Gibbs’ energy of formation of YBa2Cu3O7-x (tetragonal)

The high temperature ceramic oxide superconductor YBa2Cu3O7-x (1–2–3 compound) is generally synthesized in an oxygen-rich environment. Hence any method for determining its thermodynamic stability should operate at a high oxygen partial pressure. A solid-state cell incorporating CaF2 as the electrolyte and functioning under pure oxygen at a pressure of 1·01 × 105 Pa has been employed for the determination of the Gibbs’ energy of formation of the 1–2–3 compound. The configuration of the galvanic cell can be represented by: Pt, O2, YBa2Cu3O7−x , Y2BaCuO5, CuO, BaF2/CaF2/BaF2, BaZrO3, ZrO2, O2, Pt. Using the values of the standard Gibbs’ energy of formation of the compounds BaZrO3 and Y2BaCuO5 from the literature, the Gibbs’ energy of formation of the 1–2–3 compound from the constituent binary oxides has been computed at different temperatures. The value ofx at each temperature is determined by the oxygen partial pressure. At 1023 K for O content of 6·5 the Gibbs’ energy of formation of the 1–2–3 compound is −261·7 kJ mol−1.

Magnetic Field Dependence of Entropy And Specific Heat of YBa2Cu3O7-delta Superconductors

The change in thermodynamic quantities (e. g., entropy, specific heat etc.) by the application of magnetic field in the case of the high-T-c superconductor YBCO system is examined phenomenological by the Ginzburg-Landau theory of anisotropic type-II superconductors. An expression for the change in the entropy (Delta S) and change in specific heat (Delta C) in a magnetic field for any general orientation of an applied magnetic field B-a with respect to the crystallographic c-axis is obtained. The observed large reduction of specific heat anomaly just below the superconducting transition and the observed variation of entropy with magnetic field are explained quantitatively.

GINZBURG-LANDAU LIKE THEORY OF HIGH TEMPERATURE SUPERCONDUCTIVITY IN THE CUPRATES: EMERGENT d-WAVE ORDER

High temperature superconductivity in the cuprates remains one of the most widely investigated, constantly surprising and poorly understood phenomena in physics. Here, we describe briefly a new phenomenological theory inspired by the celebrated description of superconductivity due to Ginzburg and Landau and believed to describe its essence. This posits a free energy functional for the superconductor in terms of a complex order parameter characterizing it. We propose that there is, for superconducting cuprates, a similar functional of the complex, in plane, nearest neighbor spin singlet bond (or Cooper) pair amplitude psi(ij). Further, we suggest that a crucial part of it is a (short range) positive interaction between nearest neighbor bond pairs, of strength J'. Such an interaction leads to nonzero long wavelength phase stiffness or superconductive long range order, with the observed d-wave symmetry, below a temperature T-c similar to zJ' where z is the number of nearest neighbors; d-wave superconductivity is thus an emergent, collective consequence. Using the functional, we calculate a large range of properties, e. g., the pseudogap transition temperature T* as a function of hole doping x, the transition curve T-c(x), the superfluid stiffness rho(s)(x, T), the specific heat (without and with a magnetic field) due to the fluctuating pair degrees of freedom and the zero temperature vortex structure. We find remarkable agreement with experiment. We also calculate the self-energy of electrons hopping on the square cuprate lattice and coupled to electrons of nearly opposite momenta via inevitable long wavelength Cooper pair fluctuations formed of these electrons. The ensuing results for electron spectral density are successfully compared with recent experimental results for angle resolved photo emission spectroscopy (ARPES), and comprehensively explain strange features such as temperature dependent Fermi arcs above T-c and the ``bending'' of the superconducting gap below T-c.

Superconducting fluctuations and anomalous phonon renormalization much above superconducting transition temperature in Ca4Al2O5.7Fe2As2

Raman studies on Ca4Al2O5.7Fe2As2 superconductor in the temperature range of 5K to 300 K, covering the superconducting transition temperature T-c = 28.3 K, reveal that the Raman mode at similar to 230 cm(-1) shows a sharp jump in frequency by similar to 2% and linewidth increases by similar to 175% at T-o similar to 60 K. Below T-o, anomalous softening of the mode frequency and a large decrease by similar to 10 cm(-1) in the linewidth are observed. These precursor effects at T-0 (similar to 2T(c)) are attributed to significant superconducting fluctuations, possibly enhanced due to reduced dimensionality arising from weak coupling between the well separated (similar to 15 angstrom) Fe-As layers in the unit cell. A large blue-shift of the mode frequency between 300 K and 60 K (similar to 7%) indicates strong spin-phonon coupling in this superconductor. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4724206]

Majorana fermions in superconducting wires: Effects of long-range hopping, broken time-reversal symmetry, and potential landscapes

We present a comprehensive study of two of the most experimentally relevant extensions of Kitaev's spinless model of a one-dimensional p-wave superconductor: those involving (i) longer-range hopping and superconductivity and (ii) inhomogeneous potentials. We commence with a pedagogical review of the spinless model and, as a means of characterizing topological phases exhibited by the systems studied here, we introduce bulk topological invariants as well as those derived from an explicit consideration of boundary modes. In time-reversal symmetric systems, we find that the longer range hopping leads to topological phases characterized by multiple Majorana modes. In particular, we investigate a spin model that respects a duality and maps to a fermionic model with multiple Majorana modes; we highlight the connection between these topological phases and the broken symmetry phases in the original spin model. In the presence of time-reversal symmetry breaking terms, we show that the topological phase diagram is characterized by an extended gapless regime. For the case of inhomogeneous potentials, we explore phase diagrams of periodic, quasiperiodic, and disordered systems. We present a detailed mapping between normal state localization properties of such systems and the topological phases of the corresponding superconducting systems. This powerful tool allows us to leverage the analyses of Hofstadter's butterfly and the vast literature on Anderson localization to the question of Majorana modes in superconducting quasiperiodic and disordered systems, respectively. We briefly touch upon the synergistic effects that can be expected in cases where long-range hopping and disorder are both present.

The effect of environmental coupling on tunneling of quasiparticles in Josephson junctions

We study quasiparticle tunneling in Josephson tunnel junctions embedded in an electromagnetic environment. We identify tunneling processes that transfer electrical charge and couple to the environment in a way similar to that of normal electrons, and processes that mix electrons and holes and are thus creating charge superpositions. The latter are sensitive to the phase difference between the superconductors and are thus limited by phase diffusion even at zero temperature. We show that the environmental coupling is suppressed in many environments, thus leading to lower quasiparticle decay rates and better superconductor qubit coherence than previously expected. Our approach is nonperturbative in the environmental coupling strength.

Local structural distortions and their role in superconductivity in SmFeAsO1-xFx superconductors

EXAFS studies at the As K edge as a function of temperature were carried out in SmFeAsO1-xFx (x = 0 and 0.2) compounds to understand the role of local structural distortions in superconductivity observed in F-doped compounds. A significant correlation between the thermal variation of local structural parameters such as anion height and superconducting onset is found in the fluorinated compounds. Such a variation in anion height is absent in the non-superconducting compound. An increase in the Fe-As bond distance just below the superconducting onset temperature indicates a similarity between the distortions observed in the high-T-C cuprates and these Fe-based superconductors.

Design, Development and Calibration of HTS Wire Based LOX Level Sensor Probe

For space applications, the weight of the liquid level sensors are of major concern as they affect the payload fraction and hence the cost. An attempt is made to design and test a light weight High Temperature Superconductor (HTS) wire based liquid level sensor for Liquid Oxygen (LOX) tank used in the cryostage of the spacecraft. The total resistance value measured of the HTS wire is inversely proportional to the liquid level. A HTS wire (SF12100) of 12mm width and 2.76m length without copper stabilizer has been used in the level sensor. The developed HTS wire based LOX level sensor is calibrated against a discrete diode array type level sensor. Liquid Nitrogen (LN2) and LOX has been used as cryogenic fluid for the calibration purpose. The automatic data logging for the system has been done using LabVIEW11. The net weight of the developed sensor is less than 1 kg.

Importance of structural distortions in enhancement of transition temperature in FeSe1-xTex superconductors

Temperature (12 K <= T <= 300 K) dependent extended x-ray absorption fine structure (EXAFS) studies at the Fe K edge in FeSe1-xTex (x = 0, 0.5 and 1.0) compounds have been carried out to understand the reasons for the increase in T-C upon Te doping in FeSe. While local distortions are present near superconducting onset in FeSe and FeSe0.5Te0.5, they seem to be absent in non superconducting FeTe. Of crucial importance is the variation of anion height. In FeSe0.5Te0.5, near the superconducting onset, the two heights, h(Fe-Se) and h(Fe-Te) show a nearly opposite behaviour. These changes indicate a possible correlation between Fe-chalcogen hybridization and the superconducting transition temperature in these Fe-chalcogenides.

Majorana modes and transport across junctions of superconductors and normal metals

We study Majorana modes and transport in one-dimensional systems with a p-wave superconductor (SC) and normal metal leads. For a system with an SC lying between two leads, it is known that there is a Majorana mode at the junction between the SC and each lead. If the p-wave pairing Delta changes sign or if a strong impurity is present at some point inside the SC, two additional Majorana modes appear near that point. We study the effect of all these modes on the sub-gap conductance between the leads and the SC. We derive an analytical expression as a function of Delta and the length L of the SC for the energy shifts of the Majorana modes at the junctions due to hybridization between them; the shifts oscillate and decay exponentially as L is increased. The energy shifts exactly match the location of the peaks in the conductance. Using bosonization and the renormalization group method, we study the effect of interactions between the electrons on Delta and the strengths of an impurity inside the SC or the barriers between the SC and the leads; this in turn affects the Majorana modes and the conductance. Finally, we propose a novel experimental realization of these systems, in particular of a system where Delta changes sign at one point inside the SC.

Theoretical simulation studies of pulsed field magnetisation of (RE)BCO bulk superconductors

The magnetisation of bulk high temperature superconductors (HTS), such as RE-Ba-Cu-O [(RE)BCO, where RE is a rare earth element or Y], by a practical technique is essential for their application in high field, permanent magnet-like devices. Research to-date into the pulsed field magnetisation (PFM) of these materials, however, has been limited generally to experimental techniques, with relatively little progress in the development of theoretical models. This is because not only is a multi-physics approach needed to take account of the heating of the samples but also the high electric fields generated are well above the regime in which there are reliable experimental results. This paper describes a framework of theoretical simulation using the finite element method (FEM) that is applicable to both single- and multi-pulse magnetisation processes of (RE)BCO bulk superconductors. The model incorporates the heat equation and provides a convenient way of determining the distribution of trapped field, current density and temperature change within a bulk superconductor at each stage of the magnetisation process. An example of the single-pulse magnetisation of a (RE)BCO bulk is described. Potentially, the model may serve as a cost-effective tool for the optimisation of the bulk geometry and the magnetisation profile in multi-pulse magnetisation processes. © 2010 IOP Publishing Ltd.

Effect of thickness on the magnetic properties of melt-processed YBCO thick films

The magnetic properties of melt-processed YBa2Cu3O7-δ thick films have been measured and correlated with features in the microstructure at 4.2 and 77 K for film thicknesses between 50 and 140 μm. A qualitative model for the volume magnetization of the films at 4.2 K is proposed in terms of the individual contributions from intra H-S grain, inter H-S grain and granular Jc components.

Low-noise THz Niobium SIS Mixers

This thesis describes the development of low-noise heterodyne receivers at THz frequencies for submillimeter astronomy using Nb-based superconductor-insulator-superconductor (SIS) tunneling junctions. The mixers utilize a quasi-optical configuration which consists of a planar twin-slot antenna and antisymmetrically-fed two-junctions on an antireflection-coated silicon hyperhemispherical lens. On-chip integrated tuning circuits, in the form of microstrip lines, are used to obtain maximum coupling efficiency in the designed frequency band. To reduce the rf losses in the integrated tuning circuits above the superconducting Nb gap frequency (~ 700 GHz), normal-metal Al is used to replace Nb as the tuning circuits.

To account the rf losses in the micros trip lines, we calculated the surface impedance of the AI films using the nonlocal anomalous skin effect for finite thickness films. Nb films were calculated using the Mattis-Bardeen theory in the extreme anomalous limit. Our calculations show that the losses of the Al and Nb microstrip lines are about equal at 830 GHz. For Al-wiring and Nb-wiring mixers both optimized at 1050 GHz, the RF coupling efficiency of Al-wiring mixer is higher than that of Nb-wiring one by almost 50%. We have designed both Nb-wiring and Al-wiring mixers below and above the gap frequency.

A Fourier transform spectrometer (FTS) has been constructed especially for the study of the frequency response of SIS receivers. This FTS features large aperture size (10 inch) and high frequency resolution (114 MHz). The FTS spectra, obtained using the SIS receivers as direct detectors on the FTS, agree quite well with our theoretical simulations. We have also, for the first time, measured the FTS heterodyne response of an SIS mixer at sufficiently high resolution to resolve the LO and the sidebands. Heterodyne measurements of our SIS receivers with Nb-wiring or Al-wiring have yielded results which arc among the best reported to date for broadband heterodyne receivers. The Nb-wiring mixers, covering 400 - 850 GHz band with four separate fixed-tuned mixers, have uncorrected DSB receiver noise temperature around 5hv/k_b to 700 GHz, and better than 540 K at 808 GHz. An Al-wiring mixer designed for 1050 GHz band has an uncorrected DSB receiver noise temperature 840 K at 1042 GHz and 2.5 K bath temperature. Mixer performance analysis shows that Nb junctions can work well up to twice the gap frequency and the major cause of loss above the gap frequency is the rf losses in the microstrip tuning structures. Further advances in THz SIS mixers may be possible using circuits fabricated with higher-gap superconductors such as NbN. However, this will require high-quality films with low RF surface resistance at THz frequencies.

Investigations of noise and of quantum interference in proximity effect bridges

This work reports investigations upon weakly superconducting proximity effect bridges. These bridges, which exhibit the Josephson effects, are produced by bisecting a superconductor with a short (<1µ) region of material whose superconducting transition temperature is below that of the adjacent superconductors. These bridges are fabricated from layered refractory metal thin films whose transition temperature will depend upon the thickness ratio of the materials involved. The thickness ratio is changed in the area of the bridge to lower its transition temperature. This is done through novel photolithographic techniques described in the text, Chapter 2.

If two such proximity effect bridges are connected in parallel, they form a quantum interferometer. The maximum zero voltage current through this circuit is periodically modulated by the magnetic flux through the circuit. At a constant bias current, the modulation of the critical current produces a modulation in the dc voltage across the bridge. This change in dc voltage has been found to be the result of a change in the internal dissipation in the device. A simple model using lumped circuit theory and treating the bridges as quantum oscillators of frequency ω = 2eV/h, where V is the time average voltage across the device, has been found to adequately describe the observed voltage modulation.

The quantum interferometers have been converted to a galvanometer through the inclusion of an integral thin film current path which couples magnetic flux through the interferometer. Thus a change in signal current produces a change in the voltage across the interferometer at a constant bias current. This work is described in Chapter 3 of the text.

The sensitivity of any device incorporating proximity effect bridges will ultimately be determined by the fluctuations in their electrical parameters. He have measured the spectral power density of the voltage fluctuations in proximity effect bridges using a room temperature electronics and a liquid helium temperature transformer to match the very low (~ 0.1 Ω) impedances characteristic of these devices.

We find the voltage noise to agree quite well with that predicted by phonon noise in the normal conduction through the bridge plus a contribution from the superconducting pair current through the bridge which is proportional to the ratios of this current to the time average voltage across the bridge. The total voltage fluctuations are given by <V^2(f ) > = 4kTR^2_d I/V where R_d is the dynamic resistance, I the total current, and V the voltage across the bridge . An additional noise source appears with a strong 1/f^(n) dependence , 1.5 < n < 2, if the bridges are fabricated upon a glass substrate. This excess noise, attributed to thermodynamic temperature fluctuations in the volume of the bridge, increases dramatically on a glass substrate due to the greatly diminished thermal diffusivity of the glass as compared to sapphire.