No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
d-wave superconductive gap and related observables of PuCoGa5
Abstract
The real-axis formulation of the Eliashberg theory has been applied to PuCoGa5, assuming d-wave symmetry and phonon-mediated pairing. Here, we present the calculated temperature dependence of the superconductive gap Δ(T) for a freshly prepared sample, and the variation of Δ(T = 2 K) with increasing impurity scattering rate. We also present the calculated energy dependence of the quasiparticle density of state, together with the corresponding normalized tunnelling conductance at T = 4 K. These quantities could be compared with future tunnelling experiments that would also lead to a direct determination of the spectral density function. Finally, we show that the normal phase resistivity can be well reproduced up to room temperature assuming electron–phonon scattering within a two-band model.
... PuCoGa 5 is a prototypical heavy-fermion compound that becomes a superconductor below T c ≃ 18.5 K [1], the highest critical temperature of any heavy-fermion material. Fifteen years on its discovery, the nature of the pairing boson in PuCoGa 5 remains an open question. Superconductivity (SC) mediated by spin fluctuations (SFs) associated with the proximity to an antiferromagnetic (AFM) quantum critical point (QCP) was initially proposed. ...
... Subsequent point-contact spectroscopy measurements confirmed that the wavefunction of the paired electrons has an unconventional d-wave symmetry [3]. However, the SF conjecture was questioned [4,5] after polarized neutron diffraction failed to observe a local magnetic moment in the normal state of PuCoGa 5 [6], pointing to an extrinsic origin of the reported temperature dependent χ m . This observation is confirmed in the present article by showing that the magnetic susceptibility of an almost defect-free PuCoGa 5 single crystal is weak and temperature-independent from T c up to room temperature. ...
We have measured X-ray magnetic circular dichroism (XMCD) spectra at the Pu $M_{4,5}$ absorption edges from a newly-prepared high-quality single crystal of the heavy fermion superconductor $^{242}$PuCoGa$_{5}$, exhibiting a critical temperature $T_{c} = 18.7~{\rm K}$. The experiment probes the vortex phase below $T_{c}$ and shows that an external magnetic field induces a Pu 5$f$ magnetic moment at 2 K equal to the temperature-independent moment measured in the normal phase up to 300 K by a SQUID device. This observation is in agreement with theoretical models claiming that the Pu atoms in PuCoGa$_{5}$ have a nonmagnetic singlet ground state resulting from the hybridization of the conduction electrons with the intermediate-valence 5$f$ electronic shell. Unexpectedly, XMCD spectra show that the orbital component of the $5f$ magnetic moment increases significantly between 30 and 2 K; the antiparallel spin component increases as well, leaving the total moment practically constant. We suggest that this indicates a low-temperature breakdown of the complete Kondo-like screening of the local 5$f$ moment.
... Nevertheless, phonon-mediated superconductivity cannot be definitely ruled out in PuCoGa 5 [197]. It is unlikely to occur, considering, e.g., the "too high" critical temperature [198] or the fact that its U analogue UCoGa 5 is not superconducting, despite a phonon spectrum very similar to that of PuCoGa 5 [199]. ...
Nous présentons ici un aperçu des propriétés des supraconducteurs transuraniens, mais aussi des analogues transuraniens (non supraconducteurs) des supraconducteurs à base d'uranium. Nous examinons brièvement la supraconductivité dans les éléments d'actinides et les composés d'uranium, puis nous présentons en particulier la famille des composés PuTX5PuTX5 (T=Co,RhT=Co,Rh, X=Ga,InX=Ga,In), la série la plus étendue de supraconducteurs parmi les actinides ainsi que NpPd5Al2NpPd5Al2, le seul supraconducteur au neptunium connu à ce jour. Les effets de la substitution chimique, du vieillissement et de la pression sur les propriétés des supraconducteurs transuraniens sont également discutés.
The energy scale Ω0 of the electron-boson spectral function in the heavy-fermion, d-wave superconductor NpPd5Al2 is predicted on the basis of Eliashberg theory calculations. Assuming a spectral function shape typical for antiferromagnetic spin fluctuations, and imposing constraints provided by the experimental values for the critical temperature and the low-temperature energy gap, one obtains values of Ω0 of about 2–2.5 meV, slightly dependent from the strength of the Coulomb pseudopotential. These values are in excellent agreement with the characteristic magnetic fluctuations energy estimated from NMR measurements of the nuclear-spin-lattice relaxation time at the Al site. The calculated temperature dependence of the upper critical field, the local spin susceptibility, and the nuclear-spin-lattice relaxation rate is also in good agreement with available experimental data, showing that a coherent description of the superconducting state can be obtained assuming that the electron pairing in NpPd5Al2 is mediated by antiferromagnetic fluctuations. We finally report predictions for the London penetration depth, the energy dependence of the tunneling differential conductance at different temperatures, and the temperature dependence of the energy gap.
We report electronic structure calculations of PuCoGa5 and PuRhGa5 superconductors. The band structure, electric field gradients, and Fermi surface topologies were investigated using two methods of correlated band theory, namely the conventional static mean-field LDA+U and the local density matrix approximation (LDMA). The latter is based on the Hubbard-I approximation and includes intra-atomic dynamical correlations in a self-consistent manner. Our results show that although LDA+U and LDMA calculations do not significantly modify the Fermi surface topologies compared to LDA, they do lead to a substantial reduction of the f character of the electronic states at the Fermi energy. The calculations indicate presence of a pseudogap in the electronic spectrum. We achieve a good agreement between calculated and experimental nuclear quadrupolar resonance frequencies and a fairly good agreement between calculated and experimental photoemission spectra. Our findings can be important for the theory of superconductivity in PuCoGa5 and related compounds.
We study theoretically the electronic structure and photoemission spectra of PuCoGa5 making use of the LDA+Hubbard I approximation implemented in the full-potential LAPW basis, including self-consistency over the charge density. The calculations show relative reduction of the f-states spectral weight at the Fermi energy. There is fairly good agreement between calculated photoemission spectra and experimental results. We demonstrate that an account of Pu f-electron Coulomb correlations does not modify significantly the Fermi surface topologies but leads to substantial reduction of the f-character for the electronic states at the Fermi energy. These findings can be important for the theory of superconductivity in PuCoGa5 and related compounds.
A computational investigation of the crystallographic and electronic structure of PuCoGa5 was reported. From full-potential, relativistic total-energy calculations the equilibrium theoretical lattice parameters of PucoGa5 in the tetragonal HoCoGa5 structure was determined. The calculation identified the superconductivity in PuCoGa5 to emerge out of electronic states dominated by Pu 5f electrons.
We examine possible pairing mechanisms of superconductivity in PuCoGa5 based on spin-fluctuations or phonons as mediating bosons. We consider experimental data of specific heat C(T) and resistivity ρ(T) as input to determine a consistent scattering boson with the superconducting transition temperature of 18.5 K in PuCoGa5. Irrespective to the type of boson, the characteristic boson frequency is found to be ∼150 K from the resistivity fitting. The spin fluctuation model is most consistent with the experimental resistivity, successfully explaining the anomalous temperature dependence [∼(T2∕150 K+T)] at low temperatures as well as the saturation behavior at high temperatures. Assuming that the pairing state is a non s-wave, the large residual resistivity ρimp∼20 μΩ cm∼120 K suggests that an ideally pure sample of PuCoGa5 would have a maximum Tc of 39 K.
A large number of experimental facts and theoretical arguments favor a two-gap model for superconductivity in MgB2. However, this model predicts strong suppression of the critical temperature by interband impurity scattering and, presumably, a strong correlation between the critical temperature and the residual resistivity. No such correlation has been observed. We argue that this fact can be understood if the band disparity of the electronic structure is taken into account, not only in the superconducting state, but also in normal transport.
On the basis of electronic structure calculations we identify the superconductivity in the novel, high-temperature superconductor PuCoGa5 to be caused by the pairing of Pu 5f electrons. Assuming delocalized Pu 5f states, we compute theoretical crystallographic constants very near to the experimental ones, and the calculated specific heat coefficient compares reasonably to the measured coefficient. The theoretical Fermi surface is quasi-two-dimensional and the material appears to be close to a magnetic phase instability.
In the Bardeen-Cooper-Schrieffer theory of superconductivity, electrons form (Cooper) pairs through an interaction mediated by vibrations in the underlying crystal structure. Like lattice vibrations, antiferromagnetic fluctuations can also produce an attractive interaction creating Cooper pairs, though with spin and angular momentum properties different from those of conventional superconductors. Such interactions have been implicated for two disparate classes of materials--the copper oxides and a set of Ce- and U-based compounds. But because their transition temperatures differ by nearly two orders of magnitude, this raises the question of whether a common pairing mechanism applies. PuCoGa5 has a transition temperature intermediate between those classes and therefore may bridge these extremes. Here we report measurements of the nuclear spin-lattice relaxation rate and Knight shift in PuCoGa5, which demonstrate that it is an unconventional superconductor with properties as expected for antiferromagnetically mediated superconductivity. Scaling of the relaxation rates among all of these materials (a feature not exhibited by their Knight shifts) establishes antiferromagnetic fluctuations as a likely mechanism for their unconventional superconductivity and suggests that related classes of exotic superconductors may yet be discovered.
Many transition metal compounds show saturation of the resistivity at high temperatures, T, while the alkali-doped fullerenes and the high-Tc cuprates are usually considered to show no saturation. We present a model of transition metal compounds, showing saturation, and a model of alkali-doped fullerenes, showing no saturation. To analyze the results we use the f-sum rule, which leads to an approximate upper limit for the resistivity at large T. For some systems and at low T, the resistivity increases so rapidly that this upper limit is approached for experimental T. The resistivity then saturates. For a model of transition metal compounds with weakly interacting electrons, the upper limit corresponds to a mean free path consistent with the Ioffe-Regel condition. For a model of the high Tc cuprates with strongly interacting electrons, however, the upper limit is much larger than the Ioffe-Regel condition suggests. Since this limit is not exceeded by experimental data, the data are consistent with saturation also for the cuprates. After "saturation" the resistivity usually grows slowly. For the alkali-doped fullerenes, "saturation" can be considered to have happened already for T=0, due to orientational disorder. For these systems, however, the resistivity grows so rapidly after "saturation" that this concept is meaningless. This is due to the small band width and to the coupling to the level energies of the important phonons. Comment: 22 pages, RevTeX, 19 eps figures, additional material available at http://www.mpi-stuttgart.mpg.de/andersen/fullerene/
The author reviews some of the important successes achieved by Eliashberg theory in describing the observed superconducting properties of many conventional superconductors. Functional derivative techniques are found to help greatly in understanding the observed deviations from BCS laws. Approximate analytic formulas with simple correction factors for strong-coupling corrections embodied in the single parameter Tcomegaln are also found to be very helpful. Here Tc is the critical temperature and omegaln is an average boson energy mediating the pairing potential in Eliashberg theory. In view of the discovery of high-Tc superconductivity in the copper oxides, results in the very strong coupling limit of Tcomegaln~1 are also considered, as is the asymptotic limit when Tcomegaln-->∞. This case is of theoretical interest only, but it is nevertheless important because simple analytic results apply that give insight into the more realistic strong-coupling regime. A discussion more specific to the oxides is included in which it is concluded that some high-energy boson-exchange mechanism must be operative, with, possibly, some important phonon contribution in some cases. A more definitive application of boson-exchange models to the oxides awaits better experimental results.
A new set of basis functions is introduced, consisting of products of Fermi-surface harmonics FJ(k) and polynomials σn(ε) in the energy (ε-μ)/kBT. The former are orthonormal on the Fermi surface, and the latter are orthonormal with weight function -∂f/∂ε. In terms of this set the exact semiclassical Boltzmann equation takes a particularly simple form, giving a matrix equation which can probably be truncated at low order to high accuracy. The connection with variational methods is simple. Truncating at a 1 × 1 matrix gives the usual variational solution where φk is assumed proportional to νkx for electrical conductivity and (ε-μ)νkx for thermal conductivity. Explicit equations are given for the matrix elements QJn,J′n′ of the scattering operator for the case of phonon scattering, and a perturbation formula for ρ is given which is accurate for weak anisotropy. The matrix elements are simple integrals over spectral functions α2(±,J,J′)F(Ω) which generalize the electron-phonon spectral function α2F(Ω) used in superconductivity theory. Analogies are described between Boltzmann theory and Eliashberg theory for Tc of superconductors. The intimate relations between high-temperature resistance and the s- or p-wave transition temperature are made explicit.
Measurements of the electrical resistivity of a polycrystalline PuCoGa5 sample reveal significant modifications of the superconducting properties as a function of time, due to the increase of defects and impurities resulting from self-irradiation damage. More than four years of aging were necessary to detect a deviation from linearity in the time dependence of the critical temperature. The observed behavior is understood in the framework of the Eliashberg theory, confirming the “dirty” d-wave character which was already suggested by nuclear magnetic resonance. We show that experimental data accumulated so far can be well reproduced by assuming a phononic mechanism for superconductivity, with reasonable values of the electron-phonon coupling and Coulomb pseudopotential. Further experiments are then required to assess the role of spin fluctuations in stabilizing the superconducting state in this compound.
In a recently published paper Laughlin proposes an exchange-interaction theory of resistivity saturation based on the Altshuler-Aronov depression of the density of states at the Fermi level. In my view this contradicts the many experimental data on disordered metals in which the density of states does not decrease relative to the ordered phase, yet resistivity saturation takes place. Exchange-correlation (and localization) effects become important in the regime in which kFL∼1 and σ∼σmin. This is not the case in typical saturated metals, where kFL∼3-6 and σsat∼(10-30)σmin.
By minimizing the total energy within the density-functional method we determined lattice parameters, atom positions, interatomic forces, and electronic structure of the new PuCoGa5 superconductor. The on-site Coulomb repulsion U and Hund’s exchange J lead to changes in the electronic structure, particularly near the Fermi energy, and to a better agreement between the calculated and experimental geometries. Using this ab initio input, the phonon dispersion relations are determined and classified by their symmetries. Phonon densities of states and the lattice heat capacity are discussed. Using individual contributions due to all optical modes at the Γ point we estimate electron-phonon coupling λ∼0.7 which does not suffice to explain the observed value of Tc and suggests that electronic interactions also play a role in the pairing mechanism.
We report the results of inelastic neutron scattering experiments on NpCoGa5, an isostructural analog of the PuCoGa5 superconductor. Two energy scales characterize the magnetic response in the antiferromagnetic phase. One is related to a nondispersive excitation between two crystal field levels. The other at lower energies corresponds to dispersive fluctuations emanating from the magnetic zone center. The fluctuations persist in the paramagnetic phase also, although weaker in intensity. This supports the possibility that magnetic fluctuations are present in PuCoGa5, where unconventional d-wave superconductivity is achieved in the absence of magnetic order.
We have calculated the effect of impurity scattering on the temperature dependence of the nuclear-spin-lattice-relaxation rate and Knight shift for a two-dimensional superconductor with d2x-y2 symmetry. Lowest-order Born scattering as well as T-matrix scattering in the unitary limit is considered. Strong scattering profoundly changes the low-temperature dependences of both quantities giving rise to a constant contribution. Strong-coupling effects, which are never large, are included approximately in our simplified Eliashberg formulation of the problem.
Plutonium is a metal of both technological relevance and fundamental scientific interest. Nevertheless, the electronic structure of plutonium, which directly influences its metallurgical properties, is poorly understood. For example, plutonium's 5f electrons are poised on the border between localized and itinerant, and their theoretical treatment pushes the limits of current electronic structure calculations. Here we extend the range of complexity exhibited by plutonium with the discovery of superconductivity in PuCoGa5. We argue that the observed superconductivity results directly from plutonium's anomalous electronic properties and as such serves as a bridge between two classes of spin-fluctuation-mediated superconductors: the known heavy-fermion superconductors and the high-T(c) copper oxides. We suggest that the mechanism of superconductivity is unconventional; seen in that context, the fact that the transition temperature, T(c) approximately 18.5 K, is an order of magnitude greater than the maximum seen in the U- and Ce-based heavy-fermion systems may be natural. The large critical current displayed by PuCoGa5, which comes from radiation-induced self damage that creates pinning centres, would be of technological importance for applied superconductivity if the hazardous material plutonium were not a constituent.
The idea of superconductivity without the mediating role of lattice vibrations (phonons) has a long history. It was realized soon after the publication of the Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity 50 years ago that a full treatment of both the charge and spin degrees of freedom of the electron predicts the existence of attractive components of the effective interaction between electrons even in the absence of lattice vibrations—
a particular example is the effective interaction that depends on the relative spins of the electrons. Such attraction without phonons can lead to electronic pairing and to unconventional forms of superconductivity that can be much more sensitive than traditional (BCS) superconductivity to the precise details of the crystal structure and to the electronic and magnetic properties of a material.
By using single crystals and polarized neutrons, we have measured the orbital and spin components of the microscopic magnetization in the paramagnetic state of NpCoGa(5) and PuCoGa(5). The microscopic magnetization of NpCoGa(5) agrees with that observed in bulk susceptibility measurements and the magnetic moment has spin and orbital contributions as expected for intermediate coupling. In contrast, for PuCoGa(5), which is a superconductor with a high transition temperature, the microscopic magnetization in the paramagnetic state is small, temperature-independent, and significantly below the value found with bulk techniques at low temperatures. The orbital moment dominates the magnetization.