Theoretical Study of Specific Heat, Density of States and Free Energy of Itinerant Ferromagnetic Superconductor URhGe

Following the equation of motion method and Green’s function technique, the coexistence of itinerant ferromagnetism (FM) and superconductivity (SC) is investigated in a single band homogeneous system. Self-consistent equations for superconducting order parameter (Δ) and magnetic order parameter (Δ_FM) are derived. It is shown that there generally exists a coexistent (Δ≠0 and Δ_FM≠0) solutions to the coupled equations of the order parameter in the temperature range 0<T<min (T _C,T _FM) where T _C and T _FM are respectively the superconducting and ferromagnetic transition temperatures. Expressions for the specific heat, density of states and free energy are derived. The specific heat has a linear temperature dependence at low temperatures as opposed to the exponential decrease in the BCS theory. The density of states for a finite Δ_FM increases as opposed to that of a standard ferromagnetic metal. The free energy shows that the superconducting ferromagnetic state has lower energy than the normal ferromagnetic state and therefore is realized at low enough temperature. The theory is applied to explain the observations of URhGe. The agreement between theory and experimental results is quite satisfactory.      

Coexistence of Itinerant Ferromagnetism and Superconductivity in ZrZn<Subscript>2</Subscript>

A microscopic coexistence of itinerant ferromagnetism and superconductivity is studied in a single- band homogeneous system, using an equation of motion method and Green’s function technique. Self-consistent equations for the superconducting order parameter Δ and magnetization m are derived. It is shown that there generally exists coexistent (Δ≠0 and m≠0) solutions to the coupled equations of the order parameters in the temperature range 0<T<min (T _c ,T _FM ), where T _c and T _FM are respectively the superconducting and ferromagnetic transition temperatures. The expressions for specific heat, density of states, free energy, and critical field are also derived. The theory is applied to explain the observations in ZrZn₂. The agreement between the theory and experimental observations is quite satisfactory.      

Effect of oxygen content on the electrical properties of YBa2Cu3O7−x single crystals

The effect of oxygen content in the single crystals of high-temperature superconductor YBa₂Cu₃O_7−x on the electrical resistivity, the Hall effect in the plane perpendicular to thec axis and the energy gap Δ, measured with tunnelling electron microscope, has been studied. The distribution of the gap along the surface of the crystal was also studied. The results of the study on the relationship between the magnitude of the energy gap Δ and the superconducting transition temperatureT _c of single crystals with various oxygen contents are approximated by the linear dependence 2Δ_av=4·4kT _c .     

Increase in the exactness of measurement of physical parameters of high-temperature superconductor materials

A procedure for estimating the critical temperature T _c and width ΔT _c for the superconducting transition of high-temperature superconductor materials based on plotting the first derivative of the temperature correlation dependence of the electrical resistance of a sample is developed. The critical point of the derivative corresponds to T _c , and its width at half-height corresponds to ΔT _c . The procedure provides a decrease in the relative error of estimation of T _c and ΔT _c for qualitative samples by a factor of 1.7–2.     

Superconducting gap function and upper critical field in the presence of inhomogeneous magnetic order

Rare earth ternary superconductors are known to exhibit oscillatory magnetic orders below their superconducting transition temperatures. The study of behaviour of superconducting electrons in an inhomogeneous magnetic field is therefore important for such systems. We report here the results of our theoretical study of superconducting gap function Δ(T) and upper critical fieldH _c2 (T). The results are applied to analyse and explain the variation of Δ(T) andH _c2 (T) in case of NdRh₄B₄.     

Interplay of Superconductivity and Ferromagnetism in UGe<Subscript>2</Subscript>

The emergence of pressure induced superconductivity (SC) under the background of ferromagnetic state in 5f-electron based itinerant ferromagnetic superconductor UGe₂ is studied in the single band model by using a mean-field approximation. The solutions to the coupled equations of superconducting gap (Δ) and magnetization (m) are obtained using Green’s function technique and equation of motion method. It is shown that there generally exists a coexistent (Δ≠0, m≠0) solution to the coupled equations of the order parameters in the temperature range 0<T<min (T _C,T _FM), where T _C and T _FM are respectively the superconducting and ferromagnetic transition temperatures. The study of electronic specific heat (C/T), density of states, free energy, etc. are also presented. The specific heat capacity at low temperature shows linear temperature dependence as opposed to the activated behavior. Density of states increases as opposed to the case of a standard ferromagnetic metal. Free energy study reveals that the superconducting ferromagnetic state has lower energy than the normal ferromagnetic state and, therefore, realized at low enough temperature. The agreement between theory and experimental results for UGe₂ is quite satisfactory.      

Coexistence of Superconductivity and Itinerant Ferromagnetism in Ferromagnetic Metals UCoGe and UIr

A microscopic coexistence of itinerant ferromagnetism (FM) and superconductivity (SC) is studied in a single band homogenous system, following an equation of motion method and Green’s function technique. Self-consistent equations for superconducting order parameter (Δ) and magnetization parameter (M) are derived. It is shown that there generally exists a coexistent (Δ≠0, M≠0) solution to the coupled equations of the order parameters in the temperature range 0<T<min (T _C,T _FM), where T _C and T _FM are respectively the superconducting and ferromagnetic transition temperatures. The expressions for electronic specific heat (C/T), density of states, free energy, transition probabilities, ultrasonic attenuation, and nuclear relaxation are also derived. The theory is applied to explain the observations in UCoGe and UIr. The specific heat capacity at low temperature shows linear temperature dependence as opposed to the activated behavior. Density of states increases as opposed to the case of a standard ferromagnetic metal. Free energy study reveals that the superconducting ferromagnetic state has lower energy than the normal ferromagnetic state and, therefore, coexistence of FM and SC realized at a low enough temperature. The agreement between theory and experimental results for UCoGe and UIr is quite encouraging.     

Superconducting State Parameters of MgB<Subscript>2</Subscript>: <Emphasis Type="Italic">Ab Initio</Emphasis> Study

Harrison’s first principle pseudopotential (HFPP) technique in conjunction with BCS theory and McMillan’s formalism has been used for the investigation of superconducting state parameters viz., Coulomb pseudopotential μ ^∗, electron–phonon coupling strength λ, SC transition temperature T _C , interaction strength N ₀ V, semi band gap Δ, energy or mass renormalization parameter Z ₀ and isotope effect exponent δ. The ground state properties of MgB₂ have also been calculated employing full-potential linearized augmented plane wave (FLAPW) method. This enables us to estimate the equilibrium values of bulk modulus and its pressure derivative through optimization of the crystal structure of the system. We have also described the total density of state (DOS) and the partial DOS (PDOS) around the Fermi energy.     

Growth of high-temperature superconductor crystals from flux

Crystallization of high-temperature superconductors was studied in La-Sr-Cu-O, Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O systems. Platelet crystals YBa₂Cu₃O_6.5+x were obtained by spontaneous crystallization from homogeneous nonstoichiometric melts enriched in barium and copper oxide. La_2−x Sr _x CuO₄ was prepared by slow cooling of melts enriched in copper oxide. Bi₂(Sr,Ca) _{n + 1}Cu _n O _y , (n=1; 2) was obtained by melting zone travelling. The crystals show transition to superconducting state atT=93 K, ΔT 0.2–0.5 K (Y, Ba cuprate),T=87 K, ΔT 2K (Bi, Sr, Ca-cuprate). La, Sr-cuprate single crystals obtained by Czochralski method did not show transition to superconducting state. For flux-grown crystalsT _c was 5–26 K depending on the composition, growth and heat treatment. The short characterization of some accessory phases (Ba₃Y₂Cu₃PtO₁₀, Ca_1.75Sr_1.5Cu_0.75PtO₆, BaCuO₂, Ba₄₁Cu₄₄O₈₄Cl₂) is reported.     

Probing the Superconducting Gap from Tunneling Conductance on NdFeAsO<Subscript>0.7</Subscript> with <Emphasis Type="Italic">T</Emphasis><Subscript>C</Subscript>=51 K

We report the tunneling spectroscopy of an iron-based oxypnictide NdFeAsO_0.7 with T _C=51 K, measured by a mechanical point contact technique. Mainly two kinds of tunneling spectra have been observed reproducibly. One is tunneling conductance displaying sharp superconducting gap peaks at 6.0±1.0 mV, in which hump (or kink) structures are also observed at 20–30 mV. Another is that showing dominantly the larger superconducting gap Δ _L with sharp conductance peaks at 14±1.0 meV, in which the trace of a smaller gap (Δ _S=5–7 meV) is simultaneously observed. Our results give direct evidence for the existence of multiple gaps in the quasiparticle excitation spectrum of this multiband system, although the origin of the hump at 20–30 mV is still unclear.     

Plastic deformation — its role in fatigue crack propagation

Recognizing the fact that the effective driving force (ΔK _eff) determines the fatigue crack propagation (FCP) rate and that the shear strain, which is considered to develop due to an occurrence of crack closure, primarily contributes to the plastic deformation, an effort is made here to elucidate the role of plastic deformation in FCP by developing a correlation between the ΔK _eff and the applied driving force (ΔK) with shear strain as variable. The effect of the degree of plastic deformation (i.e. shear strain level) on the FCP rates at higher values of ΔK, where ΔK _eff approaches ΔK, approaching the Paris regime, appears minimal. On the other hand, the disparity between ΔK _eff and ΔK, which apparently increases with shear strain level, persists at lower values of ΔK. This suggests a strong influence of the degree of localized deformation on the FCP rates in the near threshold level. Hence, an improvement of FCP rates in the near threshold level should follow an effort that promotes the plastic deformation near the crack tip to a greater degree. This approach could, therefore, form the basis to explain the effect of the grain size, microstructure, environment,R-ratio and crack size on the near-threshold FCP rates.     

Correlation between changes in Curie temperature and electrical resistivity during structural relaxation in Fe27Ni53P14B6 metallic glass

Changes in Curie temperature (ΔT _c, electrical resistivity (Δϱ/ϱ) and volume (ΔV/V) caused by isochronal annealing in as-quenched and pre-annealed Fe₂₇Ni₅₃P₁₄B₆ metallic glasses were compared. It was found that the ΔT _c against annealing temperature (T _a) curves in as-quenched and pre-annealed samples are very similar to the Δϱ/ϱ against T _a curves. Particularly, almost a linear relationship was observed between ΔT _c and Δϱ/ϱ in the pre-annealed sample. The results strongly suggest that the origins of both ΔT _c and Δϱ/ϱ during structural relaxation in the pre-annealed sample are attributed to identical, reversible, short-range ordering.     

Point-Contact Spectroscopy of the Borocarbide Superconductor YNi2B2C in the Normal and Superconducting State

Point-contact (PC) spectroscopy measurements of YNi₂B₂C single crystals in the normal and superconducting (SC) state (T _c ≃ 15.4 K) for the main crystallographic directions are reported. The PC study reveals the electron–phonon interaction (EPI) spectral function with dominant phonon maximum around 12 meV and further weak structures (hump or kink) at higher energy at about 50 meV. No “soft” modes below 12 meV are resolved in the normal state. The PC EPI spectra are qualitatively similar for the different directions. Contrary, directional study of the SC gap results in Δ_{[100] ≈ 1.5 meV for the a direction and Δ_{[001] ≈ 2.3 meV along the c axis; however the critical temperature T _c in PC in all cases is near to that in the bulk sample. The value 2Δ_[001]/k _B T _c ≈ 3.6 is close to the BCS value of 3.52, and the temperature dependence Δ_[001](T) is BCS-like, while the for small gap Δ_[100](T) is below BCS behavior at T > T _c /2 similarly as in the two-gap superconductor MgB₂. It is supposed that the directional variation Δ can be attributed to a multiband nature of the SC state in YNi₂B₂C.     

Spectroscopic Evidence for Competing Order-Induced Pseudogap Phenomena and Unconventional Low-Energy Excitations in High-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> Cuprate Superconductors

The low-energy excitations of cuprate superconductors exhibit various characteristics that differ from those of simple Bogoliubov quasiparticles for pure d_x²-y²d_{x^{2}-y^{2}} -wave superconductors. Here, we report experimental studies of spatially resolved quasiparticle tunneling spectra of hole- and electron-type cuprate superconductors that manifest direct evidences for the presence of competing orders (COs) in the cuprates. In contrast to conventional type-II superconductors that exhibit enhanced local density of states (LDOS) peaking at zero energy near the center of field-induced vortices, the vortex-state LDOS of YBa₂Cu₃O_7−δ (Y-123) and La_0.1Sr_0.9CuO₂ (La-112) remains suppressed inside the vortex core, with pseudogap (PG)-like features at an energy larger (smaller) than the superconducting (SC) gap Δ_SC in Y-123 (La-112). Energy histograms of the SC and PG features reveal steady spectral shifts from SC to PG with increasing magnetic field H. These findings may be explained by coexisting COs and SC: For hole-type cuprates with PG above T _c, the primary CO gap (V _CO) is larger than Δ_SC and the corresponding COs are charge/pair-density waves with wave-vectors parallel to (π,0)/(0,π). For electron-type cuprates without PG above T _c, V _CO is smaller than Δ_SC and the CO wave-vector is along (π,π). This CO scenario may be extended to the ARPES data to consistently account for the presence (absence) of Fermi arcs in hole- (electron)-type cuprates. Fourier transformation of the vortex-state LDOS in Y-123 further reveals multiple sets of energy-independent wave-vectors due to field-enhanced pair- and spin-density waves. These results imply important interplay of SC with low-energy collective excitations.     

Photoinduced Quasiparticle Relaxation Dynamics in Near-optimally Doped SmFeAsO0.8F0.2 Single Crystals

We investigate the quasiparticle relaxation and low-energy electronic structure in a near-optimally doped pnictide superconductor with T _c=49.5 K by means of femtosecond spectroscopy. Multiple relaxation processes are evident, with distinct superconducting state dynamics and a clear “pseudogap”-like feature with an onset above 180 K indicating the existence of a temperature-independent gap of magnitude Δ _PG=61±9 meV above and below T _c. The fluence and temperature dependence of the superconducting state dynamics shows similar behaviour to the cuprate superconductors with the superconducting-condensate vaporization energy of E _va/k _B≈1.5 K per Fe ion.     

Possible Multigap Superconductivity in SmFeAsO0.8F0.2: A Point-contact Andreev-reflection Spectroscopy Study

We discuss the results of point-contact Andreev-reflection spectroscopy (PCAR) measurements in SmFeAsO_0.8F_0.2 state-of-the-art polycrystals, with critical temperature T _c≈53 K. The low-temperature conductance curves show clear peaks at about 7 meV and additional shoulders at 16–20 meV. Their shape is similar to that of PCAR spectra in MgB₂ and suggests the presence of two superconducting energy gaps even in this Fe-based superconductor. The fit of the conductance curves with a two-band BTK model, up to T _c, further supports this indication in spite of a marked asymmetry in the conductance curves for positive/negative bias. The gaps obtained from the fit are Δ₁=6.15±0.45 meV and Δ₂=18±3 meV, and they follow a nice BCS-like temperature dependence, closing both at the same T _c. Our results are discussed in comparison with experimental and theoretical results in this and other Fe-based superconductors.     

Thermodynamic behaviour of undercooled melts

The Gibbs free energy difference (ΔG) between the undercooled liquid and the equilibrium solid phases has been studied for the various kinds of glass forming melts such as metallic, molecular and oxides melts using the hole theory of liquids and an excellent agreement is found between calculated and experimental values of ΔG. The study is made for non-glass forming melts also. The temperature dependence of enthalpy difference (ΔH) and entropy difference (ΔS) between the two phases, liquid and solid, has also been studied. The Kauzmann temperature (T ₀) has been estimated using the expression for ΔS and a linear relation is found between the reduced glass transition temperature (T _g/T _m) and (T ₀)/T _m). The residual entropy (ΔS _R) has been estimated for glass forming melts and an attempt is made to correlate ΔS _R,T _g,T ₀, andT _m which play a very important role in the study of glass forming melts.     

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.     

Combined effect of staining substances on the discoloration of esthetic Class V dental restorative materials

The purpose of this study was to determine the combined effect of an organic substance (mucin as a substitute for salivary organic substances), chlorhexidine, and an iron compound/tea solution on the changes in the color of esthetic Class V dental restorative materials. Color of a glass ionomer, resin-modified glass ionomer, compomer and flowable resin composite of A2 shade, respectively, was determined according to the CIELAB color scale relative to the standard illuminant D65. Color was measured at baseline, and after sequential immersion in the following substances: Step-1, mucin in PBS (MCP) for 48 h; Step-2, chlorhexidine (CHX) for 24 h; Step-3, iron compound (IRN) or tea solution (TEA) up to 7 days; and Step-4, ultrasonic cleaning for 1 h. Color change (ΔE _ab *) was calculated by the equation: Δ E _ab* = [(Δ L*)² + (Δ a*)² + (Δ b*)²]^1/2, of which ΔL ^∗ indicates changes in value, Δa ^∗ indicates changes in red-green parameter and Δb ^∗ indicates changes in yellow-blue parameter. Δ E _ab* values after immersion in MCP and CHX were compared, and Δ E _ab* values after immersion in IRN or TEA, and subsequent ultrasonic cleaning were compared with respect to the restorative material and immersion substance. Δ E _ab* and changes in the color parameters (ΔL ^∗, ΔC _ab* and ΔH _ab*) were analyzed by repeated measures, analysis of variance and a post-hoc test at the 0.05 level of significance. Color changes after immersion in MCP were acceptable (Δ E _ab* < 3.3), and those after immersion in CHX were generally acceptable. The range of Δ E _ab* values after immersion in IRN was 3.1–19.6, and that after ultrasonic cleaning was 2.4–9.6. The range of Δ E _ab* values after immersion in TEA was 10.7–21.1, and that after ultrasonic cleaning was 11.9–14.5. Color changes of four Class V restorative materials after combined treatment with mucin, chlorhexidine and an iron compound/tea solution were not acceptable. Colors did not recover to their original values after ultrasonic cleaning. Modifications on the surface of a restoration should be considered to reduce stain accumulation.     

Role of Coexistence of Superconductivity and Paramagnetism in Magnetostriction of High-T c Superconductors

Total magnetostriction in the superconducting state for high T _c superconductors has been separated into critical state and paramagnetic components in terms of a H(x) dependent magnetic flux density. We show that the paramagnetic part is χ(2+χ)〈H(x)²〉, where χ is paramagnetic susceptibility. We have reproduced successfully ΔL/L−H _a curves measured by de la Fuente et al. (Phys. C 244:214, [1995]), in which they clearly observed coexistence of superconductivity and paramagnetism, employing the concepts presented in this work.