Non-conventional Superconductors Research Articles

Potential of non-conventional superconductors for particle accelerator cavities

Potential of non-conventional superconductors for particle accelerator cavities

A Model for Evaluating the Crystallinity Quality of Single Crystals Grown by the Floating Zone Technique

AbstractThe floating zone technique is a popular method for crystal growth of nonconventional superconductors and magnetic materials. However, the quality must be characterized with particular care with respect to their actual crystallinity since not everything grown by floating zone method is a single crystal. In this paper, the molten‐zone sensitive material LiCoPO4 has been grown by the floating zone method using Co(NO3)2∙6H2O and CoO precursors, respectively, abbreviated as LCPN and LCPO. The grown materials are characterized regarding their chemical composition, phase purity, crystal perfection, and orientation. In order to optimize crystal growth and quantitatively characterize its crystallinity quality, the development factor (V) has been proposed to determine the growth rate of the grains, while the orientation deviation factor (δ) for assessing the quality of the grown crystals. The development factors V for LCPN and LCPO are calculated to be 0.05 and 0.09, respectively, indicating that the grains of LCPO develop faster than those of LCPN. At the same time, the orientation deviation factor of LCPO exceeds that of LCPN (δ(LCPO) = 2.00, δ(LCPN) = 0.77) suggesting a higher quality for the latter. This model provides significant guidance for the evaluation of other materials grown by the floating zone method.

Stationary Josephson current in junctions involving d-wave superconductors with charge density waves: the temperature dependence and deviations from the law of corresponding states

Stationary Josephson current I c in symmetric and non-symmetric junctions involving d-wave superconductors with charge density waves (CDWs) was calculated. It was found that, if CDWs are weak or absent, there exists an approximate proportionality between I c and the product of superconducting order parameters in the electrodes (the law of corresponding states) for several factors affecting those quantities, such as the temperature, T, or one of the parameters characterizing the combined CDW superconducting phase (the degree of the Fermi surface dielectric gapping and the ratio between the parent superconducting and CDW order parameters). Otherwise, the dependences I c (T) were shown to deviate from those in the absence of CDWs, and the relevant corresponding-state dependences from linearity, the deviations being especially strong at certain rotation angles of crystalline electodes with respect to the junction plane. Hence, making use of specially designed experimental setups and analyzing the I c (T) and corresponding-state dependences, the existence of CDWs in cuprates and other non-conventional superconductors can be detected.

The metallic transport of (TMTSF)2X organic conductors close to the superconducting phase

Comparing resistivity data of the quasi-one-dimensional superconductors (TMTSF)2PF6 and (TMTSF)2ClO4 along the least conducting c⋆-axis and along the high conductivity a-axis as a function of temperature and pressure, a low temperature regime is observed in which a unique scattering time governs the transport along both directions of these anisotropic conductors. However, the pressure dependence of the anisotropy implies a large pressure dependence of the interlayer coupling. This is in agreement with the results of first-principles density functional theory calculations implying methyl group hyperconjugation in the TMTSF molecule. In this low temperature regime, both materials exhibit for ρc a temperature dependence aT + bT2. Taking into account the strong pressure dependence of the anisotropy, the T-linear ρc is found to correlate with the suppression of the superconducting Tc, in close analogy with ρa data. This work reveals the domain of existence of the three-dimensional coherent regime in the generic (TMTSF)2X phase diagram and provides further support for the correlation between T-linear resistivity and superconductivity in non-conventional superconductors.

Observing Majorana bound states of Josephson vortices in topological superconductors

In recent years there has been an intensive search for Majorana fermion states in condensed matter systems. Predicted to be localized on cores of vortices in certain nonconventional superconductors, their presence is known to render the exchange statistics of bulk vortices non-abelian. Here we study the equations governing the dynamics of phase solitons (fluxons) in a Josephson junction in a topological superconductor. We show that the fluxon will bind a localized zero energy Majorana mode and will consequently behave as a non-abelian anyon. The low mass of the fluxon, as well as its experimentally observed quantum mechanical wave-like nature, will make it a suitable candidate for vortex interferometry experiments demonstrating non-abelian statistics. We suggest two experiments that may reveal the presence of the zero mode carried by the fluxon. Specific experimental realizations will be discussed as well.

Renormalized Gaussian approach to critical fluctuations in the Landau–Ginzburg–Wilson model and finite-size scaling

This paper investigates the application of the renormalized Gaussian approach (RGA) on spatial fluctuations and their manifestations in the vicinity of the critical point. The basis for calculation is the Landau–Ginzburg–Wilson (LGW) Hamiltonian (HLGW). Within the framework of this approach, the model predictions are examined in some detail and the importance of fluctuations is established. Analytic expressions for the correlation length, susceptibility, correlation function as well as the specific heat are calculated and an approximate Ginzburg criterion is deduced. The approach also establishes the limitations of the mean-field theory description, since it is found that the mean-field critical temperature Tc is a characteristic scale of temperature linked to the thermal fluctuations rather than the transition temperature. By applying the RGA, the concept of dimensionality appears essential in the manifestation and analysis of phase transitions since the approach suggests the dependence of some critical parameters and exponents on the dimensionality, as well as the quantum character. Also, it is shown that at low temperature, the correlation length of 1D systems becomes infinite at T = 0 K in accord with the Landau and Mermin–Wagner theorems. Finally, three illustrative examples are provided as analysis support in order to demonstrate the usefulness of the approach for a variety of phase transitions: (1) non-conventional superconductors, (2) localized magnetism, and (3) ferroelectricity.

Specific heat and anisotropy of the nonconventional superconductorsPuCoGa5andPuRhGa5

We report on specific-heat measurements under a magnetic field on oriented single crystals of the nonconventional superconductors ${\mathrm{PuCoGa}}_{5}$ and ${\mathrm{PuRhGa}}_{5}$ with superconducting transition temperature ${T}_{c}\ensuremath{\sim}18$ and $9\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, respectively. In the superconducting state, the electronic specific heat follows a quadratic temperature dependence, which indicates an axial state with line nodes in the superconducting gap structure. The specific heat measured under a magnetic field applied along different crystallographic directions reveals anisotropic behavior. For both compounds, ${T}_{c}$ decreases faster for fields applied along the $c$ axis than for fields perpendicular to it. The value of the slope of the critical field at ${T}_{c}$ is higher in the case of ${\mathrm{PuCoGa}}_{5}$, while the anisotropy effect is stronger in ${\mathrm{PuRhGa}}_{5}$. Further results are discussed in the context of the isostructural Ce- and Np-based materials. The possibility of the appearance of a Fulde-Ferrell-Larkin-Ovchinnikov state and/or strong spin-orbit coupling, related to the observed low-temperature linear shape of the critical field deviating from the common $d$-wave superconductor behavior, is considered, especially in the ${\mathrm{PuRhGa}}_{5}$ case.

Sound wave anomalies in superconducting compounds

Temperature dependence of the elastic constants in the superconducting state is described on the basis of the Ginsburg-Landau theory. This approach shows very general character and allows to describe quantitative renormalization of the elastic constants in the superconducting state for different materials including non-conventional superconductors. Various examples (A-15 compounds, Chevrel compounds, CeRu2, Ba0.63K0.37BiO3, Yb3Rh4Sn13, Ca3Rh4Sn13, HfV2, some heavy fermion compounds and Sr2RuO4) are given.

Correlation between characteristic energies in non- s-wave pairing superconductors

By solution of the Bethe–Goldstone equation for the Cooper pairing problem, an approximate analytic relation is derived between coherence length ξ and the binding energy of the Cooper pair. This relation is then qualitatively confirmed by numerically solving the corresponding self-consistent gap equations, following the crossover from weak to strong coupling, in non- s-wave superconductors. The relation applies to non-conventional superconductors, and in particular to heavy Fermions and to high- T c cuprates. Utilizing in addition a phenomenological link between k B T c and a characteristic energy ε c=ℏ 2/2m ∗ξ 2 , with m ∗ the effective mass, major differences are exposed in the functional relation between k B T c and ε c for s-wave materials and for non-conventional superconductors. The relation between critical temperature and ε c thereby proposed correctly reflects the qualitative properties of heavy Fermion superconductors.

On-site repulsion as the source of pairing in carbon nanotubes and intercalated graphite

We show that different non-conventional superconductors have one fundamental feature in common: pair eigenstates of the Hamiltonian are repulsion-free, the W=0 pairs. In extended Hubbard models, pairing can occur for resonable parameter values. For $(N,N)$ nanotubes the binding energy of the pair depends strongly on the filling and decreases towards a reduced but nonzero value for the graphite sheet $N \to \infty$.

Quantum oscillations in non-conventional superconductors

We discuss the possibility to observe the de Haas–van Alphen (dHvA) effect in the vortex lattice regime when vortex cores do not overlap ( H c1⪡ B⪡ H c2). The main part of a superconductor is then in the “gapped” state, while the magnetic field is practically homogeneous. We developed the method to treat oscillations in this limit. It is shown that for a gap parameter with lines of zeroes the dHvA-oscillations may become observable for the magnetic field along high symmetry directions, although the signal is reduced by scattering of electrons on periodic supercurrents. For a “d-wave”-like superconductor no considerable effect is expected. Structure of magnetic levels in superconducting state is briefly discussed.

Superfluid characteristics of the attractive Hubbard model for various lattice structures

We study the basic thermodynamic and electromagnetic properties of the superconductor described by the negative- U Hubbard model (gap parameter Δ, critical temperature T c, London penetration depth λ, thermodynamic critical field H c and Ginzburg-Landau correlation length ξ GL). The calculations are performed for square (SQ, d = 2), simple cubic (SC, d = 3) and face-centered cubic (FCC, d = 3) lattices. We analyze the results as a function of electron density n and interaction U using the Hartree-Fock approximation in the weak-to-intermediate U case combined with the conclusions from the perturbation theory valid in the strong coupling limit. From the equality: λ/ ξ GL = 1/√2 we find the boundaries between local and nonlocal electronic behaviour of the U < 0 Hubbard model in the U- n parameter space. Using the calculated values of T c and λ we compare the “universal plot” of T c/ T c m versus [ λ(0)/ λ m(0)] 2 (where: T c m denotes maximum T c as a function of n and λ m(0) corresponds to T c m) with the recent experimental data for various families of nonconventional superconductors and conclude that the best agreement can be obtained for intermediate values of the local attraction.

Thermal conductivity and thermally induced charge imbalance in heavy-fermion systems

We study the effects of a magnetic field and a supercurrent flow on the thermal conductivity of nonconventional superconductors with an energy gap vanishing at either points or on a line or lines on the Fermi surface. A study of the thermally induced charge imbalance is also presented. Our calculations are done using a Boltzmann equation approach, and elastic scattering by nonmagnetic impurities is assumed to be the main source of relaxation; the relaxation rate is calculated in the low-temperature limit, assuming the phase shift of the scatterers to be π/2 in the normal state. Our calculations indicate that the effects we predict are large enough to be experimentally observable.