.

High- T c superconductors tailored on the nanometre-scale

High- T c superconductors are characterized by an unusually small coherence length, which amounts to a few angstroms only. As the coherence length is the length scale in which a superconductor has to be structured to achieve Josephson junction behaviour, considerable effort has been devoted by many groups to modify high- T c films in the nanometre scale. Because the high- T c cuprates do not lend themselves for nanostructuring, new concepts have to be developed to achieve this goal. These developments will be discussed and an overview of the state of the art of the field will be presented with a special focus on the ultimate limitations of nanoscale structuring of superconductors.

Mo6Se8-cluster-based superconducting compounds Cs2Mo12Se14 and Rb4Mo18Se20: Evidence for a strongly correlated and anisotropic electron system.

We studied the normal and superconducting states of the title compounds by measuring the conductivity and magnetization of single crystals and powder samples. From the upper and lower critical fields we deduced the characteristic lengths and thermodynamical fields. These results are borne out by our specific-heat measurements. We recognize in these compounds many features of the Chevrel-phase superconductors, including very small coherence lengths and strong-coupling-like effects. However, we show that the electron system is much more anisotropic and still less delocalized in these materials where the ${\mathrm{Mo}}_{6}$${\mathrm{Se}}_{8}$ clusters have condensed in ${\mathrm{Mo}}_{6\mathit{n}}$${\mathrm{Se}}_{6\mathit{n}+2}$ finite chains. This condensation is accompanied by an enhancement of the magnetic response whereas the lengthening of the chains leads to a counteracting reduction of the density of carriers. This indicates that superconductivity is built upon highly correlated molecular states. Reviewing the available data on the other Chevrel-cluster-based superconductors confirms this picture and suggests that the small coherence lengths reflect the local character of the electron pairing. This comparison also shows that forming finite chains of ${\mathrm{Mo}}_{6}$${\mathrm{Se}}_{8}$ clusters makes the electron correlations more repulsive and pushes the electron system near the borderline between superconductivity and magnetism. In this respect these compounds could provide valuable complementary information on issues which are at the center of the research upon high-${\mathit{Y}}_{\mathit{c}}$ superconductivity.

Relativistic theory of superconductivity

A relativistic generalization of the Bogolubov-de Gennes equations is derived where the particle and hole amplitudes are Dirac spinors. In the weakly relativistic limit one obtains, besides the usual spin-orbit, Darwin and kinetic energy corrections, a new “spin-orbit” and a new “Darwin” term involving the pair potential in place of the electrostatic potential. The results indicate the significance of the relativistic corrections for superconductors with a high Fermi velocity, a small coherence length or heavy elements in the lattice.

Lattice relaxation of AlGaAs layers grown on GaAs(100) substrate plane by organometallic vapor phase epitaxy

In order to investigate the behavior of AlxGa1−xAs lattice relaxation caused by opposite directions of biaxial stress, i.e., tensile or compressive stress, AlxGa1−xAs (X=0–0.45) layers were grown on undoped and heavily In-doped GaAs substrates by organometallic vapor phase epitaxy. Al0.45Ga0.55As layers on undoped GaAs substrates are subject to biaxial compressive stress and have a large coherent length. Al0.3Ga0.7As layers grown on heavily In-doped GaAs substrates with a lattice constant larger by about 0.1% than that of undoped GaAs are subject to biaxial tensile stress and have much smaller coherent length. Furthermore, it is found that the coherent length depends on the growth temperature and that an increase in coherent length is brought in by the introduction of even a small amount of Al in the layers.

Analysis of poorly crystallized polymers using resolution enhanced X-ray diffraction scans

The use of resolution enhanced X-ray diffraction scans for studying small differences in the structures in poorly crystallized semicrystalline polymers is illustrated with examples from three polymers with different crystallization behaviour, namely nylon 6,6, nylon 6 and poly(chlorotrifluoro ethylene). The effects of small coherence length were deconvolved using maximum entropy methods to obtain clearly resolved peaks. In polymers such as nylon 6,6, the crystalline structure at low levels of crystallinity can be regarded as highly disordered (‘paracrystalline’) forms of the structures present in highly crystalline samples. In polymers such as nylon 6, it is necessary to identify the presence of less stable crystalline phases. Finally, in some instances, such as in rapidly quenched films of poly(chlorotrifluoro ethylene), transient crystalline phases could be present during initial phases of crystal growth. Coexistence of the crystalline phases, transient crystalline phases and the amorphous phase are discussed.

Comparative study of the magnetoresistivity of YBa 2Cu 3O 7− δ and Bi 2Sr 2Ca Cu 2O 8+ x epitaxial thin films in the fluktuation regime

We measured the magnetoresistivity of high quality, c-axis oriented epitaxial YBa 2Cu 3O 7− δ and Bi 2Sr 2Ca Cu 2O 8+ x (BSCCO) thin films in the fluctuation regime above the critical temperature. The measurements have been performed in magnetic fields up to 12 Tesla applied parallel and perpendicular to the CuO 2-planes. The experimental data was analysed in the framework of the Lawrence-Doniach model with the appropriate clean limit expressions for the Aslamazov-Larkin- and Maki-Thompson- fluctuation conductivities. Orbital as well as Zeeman contributions to the magnetoconductivity have been taken into account. With the thermodynamic critical temperature T c , the coherence lengths parallel and perpendicular to the ab-plane ξ ab and ξ c , respectively, and the product of the mean free path l and the phase breaking time τ φ as fitting parameters, good agreement between experiment and theory was found for YBCO, whereas for BSCCO no convincing fit could be obtained. Fitting the data for YBCO we obtained T c = 90.2 K, ξ ab = 13.8 A ̊ , ξ c = 3.1 A ̊ , and (lτ gf) 100 K ≅ 1.5 × 10 −22 sm . These values are close to those derived from measurements of the transport energy of magnetic flux lines via the Nernst effect at temperatures below T c . For BSCCO we obtained T c ≅ 90 K and ξ ab ≅ 24 to 30 Å. The very small coherence length in c-direction ξ c ≤ 0.4 Å reflects the quasi 2-dimensional nature of this material.

Resistivity broadening, upper critical fields and irreversibility lines in bulk PbMo 6S 8 and SnMo 6S 8 Chevrel phase superconductors

Resistive (R(B,T)) transitions for both PbMo 6S 8 (PMS) and SnMo 6S 8 (SMS) compounds were measured in applied magnetic fields. For both compounds, the pseudo upper critical field B c2 ∗ (T) lines determined at different constant resistance criteria show a deviation from the expected thermodynamic B c2(T). The deviation is more pronounced in the PMS sample which has a smaller coherence length. The activation energy barriers U b(B) extracted from the Arrhenius plots of resistivity are lower for PMS (U b(9T) = 1570 K) and for SMS (U b(9T) = 2250 K).

Microstructure and properties of high temperature superconducting materials

The properties of high T c superconducting oxides are correlated with the microstructural features such as point defects, dislocations, and grain boundaries. The magnetic properties of the high T c superconductors, especially the field vs. temperature, are shown to exhibit different behavior from that of conventional superconductors. The irreversibility line and its significance in flux lattice melting are discussed to highlight the important limitations of the current-carrying capacity of the high T c superconductors in an applied magnetic field. The mechanisms of flux pinning by oxygen vacancies, dislocations and grain boundaries are described quantitatively. The pinning energies associated with these defects are shown to be small enough that the critical current density cannot be increased considerably at higher temperatures where flux melting takes place. Grain boundaries are shown to be important weak links in the high T c superconductors. The small coherence length relative to the dimensions of the width of the grain boundary is shown to be responsible for the large reduction in the critical current density associated with the boundaries. The atomic structure of different types of boundary is described in the light of the earlier theories of grain boundaries, and the structural features are shown to be similar. The four important factors contributing to the weak link behavior of the grain boundaries are analyzed and the critical current density associated with the boundaries is derived. The experimental results of the dependence of the critical current density on the misorientation angle, temperature and the magnetic field have been explained based on the grain boundary modelling. More importantly, the spatial dependence of the critical current density around the grain boundary is derived and shown to explain the experimentally observed features.

Magnetic and transport properties of HgBa 2CuO 4+δ

The upper critical field and the critical current density of a ceramic sample of superconducting HgBa 2CuO 4+δ have been estimated from resistivity measurements and magnetic hysteresis loop data. The resistivity measurements were done over a temperature range from 10 to 350 K and in a magnetic field up to 5 T. The results showed that the resistive transition has a strong field dependence. A small coherence length of 2.7 nm was estimated in this HgBa 2CuO 4+δ compound. Furthermore the inductive critical current density, deduced from magnetic hysteresis loop d3ta taken in fields up to 1 kOe, is estimated as 16 × 10 5 A/cm 2 at T = 5 K. This value is relatively low in comparison with the well-studied oxide superconductor YBa 2Cu 3O 7−δ.

Possible origin of the anomalous magnetization behavior in melt-textured Y1Ba2Cu3O7−δ crystallites

Magnetization measurements of the hysteresis loop, M(B), of melt-textured Y1Ba2Cu3O7−δ (YBCO) crystallites were performed in external magnetic fields up to 10 T. The M(B) curves exhibit, between the superconducting transition temperature Tc and almost 39 K, a peak at a finite field B* which increases with decreasing temperature. The crystallites possess a high density of dislocations which could have been introduced during the high temperature treatment and/or by stresses created due to differences in the lattice parameter of small inclusions and the YBCO matrix. The large dislocation density together with the high sensitivity of the superconducting order parameter on deviations from the regular crystal structure and the small coherence length are suggested to be responsible for the observed fishtail shape of the magnetization curves.

Methane tunneling in disordered solid argon–nitrogen phases

Methane has been matrix isolated in solid Arc(N2)1−c, 0≤c≤1. Neutron spectra and diffractograms from identical samples are reported. In addition vapor-deposited argon and its mixtures with methane and nitrogen were studied by low temperature x-ray powder diffraction. The diffractograms and spectra were interpreted in terms of five different types of sites (I–V) in the vapor-deposited matrix after deposition at temperatures of 7–25 K. Shifts and broadenings of the methane tunneling spectra are caused by these sites: (I) Methane in regular fcc substitutional sites of solid pure argon or pure nitrogen in thermodynamic equilibrium shows nearly free rotation. The effective hindrance potential in nitrogen is lower than that in argon. In earlier IR-absorption work a site splitting of the vibrations was assigned as a splitting of the J=1 level of methane. INS shows that the latter is smaller than 0.030 meV. (II) Due to the nonequilibrium conditions during vapor-deposition, stacking faults and grains with hcp symmetry are formed both in pure argon and krypton, but not in pure nitrogen. Rather sharp lines in the methane spectra at 0.6 meV neutron energy transfer are assigned to such sites. (III) Argon and nitrogen form solid mixtures with an fcc structure in the argon rich phase (c≥0.45). By the addition of nitrogen the concentration of stacking faults and grains with hcp structure is enhanced. Both the peaks at 0.9 and at 0.6 meV are seen without major shift or broadening compared to the spectra of methane in pure argon. (IV) In nitrogen rich mixtures (c≤0.45) broad features in the energy range below 1 meV are observed. They are fitted by a simple mean field model. The fit shows that replacing of nitrogen next neighbors of a methane molecule by argon atoms strongly enhances the hindrance potential in this concentration range. (V) A major amount of the argon and krypton matrices is strongly distorted and has a very small coherence length. It is speculated that distorted zones are present as small clusters or on surfaces and small angle grain boundaries. The corresponding trapping sites for methane have a very low symmetry. A broad distribution of tunnel transitions around the elastic line occurs in samples which are, to a significant amount, composed of distorted lattices.

Large steps in long Josephson junctions

Large constant voltage-current steps were observed in the I-V characteristics of long NbN-MgO-NbN Josephson junctions in the presence of external magnetic fields of a few Gauss. The steps are separated by a voltage corresponding roughly to three to five times the voltage spacing expected between adjacent Fiske steps. Models addressing the origin of such steps are presented. Simultaneous nucleation of fluxons at several sites along the junction with thin electrodes, favored by the large London penetration depth of NbN, would introduce a large amount of magnetic flux into the junction at once, leading to large steps. A model which involves pinning of fluxons in the junction is given. Due to the granularity of NbN and its very small coherence length, there will be pinning sites in the junction preventing single fluxons from moving at low bias currents. At particular junction parameter values the steps become very regular and sharp. The sharp steps can be used as a voltage standard without external RF bias or as a high-power oscillator when the device is suitably biased.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>