Submillimeter surface impedance and relaxation: A case study of quasi-two-dimensional YBa2Cu3Ox

Surface impedance measurements in the normal and superconducting state are an excellent method to study the conduction electron dynamics in metals. This holds especially in the relaxation range, i.e., for distances traveled in one r.f. periods= _F/(_f is the Fermi velocity) being smaller or of the order of the penetration depth and mean free pathl. For materials with _F<-10⁷ cm/sec the relaxation range is easily accessible forf>0.1 THz. Then, in the normal state, relaxation defines the surface impedance with a penetration depth approaching the London penetration depth _L, andR _0l/2 as surface resistance allowing a measure of _L and relaxation time (T, ). In the superconducting state the photon interaction scales with _F/_L=l/ ( _f is the dimension of Cooper pairs for l) and causes at low frequencies an absorption rate growing with, which is decreasing with _F/l. The rate increase proportional to turns to a decrease above 0.1 THz, being accompanied by a decrease of with frequency which is stronger for large and small _F/l. These characteristic dependences allow a measurement of material parameters, anisotropy, and dynamics of electrons. To evaluate the consequences of theâ, b, and-direction anisotropy, the integral kernels for normal and superconducting surface impedances in its nonintegrated, angle-dependent form are presented, analyzed, and compared with impedance measurements above 0.1 THz of YBa₂Cu₃O_x.     

Measurement of the Ginzburg-Landau parameter of the superconducting tin films from the supercooling field

Within the framework of Ginzburg-Landau (GL) theory we study the supercooling fields of pure tin films. We have systematically measured the supercooling field as functions of inverse thickness and temperature in both perpendicular and parallel orientations for films obtained by electrolytic deposition. By analyzing the solution of the linearized GL equation, we show that the GL parameter K of bulk material can be reliably obtained from the reduced supercooling field. The extrapolation to infinite thickness and to temperature close to the critical temperature of supercooling field allows to obtain the GL parameter of pure tin, the coherence length ξ₀, the penetration depth λ(0), the London penetration depth λ_L(0) and the zero-thermodynamic perpendicular critical field H_c(0). Our results are consistent with those obtained from supercooling fields of bulk spheres. They provide an explanation for discrepancy previously observed between values of the GL parameter in bulk samples and those deduced from superheating and supercooling fields on superconducting granules. Our results are compared with previous experimental work.     

Parallel-plate resonator of variable spacer thickness for accurate measurements of surface impedance of high-T c superconductive films

Measurements of microwave surface impedance of high-T _c films at gigahertz frequencies and nitrogen temperature are performed. A simple technique employing a parallel-plate resonator with liquid nitrogen as a dielectric spaces is suggested. The use of a precise mechanical device provides smooth changing of distance between films from 200μm down to zero. Coupling to the resonator is accomplished by means of two small antennas-half-wave vibrators for frequency 10 GHz. The method for determining resistivity and magnetic field penetration depth was based on the analysis of spacer thickness dependences of the resonator quality factor and frequency. YBa₂Cu₃O₇ films produced by a laser deposition technique on CaNdAlO₄ substrates withT _c =91 K andj _c =10⁷ A/cm² and on NdGaO₃ substrates withT _c =91 K andj _c =10⁶ A/cm² are examined, and the valuesR _s =0.6 mΩ,λ=348 nm atf=8.97 GHz andR _s =0.5 mΩ,λ=250 nm atf=10.12 GHz, respectively, are obtained at 77 K.     

Broadband Microwave Measurements of Overdoped Y0.9Ca0.1Ba2Cu3O7−δ Films Using Corbino Geometry

The surface impedance of Y_0.9Ca_0.1Ba₂Cu₃O_7?δ thin films was measured using the Corbino spectroscopy method. This special geometry, in which the sample dimensions are well defined by a ring pattern, is ideal for broadband high frequency reflection measurements. Using the complex reflected signal, S ₁₁, measured by a vector network analyzer, one can find the surface impedance of the thin film, from which the complex conductivity can be deduced. In the current work we present the three-standard approach for calibration of the Corbino method and demonstrate the benefits of this approach in measuring superconducting Y_0.9Ca_0.1Ba₂Cu₃O_7?δ thin films up to 20 GHz and down to 6 K. For the data analysis the well-known generalized two-fluid model was implemented, taking into account a film thickness which is much smaller than the normal state skin depth and superconducting penetration depth.     

Charge density wave transition and superconductivity in 2H-NbSe2. Direct measurement of the penetration depth in a layered superconductor

The Schawlow-Devlin self-inductance method of direct measurement of the penetration depth has been adapted for layered superconductors, for which this method is especially suitable because the calibration procedure is very simple for them. The ratio of coherence length to mean free path ₀/l within the layer is deduced from the penetration depth measured by the new method and the resistivity, and is found to be 0.14 for a pure crystal of 2H-NbSe₂ with RRR of about 50. The effect of the CDW transition on the superconductivity in 2H-NbSe₂ is investigated through the measurement of the penetration depth. In addition to pure crystals, some modified crystals are investigated where the CDW transition is suppressed. The London penetration depth _L(0) as well as the superconducting transition temperatureT _c show a slight but apparent increase with decreasing CDW transition temperature T _D of the samples. Both behaviors may be explained by a decrease in the reduction ofN(E_F) due to the suppression of the CDW transition, whereN(E _F) is the density of states at the Fermi energy. The result also suggests a systematic increase of the ratio of effective mass to electron densitym/n of the electron system with the suppression of the CDW transition.     

First-Principles Study of the Electronic Structure of Heavy Fermion YbNi2

We investigate the electronic properties of YbNi₂ by means of band structure calculations based on the density functional theory within LDA (local density approximation), fully relativistic, and LDA+U schemes. The 4f derived bands are studied within a relativistic framework which yields flat and spin-orbit split bands, and a correlated band method (LDA+U) that includes correlation corrections. In both cases, the 4f bands, which is located roughly 200 meV below the Fermi level (E _F ), hybridize weakly with the dispersive Ni-3d bands. When the fully relativistic scheme is applied, the 4f derived bands split into lower and higher bands due to spin-orbit coupling effects. The 4f electrons are delocalized through the hybridization with conduction electrons, and the hybridization between f and conduction d electrons also plays a important role in YbNi₂. The on-site Coulomb potential is added to the Yb-derived 4f orbitals, the degeneracy between the 4f orbitals would be lifted partially and they are split into three manifolds bands. The Fermi surface splits into three different sheets which are from main the Yb-4f derived bands and Ni-3d bands. Band structure calculations reveal a saddle points existence at the L point in the energy dispersion curve closed to E _F , whereby, we think YbNi₂ might have a superconducting properties. In addition, the quasiparticle mass enhancement inferred by comparing γ to the density of states (DOS) at the Fermi level indicates the effective mass of YbNi₂ enhanced with the fully relativistic results.     

Pair and Quasiparticle States of YBa2Cu3O7−x Films Deduced from the Surface Impedance and a Comparison with Nb3Sn

Surface impedance data at 19 and 87 GHz of high-quality epitaxial YBCO films on different substrates are compared with data for Nb₃Sn films on sapphire in terms of pair and quasiparticle (qp) transport. Surface resistance R _s and penetration depth λ of YBCO are strongly affected by temperature dependent qp scattering, which is depressed in films with enhanced lattice strain. All films showed a comparable residual resistance R _res(19 GHz)～90 μΩ constituting a qp reservoir which is likely to be caused by the electronic configuration and by impurities. Subtracting R _res from R _s (T) revealed activated behavior with a reduced energy gap Δ₀/k _B T _c～0.9 for a film on sapphire, but power-law behavior for the other films. The penetration depth did not reveal power-law dependences at T≤0.5 ·T _c, but was consistent with a reduced energy gap of 0.45 for a film on MgO. The increase of λ(T) at T≥0.5 · T _c was related to qp scattering, which also caused an extremal conductivity σ₁(T). A shoulder in λ(T) at T=(0.6–0.7) · T _c confirmed evidence for the existence of two superconducting bands. The magnetic-field induced recovery of λ(B) of various YBCO films hinted for an important role of magnetic scattering. The results are in contradiction to a d-wave symmetry of the order parameter, at least for the chain band.     

The penetration depth of HgBa2CuO4+δ with 0.07 ≤ δ ≤ 0.35

The magnetic penetration depth λ(T) of three HgBa₂CuO_4+δ samples with 0.16 < δ ≤ 0.27 has been determined from the reversible magnetization. The obtained λ follows a BCS-like correlation of 1/λ² ∝ 1?(T/T_c)² over whole measured temperature range in an underdoped sample with T_c ～ 90 K, but deviates significantly from similar fits in an overdoped sample with the same T_c and an optimum doped sample, whose 1/λ² 's depends on T nearly linearly below T_c/2. This asymmetry between the underdoped and overdoped samples suggests that the T-dependence of 1/λ² is affected by doping in a complicated way.     

Vortices in superconductors

In type II superconductors where the London penetration depthλ is larger than the coherence lengthξ, there is a possibility of flux penetration inside the sample for magnetic field greater than \(H_{0_1 } \left( { = \frac{{\phi _0 }}{{4\pi \lambda ^2 }}ln \lambda /\xi , \phi _0 = \frac{{hc}}{{2e}}} \right).\) The flux penetrates in the form of vortices with core of sizeξ. However these vortices differ from those in superfluid He⁴ in variation of currentj(r) circulating around them. For superconductorsj(r) ～ 1/r only up to a distanceλ and then it falls exponentially whilev(r) ～ 1/r for all distances in superfluids. The reason is that in superconductors vortex carries a magnetic flux which is screened by conduction electrons. This coupling of order parameter field (the pairing wavefunction) with the gauge field has many interesting implications for superconductors and for non-Abelian gauge theories. Some examples are as follows:

1. The energy of the vortices is reduced. The energy of vortex of lengthL (ind = 3 sample) is of orderL lnL for a superfluid, is of orderL in a superconductor, and (in ad = 2 sample) the energy of a vortex point which diverges like lnR (whereR is the size of the sample) in a superfluid becomes finite in a superconductor.
2. The superconducting-normal transition in three dimension is very weak first order, because the fluctuations of the gauge field, when summed over, add to Ginzburg Landau free energy a term proportional to |ψ|³, whereψ is the order parameter.
3. Because of the lnr behaviour of interaction energy of vortices, a two-dimensional superfluid sample can exhibit a Kosterlitz-Thouless type transition whereas a strictlyd = 2 superconductors should not have any. However for dirty superconducting films whereλ is large vortex binding-unbinding transition can be observed with quite a rich phase diagram.

The paper presented at the discussion meeting discusses the above in detail. Here we give only a brief summary of results and some relevant references.     

Josephson Bicrystal Junctions on Sapphire Substrates for THz Frequency Application

Thin film metal oxide superconducting bicrystal junctions on sapphire substrates with I _c R _N products up to 2.5 mV at 4.2 K for width 4 μm and normal-state junction resistance 10–60 Ω were fabricated and characterized at dc and THz frequency. Three types of samples—one with broadband log-periodic antenna, another with double-slot antenna for 300 GHz and third one with double-slot antenna for 400 GHz—have been investigated at THz frequency. New design of antenna coupling with Josephson junction was elaborated for minimization of THz frequency losses in superconducting film. For a particular case of f=320 GHz double-slot antenna, a ratio for bandwidth Q = f/Δf ≈ 10 was measured.     

Finite-size and gravity effects on the thermal conductivity of4He near the λ line

This paper reviews the opportunities for microgravity and Earth-based measurements of the thermal conductivityλ(t, L) of⁴He confined in cylindrical geometries of radiusL with axial heat flow at temperatures near the bulk superfluid-transition lineT _λ (P) (t is the reduced temperatureT/T _λ −1). It provides an evaluation of existing data forL=1 μm nearT _λ at saturated vapor pressure (SVP), and uses these to derive a scaling function for the resistivityR(t, L)=1/λ(t, L). The purpose of future measurements over a wide range ofL and of the pressureP will be to test the applicability of this function. In the present paper the scaling function is used to assess quantitatively the effect of gravity on potential Earth-based measurements. It is found that the gravity effect forR is particularly severe belowT _λ . For typical three-mm-high samples at SVP, values ofL significantly larger than 8 μm can only be investigated fully in micro-gravity. At higher pressures the gravity effect is larger. At 30 bar, three-mm samples withL≳4 μm require microgravity for measurements belowT _λ (P). Modern thermometry has sufficient resolution to permit quantitative measurements in micro-gravity of the anticipated finite-size effect for values ofL as large as 50 μm.     

Normal form for Mueller Matrices in Polarization Optics

Abstract

The normal (canonical) form for Mueller matrices in polarization optics is derived: it is shown that a non-singular real 4 × 4 matrix M qualifies to be the bona fide Mueller matrix of some physical system if and only if it has the canonical form M = L′ ΛL, where L and L′ are elements of the proper orthochronous Lorentz group L ^↑ ₊, and where Λ = diag (λ₀, λ₁, λ₂, λ₃) with λ₀ ≥ ¦λ_j¦ > 0. It is further shown that λ₁ and λ₂ can be taken to be positive so that the signature of λ₃ is the same as that of det M. Several experimentally measured Mueller matrices are analysed in the light of the normal form. The case of singular Mueller matrices is briefly discussed as a limiting case.     

Single Crystals of HgBa2Can−1CunO2n+2+δ (n=1−5) and Layers of HgBa2CuO4+δ Grown at Gas Pressure 10 kbar

Single crystals of Hg-12(n?l) have been grown using high-pressure gas-technique. Due to the high density of Ar gas at 10 kbar the evaporation of Hg is strongly suppresed. An influence of structure defects on magnetic properties will be discussed. Superconducting parameters λ _ab ,ξ _ab and γ have been studied using torque magnetometry. Layers of Hg-1201 compound have been grown from flux.     

Surface Impedance of YBa2Cu3O7−δ Films Grown on MgO Substrate as a Function of Film Thickness

The surface impedance characteristics of epitaxial YBa₂Cu₃O_7?δ films of thickness d _f = 75, 150, 300, 600 nm, produced by magnetron thermal co-evaporation onto single crystal MgO substrates was studied using measurement technique based on Ka-band whispering gallery mode (WGM) dielectric resonator (DR) fabricated from single crystal sapphire. Characterization of the unpatterned films was carried out in temperature interval from 20 K to 90 K. It was shown that the effective surface resistance approaches the minimum value for d _f >300 nm. At the same time, intrinsic impedance properties are practically independent on d _f in the studied interval of d _f values. The temperature dependence of London penetration depth was estimated experimentally and approximated with the model expressions. Effect of reducing the surface resistance of approximately two times at low temperatures one year later after their manufacture was registered for all films(except the film of 75 nm thickness). The effect may be explained by changes of the film parameters in time after the film light overdoping.     

Importance of Magnetoresistivity Properties and Decrement of the Flux Pinning Energy in YBa2Cu3O7−x Bulk Superconductors Doped with Gd Nanoparticles

Magnetoresistivity performance of the polycrystalline YBa₂Cu_3?x Gd _x O_7?x (Y123) superconductors is discussed by the change of the flux pinning mechanism using magnetotransport measurements performed in the magnetic field range from 0 to 7 T. The critical transition temperatures, irreversibility fields (μ ₀ H _irr), upper critical fields (μ ₀ H _c2), penetration depths (λ) and coherence lengths (ξ) of the Y123 materials are deduced from the magnetoresistivity curves. Further, activation (flux pinning) energies belonging to the samples are determined from thermally activated flux creep (TAFC) model. The results obtained display that the flux pinning energies reduce with enhancing the applied magnetic field. This may be attributed to the fact that Gd nanoparticles inserted in the Y123 superconducting core lead to exhibit much weaker flux pinning, lesser crystallinity and connectivity between grains as compared to the pure sample due to the presence of stronger pair-breaking mechanism.     

Influence of Electron–Phonon Interaction on Superconducting State Parameters of MgB2

A three-square well model is employed for the three interactions namely, electron–acoustic phonon, electron–optical phonon, and Coulomb in the calculation of superconducting transition temperature (T _c) for layered structure MgB₂. The analytical solutions for the energy gap equation allow us to understand the relative interplay of these interactions. The values of the coupling strength and of the Coulomb interaction parameter indicate that the test material is in the intermediate coupling regime. The superconducting transition temperature of MgB₂ is estimated as 41 K for λ_ac ≈ 0.3, λ_op ≈ 0.1, and μ* ≈ 0.07. We suggest from these results that both the acoustic and optical phonons within the framework of a three-square well scheme consistently explains the effective electron–electron interaction leading to superconductivity in layered structure MgB₂.     

Doping Dependent Quasiparticle Relaxation Dynamics in?SmFeAsO1?x F x Single Crystals: Comparison of?Spin-Density Wave and Superconducting States

We use optical femtosecond spectroscopy to investigate the quasiparticle relaxation and low-energy electronic structure in undoped and near-optimally doped SmFeAsO_1?x F _x iron-pnictide superconductor single crystals (SC). In the undoped SC, a single relaxation process with a divergent-like relaxation time at the spin density wave (SDW) transition is observed. From the relaxation time in the normal state, significantly above T _SDW, the second moment of the Eliashberg function is determined to be ?????? ²????135?meV². Below T _SDW, the temperature dependence of the photoexcited reflectivity transients indicates the appearance of a bottleneck due to opening of a SDW gap with a BCS-like temperature dependence and the characteristic magnitude, 2??_SDW/k _B T _SDW=7??3, at?4.2?K. In the superconducting SC, multiple relaxation processes are present. In addition to the relaxation processes observed in the normal state, a distinct superconducting state relaxation component is observed consistent with the presence of BCS T-dependent gaps.     

Solutions of the Eliashberg equations with abnormally large values of 2Δ(0)/T C

We consider the Eliashberg equations with an electron-phonon matrix elementg(k, k, q) possessing a low-energy cutoffξ ₁. In the superconducting state, we assume that this cutoff is bound from below by the superconducting gap 2Δ. We solve for Δ andξ ₁ self-consistently, as a function of temperature, and find that the ratio 2Δ(0)/T_c is very large; for parameters that we consider realistic for the cuprates, this ratio is approximately 10. This calculation applies to materials where the mean free path is long (clean limit). We also find that a hysteretic behavior is in principle possible.     

Fluctuation Induced Conductivity in (Cu0.5Tl0.5)Ba2Ca2Cu3O10?δ Superconductor Synthesized at Different Temperatures

The fluctuation induced conductivity (FIC) analysis of (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_10?δ superconductor synthesized at different temperatures has been carried out in the frame work of Aslamazov-Larkin (AL) theory. Almost all the superconducting parameters studied in this research work have been improved with the increase of synthesis temperature up to 850°C, which is most likely due to (Cu_0.5Tl_0.5)Ba₂Ca₂Cu₃O_10?δ superconducting phase stability at this synthesis temperature. The parameters calculated from FIC analysis are cross-over temperature (T ₀), zero temperature c-axis coherence lengths ξ _c (0), interlayer coupling strength (J) and the exponents (λ _3D and λ _2D). The FIC analysis has shown an increase in T ₀ and the shift of three dimensional (3D) Aslamazov-Larkin (AL) regions to the higher temperature with the increase in synthesis temperature up to 850°C.