Quasi-particle excitations around a pair of half-quantum vortices in p- wave superconductors

Triplet superconductors such as Sr₂RuO₄ and Na_xCoO₂⋅yH₂O are now found to be p-wave (p_x ± ip_y) or f-wave ((p_x ± ip_y) cos cp_z) superconductors. It was phenomenologically suggested that in these p-wave or f-wave superconductors, a pair of half-quantum vortices (HQVs) becomes stable. Using the Bogoliubov-de Gennes equation, previously we have analyzed quasi-particle excitations around an HQV at one end of a d-soliton for simplicity. In next study, we will investigate the stability of the pair of HQV’s, which are connected by the d-soliton. For this purpose, we have developed a new numerical method to solve the Bogoliubov-de Gennes equation for two vortices state, using Mathieu functions.     

A new numerical method for quasi-particle spectroscopy around a pair of vortices in triplet superconductors

Triplet superconductors such as Sr₂RuO₄ and Na_xCoO₂·yH₂O are now found to be p-wave (p_x±ip_y) or f-wave ((p_x±ip_y)coscp_z) superconductors. In conventional singlet superconductors, vortices are quantized because phase of order parameter must rotate by 2π around a vortex. But triplet superconductors have a degree of freedom of spin, which is described by d-vector. The d-vector and phase can rotate by π around a vortex, separately. Therefore appearance of HQVs is predicted. Theoretically, it is found that a pair of HQVs is more stable than a singly quantized vortex, for several parameter regions.In this study, in order to investigate quasi-particle bound states around two vortices in s-wave superconductors, we have developed a new numerical method to solve the BdG equation for two vortices state, using Mathieu functions. We confirmed the validity of this method for two vortices state and applied it in case of a pair of vortices. And we solved it.     

Spontaneous internal field around the non-magnetic impurity in spin-triplet p-wave superconductivity

The electronic structure around an impurity in spin triplet p-wave superconductors is investigated by the Bogoliubov–de Gennes theory on a tight-binding model. We calculate the spontaneous current and the local density of states around the impurity and discuss the difference between -wave and -wave superconducting states.     

Vortex structure in Sr2RuO4

The vortex structure in p-wave superconductors is investigated by the Bogoliubov–de Gennes theory on a tight-binding model. We calculate the temperature dependence of the electronic state at each site in the vortex lattice state, and show the difference between sin p_x+i sin p_y-wave and sin p_x−i sin p_y-wave superconducting state. Furthermore the relation of the electronic structure and the site-dependence of the nuclear magnetic relaxation time is also discussed.     

Exotic superconducting state embedded in the hidden order state of URu2Si2

The heavy-fermion compound URu₂Si₂ has mystified researchers since the superconducting state (T_c = 1.45 K) is embedded within the enigmatic ‘‘hidden order” phase (T_h = 17.5 K). Here, we report charge and thermal transport measurements on ultraclean single crystals of URu₂Si₂ with very large residual-resistivity-ratio down to 30 m K (∼T_c/50), which reveal a number of unprecedented superconducting properties. The results provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology. We propose a gap function with chiral d-wave form Δ(k) = Δ₀k_z(k_x + ik_y). We also demonstrate that a distinct flux line lattice melting transition with outstanding characters occurs well below the upper critical fields even at sub-Kelvin temperature. The intriguing superconducting state of URu₂Si₂ adds a unique and exciting example to the list of unconventional superconductors.     

Momentum dependence of pseudogap and superconducting gap in variation theory

To consider the origin of a pseudogap and a superconducting (SC) gap found in the high-T_c cuprates, we evaluated the momentum dependence of the singlet gap corresponding to the pseudogap and the SC gap in the t–J model, using an optimization variational Monte Carlo (VMC) method. In the underdoped regime, the singlet gap is significantly modified from the simple d_x²-y²(d)-wave gap (∝ cos k_x − cos k_y) by the contribution of long-range pairings. Its angular dependence at the quasi Fermi surface is qualitatively consistent with those experimentally observed in both hole and electron-doped cuprates. On the other hand, a SC gap is almost unchanged, preserving the original simple d-wave form. Thus, it seems that the incoherent part of the singlet gap mainly influences the forms of observed gaps.     

Quasi-particle structure around a single vortex in high-Tc superconductors

For analyzing the checker-board like modulation of the local density of states (LDOS) around a vortex observed in the slightly overdoped Bi₂Sr₂CaCu₂O_x, we examined the effect of pseudogap state of high-T_c superconductors to the LDOS around the vortex. We first derived the Bogoliubov-de Gennes equation for d-wave superconductivity (d-SC) in the presence of d-spin density wave (d-SDW). Using the Fourier–Bessel expansion, we solved this equation for a single vortex state, numerically. We found that the peak of the bound states around E = 0 becomes small and modulation of the LDOS is observed for larger d-SDW order parameter.     

Water incorporation into the Ba2(In1 − xMx)2O5‪ (M = Sc 0 ≤ x < 0.5 and M = Y 0 ≤ x < 0.35) system and protonic conduction

Ba₂(In_1 − xM_x)₂O_{5 − y / 2}(OH)_y‪□_{1 − y / 2} (y ≤ 2; M = Sc³⁺ 0 ≤ x < 0.5 and M = Y³⁺ 0 ≤ x < 0.35) compounds were prepared by reacting Ba₂(In_1 − xM_x)₂O₅‪ phases with water vapor. This reaction is reversible. Analyses of the hydration process by TG and XRD studies show that the thermal stability of hydrated phases increases when x increases and that the incorporation of water is not a single-phase reaction inducing either a crystal system or space group modification. Fully hydrated (y = 2) and dehydrated (y = 0) samples have been stabilized at room temperature and characterized for all compositions. In wet air, all phases show a proton contribution to the total conductivity at temperatures between 350 and 600 °C. At a given temperature, proton conductivity increases with the substitution ratio and reaches at 350 °C, 5.4 10^− 3 S cm^− 1 for Ba₂(In_0.65Sc_0.35)₂O_4.2□_0.2(OH)_1.6.     

On the Fundamental Solution of a Linearized Homogeneous Coagulation Equation

We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel K(x, y) = (xy)^λ/2, around the steady state f(x) = x ^?(3+λ)/2 with ${\lambda \in (1, 2)}We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel K(x, y) = (xy)^λ/2, around the steady state f(x) = x ^−(3+λ)/2 with l ? (1, 2){\lambda \in (1, 2)} . Detailed estimates on its asymptotics are obtained. Some consequences are deduced for the flux properties of the particles distributions described by such models.     

Inelastic X-ray scattering investigations of lattice dynamics in SmFeAsO1−xFysuperconductors

We report measurements of the phonon density of states as probed with inelastic X-ray scattering in SmFeAsO_1−xF_y powders. An unexpected strong renormalization of phonon branches around 23 meV is observed as fluorine is substituted for oxygen. Phonon dispersion measurements on SmFeAsO_1−xF_y single crystals allow us to identify the 21 meV A_1g in-phase (Sm,As) and the 26 meV B_1g (Fe,O) modes to be responsible for this renormalization, and may reveal unusual electron-phonon coupling through the spin channel in iron-based superconductors.     

Structure and electrical properties of Bi0.5(Na, K)0.5TiO3−BiGaO3 lead-free piezoelectric ceramics

Lead-free piezoelectric ceramics (1 − x − y)Bi_0.5Na_0.5TiO₃−xBi_0.5K_0.5TiO₃− yBiGaO₃ have been fabricated by an ordinary sintering technique, and their structure and electrical properties and depolarization temperature have been studied. The results of X-ray diffraction reveal that Bi_0.5K_0.5TiO₃ and BiGaO₃ diffuse into the Bi_0.5Na_0.5TiO₃ lattices to form a new solid solution with a pure perovskite structure. An obvious change in microstructure with increasing concentration of Bi_0.5K_0.5TiO₃ and BiGaO₃ was observed. The piezoelectric constant d₃₃ and the electromechanical coupling factor k_p of the ceramics attain maximum values of 165 pC/N and 0.346 at y = 0.01(x = 0.18) and x = 0.21(y = 0.01), respectively. The temperature dependence of dielectric constant indicates an obvious relaxor characteristic with strong frequency dependence of dielectric constant. The depolarization temperature decreased with increasing content of BiGaO₃ and first decreases and then increases with increasing amount of Bi_0.5K_0.5TiO₃.     

Relation between vortex excitation and thermal conductivity in superconductors

Thermal conductivity κ _xx(T) under a field is investigated in d _{x2 - y2}-wave superconductors and isotropic s-wave superconductors by the linear response theory, using a microscopic wave function of the vortex lattice states. To study the origin of the different field dependence of κ_xx(T) between higher and lower temperature regions, we analyze the spatially-resolved thermal conductivity around a vortex at each temperature, which is related to the spectrum of the local density of states. We also discuss the electric conductivity in the same formulation for a comparison. Received 8 December 2001 and Received in final form 20 March 2002 Published online 6 June 2002     

Structure, ferroelectric and piezoelectric properties of (Bi1−x−yNa0.925−x−yLi0.075)0.5BaxSryTiO3 lead-free piezoelectric ceramics

Lead-free multi-component ceramics (Bi_1−x−yNa_{0.925−x−y}Li_0.075)_0.5Ba_xSr_yTiO₃ have been prepared by an ordinary sintering technique and their structure and electrical properties have been studied. All the ceramics can be well-sintered at 1100 °C. X-ray diffraction patterns shows that Li⁺, Ba²⁺ and Sr²⁺ diffuse into the Bi_0.5Na_0.5TiO₃ lattices to form a new solid solution with a pure perovskite structure, and a morphotropic phase boundary (MPB) is formed at 0.04 < x < 0.08. As compared to pure Bi_0.5Na_0.5TiO₃ ceramic, the coercive field E_C of the ceramics decreases greatly and the remanent polarization P_r of the ceramics increases significantly after the formation of the multi-component solid solution. Due to the MPB, lower E_C and higher P_r, the piezoelectricity of the ceramics is greatly improved. For the ceramics with the compositions near the MPB (x = 0.04–0.08 and y = 0.02–0.04), piezoelectric coefficient d₃₃ = 133–193 pC/N and planar electromechanical coupling factor k_P = 16.2–32.1%. The depolarization temperature T_d reaches a minimum value near the MPB. The temperature dependences of the ferroelectric and dielectric properties suggest that the ceramics may contain both the polar and non-polar regions at temperatures near/above T_d.     

Impurity scattering in f-wave superconductor UPt 3

We study theoretically the effect of impurity scattering in f-wave (or E_2u) superconductors. The quasi-particle density of states of f-wave superconductor is very similar to the one for d-wave superconductor as in hole-doped high T _c cuprates. Also in spite of anisotropy in Δ( ), both the reduced superfluid density and the reduced electronic thermal conductivity is completely isotropic. Received 11 October 2000     

Crystalline structural phase boundaries in (K,Na,Li)NbO 3 ceramics

Lead-free (K_xNa_1−x)_1−yLi_yNbO₃ ceramics (with x=0.50, y=0–0.08 and x=0.30–0.70, y=0.06, respectively) were synthesized using the conventional solid-state reaction technique. Compositional influences of K, Na and Li constituents on microstructures, crystalline structures, dielectric and piezoelectric properties were investigated. It has been known that microstructures change largely with the alkali constituents and that there exist three orthorhombic-tetragonal phase boundaries at room temperature. One occurs in (K_0.50Na_0.50)_1−yLi_yNbO₃ ceramics at y=0.05–0.06, which corresponds to the previously reported morphotropic phase boundary (MPB). The other two appear in (K_xNa_1−x)_0.94Li_0.06NbO₃ ceramics near x=0.40 and x=0.60, respectively. (K_0.50Na_0.50)_0.935Li_0.065NbO₃ and (K_0.45Na_0.55)_0.94Li_0.06NbO₃ ceramics show high piezoelectric properties with the d₃₃ values over 200 pC/N and the k_p values around 45% at room temperature. It is thought that the observed high piezoelectric properties are largely affected by the temperature-driven orthorhombic-tetragonal phase transition.     

Connection Considerations of Gravitational Field in Finsler Spaces

Some alternative connection structures of the Finslerian gravitational field are considered by modifying the independent variables (x,y) (x: point and y: vector) in various ways. For example, (x ^k ,y ⁱ ) (k,i = 1,2,3,4) are changed to (x ^k ,y ⁰) (y ⁰: scalar) or (x ⁰,y ⁱ ) (x ⁰: time axis); (x ^k ,y ⁱ ) are generalized to (x ^k ,y ⁱ ,p _i ) (p _i : covector dual to y ⁱ ) or (x ^k ,y ⁱ ,q _a ) (q _a : covector different from p _i ); (x ^k ,y ⁱ ) are further generalized to (x ^k ,y ^(a)i ) (a = 1,2,…,m), (y ^(a): (a)th vector), etc.     

Surface states and tunneling spectroscopy of high-Tcsuperconductors

Recent studies of high- T_csuperconductors have clarified new aspects of tunneling spectroscopy. The unconventional pairing states, i.e. d-wave symmetry in these materials have been established through various measurements. Differently from isotropic s-wave superconductors, d-wave pairing states have an internal phase of the pair potential. The internal phase modifies the surface states due to the interference effect of the quasiparticles. Along these lines, a novel formula of tunneling spectroscopy has been presented that fully takes into account of the anisotropy of the pair potential. The most essential difference of this formula from conventional ones is that it suggests the phase-sensitive capability of tunneling spectroscopy. The formula suggests that the symmetry of the pair potential is determined by the orientational dependence measurements of tunneling spectroscopy. Along these lines, several experiments have been performed on high-T_c superconductors. The observation of the zero-bias conductance peaks (ZBCP) on Y Ba₂Cu₃O_{7 − δ}strongly suggests the d_{x² − y²}-wave pairing states of hole-doped high-T_c superconductors. On the other hand, the absence of ZBCP on (electron-doped)Nd_1.85Ce_0.15CuO_{4 − δ}indicates that the pair potential of this material is a nodeless state. In this paper, recent developments of tunneling spectroscopy for anisotropic superconductors are reviewed both on theoretical and experimental aspects.     

Muon spin relaxation study on magnetism in high quality single crystal of a high transition temperature superconductor La2−xSrxCuO4−σ (0.11≤x≤0.14)

The positive muon spin relaxation method is applied to probe magnetic ordering in the superconducting phase of a high quality single crystal of La_2−xSr_xCuO_4−σ (0.11≤x≤0.14). The well characterized crystal ofx=0.11 (T _c=34.5 K) with nearly complete flux exclusion exhibits spin freezing at 8K(T _f) with significant spin fluctuation up to 20 K. The onset of spin fluctuation andT _f decrease against increasingx towardsx=0.15, suggesting an existence of a magnetic phase boundary aroundx whereT _c becomes maximum.     

Impurity induced resonance states at the superconducting interface LaAlO3/SrTiO3

Motivated by the recent discovery of superconductivity on the heterointerface LaAlO₃/SrTiO₃, we theoretically investigate the impurity-induced resonance states with coexisting spin singlet s- and triplet p-wave pairing symmetries by considering the influence of Rashba-type spin-orbit interaction (RSOI). Due to the nodal structure of the mixed gap function, we find single nonmagnetic impurity-induced resonance peaks appearing in the local density of state. We also analyze the evolutions of density of states and local density of states with the weight of triplet pairing component determined by the strength of RSOI, which will be widely observed in thin films of superconductors with surface or interface-induced RSOI, or various noncentrosymmetric superconductors in terms of point contact tunneling and scanning tunneling microscopy, and thus shed light on the admixture of the spin singlet and RSOI-induced triplet superconducting states.     

Minimum Polynomial for Single-Mode Parabose Parasupercharge and Hamiltonian

We calculate the minimum polynomial φ(x,y) of parasupercharge Q and Hamiltonian H for single-mode parabose parasupersymmetry (P-PSUSY). Suppose that φ(x,y) satisfies the homogeneity ∀ λ∈ℝ,φ(λ x,λ ² y)=λ ⁿ φ(x,y), then the parafermionic order p _f is restricted to either 1, 2, or 4. Under the P-PSUSY, the homogeneity of the φ(x,y) is equivalent to the parasuperconformality of Q and H. The physical meaning of the parasuperconformality is discussed, in connection with the spin of the elementary particle.