Gorter-Casimir Two-fluid Model Research Articles

Plasmon resonance at the interface dielectric - nanocomposite material with superconducting inclusions

This article theoretically considers surface plasmon resonance in composite structures. The features of the surface plasmon resonance arising at the interface with media containing nanoparticles from a high-temperature superconductor are investigated. The dielectric constant of spherical superconducting inclusions is considered taking into account Gorter-Casimir two-fluid model. The temperature dependence of the electrodynamic parameters of the superconductor is taken into account. The two-fluid model, the dependence of the concentration of non-superconducting electrons in a superconductor is often used as the fourth power of temperature nn~T4. In this work, a phenomenological model is used, according to which the electron concentration of non-superconducting electrons in a superconductor is determined by the formula nn~Tγ with γ=1.3÷2. This model is in good agreement with experimental data for high-temperature ceramic superconductors. The dispersion characteristics of surface plasmons arising in a planar structure with a thin nanocomposite superconductor layer are investigated. It is shown that the dispersion characteristics depend significantly on temperature.

Analysis of Photonic Bandgap Extension in One-Dimensional Quasiperiodic Superconducting Photonic Slabs

One-dimensional superconducting photonic slabs made of alternated layers of isotropic dielectric (SiO2) and a high-Tc superconductor (YBCO) are theoretically investigated by the Gorter Casimir two fluid model (GCTFM) and the transfer matrix method (TMM). The proposed photonic quasicrystals are built according to the inflation rule of quasiperiodic sequences. The enhancement of the photonic band gap is theoretically investigated. Extending photonic band gap (E-PBG) is achieved for suitable quasiperiodic chains. The bandwidth of the photonic band gap can be enhanced by changing the temperature of superconductor, parameter of quasiperiodic sequence. An overall photonic band gap is obtained in the visible frequency range and can be enhanced by applying a typical thickness’ deformation along the superconducting photonic sample.

Tunable high Tc superconducting photonic band gap resonators based on hybrid quasi-periodic multilayered stacks

One-dimensional hybrid photonic quasicrystals made of superconductor (HgBa2Ca2Cu3O8+δ) and Dielectric (Si) materials are theoretically investigated by the Gorter Casimir two fluid model (GCTFM) and the transfer matrix method (TMM). The proposed quasicrystals super-lattices are built according the ternary configuration GF/GTM/GF. Where, GF and GTM are the generalized Fibonacci and Thue-Morse sequences, respectively. An interesting multi- photonic band gaps (m-PBGs) are achieved for suitable hybrid quasiperiodic system. The characteristic of these m-PBGs can be manipulated by the temperature of the superconductor and pressure of the system. The transmittance spectra exhibit tunable resonant peaks within the m-PBGs very sensitive to photonic system parameters. A superconducting resonator can be achieved by tuning the temperature, pressure, and thicknesses of the photonic system materials.

Design of structural gigahertz multichanneled filter by using generalized Fibonacci superconducting photonic quasicrystals

Abstract The design-properties of one-dimensional photonic quasicrystals (PQC) are studied in a microwave frequency range using the transfer matrix method (TMM) and Gorter Casimir Two-Fluid Model (GCTM). The PQC is constructed by a dielectric (SiO2) and High Tc superconducting BSCCO (Bi2Sr2CaCu2O8) materials and organized following the Generalized Fibonacci class (GFC). We have shown that similar channels with zero transmission easily controlled by the order and the lattice parameters of quasiperiodic systems. The cutoff frequency of the opened central gap found at specific arrangement (m = n) is adjusted with changing the temperature and layer thickness of superconductor. The main heterostructure can be useful to design a gigahertz multi channeled filter with similar channels.

Efficient CAD Model to Analysis of High Tc Superconducting Circular Microstrip Antenna on Anisotropic Substrates

In this paper, an electromagnetic approach based on cavity model in conjunction with electromagnetic knowledge was developed. The cavity model combined with London’s equations and the Gorter-Casimir two-fluid model has been improved to investigate the resonant characteristics of high Tc superconducting circular microstrip patch in the case where the patch is printed on uniaxially anisotropic substrate materials. Merits of our extended model include low computational cost and mathematical simplify. The numerical simulation of this modeling shows excellent agreement with experimental results available in the literature. Finally, numerical results for the dielectric anisotropic substrates effects on the operating frequencies for the case of superconducting circular patch are also presented.

Analysis of photonic spectra in Thue-Morse, double-period and Rudin-Shapiro quasiregular structures made of high temperature superconductors in visible range

The present paper attempts to determine the properties of photonic spectra of Thue-Morse, double-period and Rudin-Shapiro one-dimensional quasiperiodic multilayers. The supposed structures are constituted by high temperature HgBa2Ca2Cu3O10 and YBa2Cu3O7 superconductors. Our investigation is restricted to the visible wavelength domain. The results are demonstrated by the calculation of transmittance using transfer matrix method together with Gorter-Casimir two-fluid model. It is found that by manipulating the parameters such as incident angle, polarization, the thickness of each layer and operation temperature of superconductors the transmission spectra exhibit some interesting features. This paper, provides us a pathway to design tunable total reflector, optical filters and optical switching based on superconductor quasiregular photonic crystals.

Electrostatic Potential in High-Temperature Superconducting Cuprates: Extended Ginzburg-Landau Theory

The electrostatic potential and the associated charge distribution in the vortices of high- superconductors involving mixed symmetry state of the order parameters have been studied. The work is carried out in the framework of an extended Ginzburg-Landau (GL) theory involving the Gorter-Casimir two-fluid model and Bardeen's extension of GL theory applied to the high- superconductors. The properties are calculated using the material parameters relevant for the high- cuprate YBCO.

Temperature dependence of penetration and coherence lengths in lead nanowires

Magnetization curves well belowTc of a lead nanowire array electrodeposited under pulsed voltage conditions areconsidered. Numerical simulations based on a two-dimensional resolution (2Dmodel) of the Ginzburg–Landau (GL) equations for cylindrical configurationshave also been developed. By freely adjusting the GL phenomenological lengthsλ(T) and ξ(T), the experimental magnetization curves are reproduced to within a 10% error margin. The 2Dmodel also allows us to check the cylindrical symmetry of the obtained configurations. Beyond theexperimental–theoretical agreement, the question of whether the GL model remains valid far belowTc is also addressed. The temperature dependence of the adjusted characteristic lengths iscompared with different theoretical and empirical laws. The most satisfactory agreement isachieved for the Gorter–Casimir two-fluid model. A comparison with a lead nanowire arrayelectrodeposited under constant voltage conditions allows us to distinguish both samples interms of their electronic mean free paths. The characterization of the latter quantitiesconcurs perfectly with the experimental expectation given the different electrodepositiontechniques.

Mean Field Theory Applied to the High-Tc Superconductivity

We propose an effective transverse Ising model (TIM) as a means to treat both metallic and high-temperature superconductivity. The model is inspired by features which are present in the Gorter-Casimir two-fluid model of superconductivity, but it encompasses also the formalism used to treat the phase transitions in hydrogen-bonded ferroelectrics. We treat the model in the random-phase approximation, and as a consequence, the superconducting state reveals a structure of a gas of elementary excitations where the energy gap appears in a quite natural way.

Photoresponse of the high-temperature superconductor YBa 2Cu 3O 7− δ to ultrashort 10 μm CO 2laser pulses

We have measured the photoresponse of the high-temperature superconductor YBa 2Cu 3O 7− δ (YBCO) to pulsed infrared radiation of 10 μm wavelength and analysed its mechanisms. For this purpose, c-axis oriented YBCO films with a thickness between 130 and 280 nm were deposited on single crystal MgO (100) substrates and patterned in a meander structure. The aim of the meander structure was to increase the responsivity at temperatures below the transition temperature. These films were irradiated with 10 μm 35 ps pulses generated by an optical free induction decay (OFID) 10 μm CO 2 laser system developed in our laboratory. We have observed that the form of the transients depends on the temperature. At temperatures below the transition temperature, the photoresponse consists of a 700 ps FWHM peak followed by a slow negative transient. This is the first time that such short transients were observed with 10 μm irradiation. At temperatures above the transition temperature, the transients exhibit a decay in the nanosecond range. We have developed a bolometric model which reproduces well the measured dependence of the peak amplitude of the slow transients on the temperature. We have also investigated the dependence of the fast transients on the bias current and temperature. The observed linear dependence of the peak amplitude of the fast transients on the bias current and the negative transient following the main peak exclude flux-flow and nonequilibrium effects as photoresponse mechanisms, whilst these characteristics agree well with a kinetic-inductance model. The measured dependence of the peak amplitude on the temperature permits one to distinguish between several models for the superfluid fraction ƒ sc. Thus, we have established that the models with superfluid fractions ƒ sc= 1 − ( T/T c) 2 and ƒ sc given by the BCS theory are compatible with our results, whereas the model with ƒ sc = 1 − ( T/T c) 4 corresponding to the Gorter-Casimir two-fluid model does not match our results. The analysis of the amplitude and temporal variation of the negative transient following the fast transient yields a London penetration depth λ L(0 K) ≈ 220 nm in agreement with those determined by other techniques for superconducting films with similar resistivities and critical temperatures.

Complex conductivity of YBa 2Cu 3O 7 single crystals at radiowave frequencies

The complex (surface) impedance of superconducting YBa 2Cu 3O 7−d single crystals have been measured as function of temperature in the vicinity of superconducting phase transition. A technique using a resonance circuit at frequencies 200 MHz and 1 GHz was utilized. The penetration depth λ(T) and the complex conductivity σ ∗(T) can be evaluated from these measurements. The temperature dependence of the penetration depth is well described by the Gorter-Casimir two-fluid model, yielding the surface reactance X(0) at OK. The complex conductivity is compared with the predictions of the BCS theory. While the imaginary part can well be described using a dirty parameter ξ 0/ l∼0.1, the real part of the conductivity does not follow the BCS predictions (even with the addition of the distribution of transition temperatures T c's).

Thermal pair-breaking in superconductors with strong electron-phonon interaction

The influence of inelastic scattering in superconductors with a strong electron- phonon interaction was considered. The pair-breaking scattering leads to smearing of singularities in the electron density of states and to the appearance of states inside a “gap”. Normal electrons in such superconductors appear due to the filling of the states instead of the excitations across the gap. This leads to the temperature dependencies of some thermodynamic and kinetic characterics to be more close to the phenomenological Gorter-Casimir two-fluid model rather then BCS theory.

Temperature dependence of the penetration depth in epitaxial Y 1Ba 2Cu 3O 7−x thin films

A novel technique for measuring the temperature dependence of the penetration depth λ ( T) for HTSC films has been demonstrated started using the resonance frequency of the LC circuit with a one-pancake spiral coil. The λ ( T) dependence is in agreement with two-coil mutual inductance method data and with BCS theory and the Gorter-Casimir two-fluid model. A difference between T c as determined from the λ ( T) and ϱ ( T) dependences is observed.

Observation of an energy gap in the condensed phase of a GaAs/Ga0.77Al0.23As heterojunction

A microwave photoconductivity technique has been used to observe directly an energy gap in the condensed phase of a GaAs/Ga0.77Al0.23As heterojunction. In this technique, microwaves are used to excite electrons across the gap, and the accompanying change in the DC conductivity is detected. In addition, the phase diagram in magnetic-field-temperature space has been determined experimentally, and the temperature dependence of the critical field is found to be the same as that predicted by the Gorter-Casimir two-fluid model of superconductivity.

Theory of Boundary Effects of Superconductors

An extension of the phenomenological London equations to take into account a space variation of the concentration of superconducting electrons is presented. The theory differs from that of Ginsburg and Landau in that it makes use of the Gorter-Casimir two-fluid model rather than an order parameter to derive an expression for the free energy. An effective wave function is used for the superconducting electrons. The theory is applied to calculate the boundary energy between normal and superconducting phases and the relative change $\frac{\ensuremath{\Delta}\ensuremath{\lambda}}{\ensuremath{\lambda}}$ of penetration depth with magnetic field. Calculated values of boundary energies are somewhat larger, and of $\frac{\ensuremath{\Delta}\ensuremath{\lambda}}{\ensuremath{\lambda}}$ somewhat smaller, than observed. It is suggested that additional nonlinear terms are required to account for the observed $\frac{\ensuremath{\Delta}\ensuremath{\lambda}}{\ensuremath{\lambda}}$ at low temperatures. The connection of the theory with Pippard's ideas on range of order is discussed briefly.