重费米子超导与竞争序

与其他非常规超导系列相比, 重费米子超导体往往具有丰富多样的竞争序, 超导与各种竞争序相伴而生, 电子配对与反铁磁涨落、铁磁涨落、价态涨落、电四极矩涨落等量子临界涨落密切相关, 扩充了非常规超导的研究内容. 重费米子材料中的f电子往往同时参与超导与各种竞争序的形成, 表现出局域与巡游的二重性. 重费米子二流体理论为理解重费米子超导与竞争序的关系提供了新的思路.     

Neutron scattering studies on heavy-fermion superconductors

We review recent neutron scattering studies on uranium-based heavy-fermion superconductors. The coupling between magnetic and superconducting order parameters was observed in UPt₃, UPd₂Al₃, URu₂Si₂, and UNi₂Al₃. In UPd₂Al₃, the superconducting gap appears in the spin excitation spectra. These results are indicative of the strong interplay between magnetism and superconductivity. We also report the unusual behaviors of the weak antiferromagnetic ordering, the long-range magnetic correlation in UPt₃ at ultra-low temperatures, and the pressure-induced magnetic transition from the weak (0.02μ_B/U) to a high moment state (0.4μ_B/U) at 1.5 GPa in URu₂Si₂.     

Itinerant f-electron systems of cerium and uranium compounds

The f-electron systems of the cerium and uranium compounds have attracted attention in the context of heavy fermion and anisotropic superconductivity. We clarified an itinerant f-electron nature for UPt₃ by the de Haas–van Alphen experiments, detecting heavy conduction electrons with 100m₀. The dHvA oscillation was also observed clearly in both the normal and superconducting mixed states in CeRu₂,URu₂Si₂ and UPd₂Al₃. An anisotropic energy gap with a line node for URu₂Si₂ was discussed from the angular dependence of the dHvA amplitude in the mixed state.     

Heavy fermion superconductivity

The quest for a precise identification of the symmetry of the order parameter in heavy fermion systems has really started with the discovery of the complex superconducting phase diagram in UPt₃. About 10 years latter, despite numerous experiments and theoretical efforts, this is still not achieved, and we will quickly review the present status of knowledge and the main open question. Actually, the more forsaken issue of the nature of the pairing mechanism has been recently tackled by different groups with macroscopic or microscopic measurement, and significant progress have been obtained. We will discuss the results emerging from these recent studies which all support non-phonon-mediated mechanisms.     

Spin fluctuations in intermetallics

A review is given of investigations of the quasiparticle spectra and of the magnetic fluctuations spectra of metals with strong longitudinal magnetic susceptibilities which were performed by means of the de Haas-van Alphen effect and inelastic neutron scattering. Among the systems investigated are the incipient ferromagnets Ni₃Ga and TiBe₂, the low temperature ferromagnets Ni₃Al, YNi₃, ZrZn₂ and MnSi, the light rare earth metals including PrCu₂ which are close to antiferromagnetic instabilities at low temperatures, and the actinide heavy fermion superconductors UPt₃ and UBe₁₃. The strong renormalisation of the quasiparticle masses and the temperature dependence of the heat capacity and of the magnetic equation of state of these systems are discussed in terms of a quantitative model based on the relaxation frequency of very low lying spin fluctuations.     

Uranium-based heavy-fermion superconductors: an experimental survey

The uranium-based heavy-fermion superconductors were discovered almost one decade ago. Here, we present an experimental survey of their interesting normal and superconducting state properties. It appears that most of the unusual normal-state properties can be attributed to the proximity of an antiferromagnetic instability and the presence of competing electronic interactions. The discovery of a superconducting instability in these strongly-correlated electron systems came totally unexpected. The parameters describing the superconducting state yield strong deviations from the standard BCS behaviour. Accumulating evidence has been gathered for a nontrivial superconducting pair function (L ≠ 0). We illustrate recent developments by a number of prime studies, like high-field measurements and alloying experiments, and give special attention to multicomponent superconductivity in UPt₃ and (U, Th)Be₁₃.     

Neutron scattering studies of magnetic properties of actinide systems

In this article we review neutron scattering studies of the magnetic properties of actinide systems over the last 15 years, with particular emphasis on the work since 1984 and the reviews by Rossat-Mignod et al. and Buyers and Holden. In section 2 the results obtained on the actinide dioxides UO₂, NpO₂ and PuO₂ at spallation sources and the recent observation of intermultiplet transitions in UPd₃ and UPt₃ are presented. In section 3 a discussion is given of magnetization densities, starting with the almost localized system such as PuSb and continuing to more recent work on itinerant intermetallic systems such as UNi₂, UFe₂ and PuFe₂. In these latter systems the ratio μ_L/μ_S of the orbital and spin moments may be determined by neutrons and compared to theory. In section 4 we present work on compounds with the NaCl crystal structure. This includes complex magnetic phase diagrams, as found for example in UAs and NpAs, the discussion of the results of critical scattering experiments, and neutron inelastic experiments on ferromagnets such as PuSb and UTe. In section 5 the work on single crystals of U-containing heavy fermions is presented. In these systems neutron scattering has been able to characterize the small magnetic moments and the nature of the magnetic correlations, which are frequency dependent. A summary of the significant progress and problems remaining is given in section 6.     

Orbital pairing form and gap topology of triplet superconductivity in UPt3

The orbital symmetry of the order parameter in UPt₃ is determined by evaluating transport coefficients. The result leads to an order parameter of either the non-unitary bipolar state: or the unitary planar state: where , or with the hexagonal unit vectors and . The d vector is rotatable in the plane spanned by and perpendicular to under weak applied c-axis field. Experiments are proposed to distinguish between these equally possible states.     

Origin of intrinsic Josephson coupling in the cuprates and its relation to order parameter symmetry: An incoherent hopping model

Experiments on the cuprate superconductors demonstrate that these materials may be viewed as a stack of Josephson junctions along the direction normal to the CuO₂ planes (the c-axis). In this paper, we present a model which describes this intrinsic Josephson coupling in terms of incherent quasiparticle hopping along the c-axis arising from wave-function overlap, impurity-assisted hopping, and boson-assised hopping. We use this model to compute the magnitude and temperature T dependence of the resulting Josephson critical current j_c(T) for s- and d-wave superconductors. Contrary to other approaches, d-wave pairing in this model is compatible with an intrinsic Josephson effect at all hole concentrations and leads to j_c(T) T at low T. By parameterizing our theory with c-axis resistivity data from YBa₂Cu₃O_7−δ (YBCO), we estimate j_c(T) for optimally doped and underdoped members of this family. j_c(T) can be measured either directly or indirectly through microwave penetration depth experiments, and current measurements on Bi₂Sr₂CaCu₂O₈ and La_2−xSr_xCuO₄ are found to be consistent with s-wave pairing and the dominance of assisted hopping processes. The situation in YBCO is still unclear, but our estimates suggest that further experiments on this compound would be of great help in elucidating the validity of our model in general and the pairing symmetry in particular.     

Magnetic study of the UPt3 superconducting phases

In order to distinguish the UPt₃ superconducting (s.c.) phases we have studied their magnetic properties at low fields in a SQUID magnetometer and up to fields >H_c2(0) with a capacitive torque-meter. With the SQUID we measure the magnetic penetration depth and find the second s.c. transition at T_c⁻ when the field is applied along the c-axis, but not with . This result, combined with power-law behavior at low temperature T, is most consistent with the two-dimensional E_2u s.c. order parameter. Below 20 mK we find an additional diamagnetic signal that we ascribe to the normal state magnetism. In high fields our torque measurements show a kink of the perpendicular magnetization component at the B–C phase line, pointing to an enhanced Ginzburg–Landau parameter in the C phase.     

Structurally tuned superconductivity in heavy-fermion CeMIn5 (M=Co, Ir, Rh)

We discuss systematic trends in the high-temperature physical properties of the heavy Fermion superconductors (HFS) CeCoIn₅ (T_c=2.3 K, γ=300 mJ/molK²), CeIrIn₅ (T_c=0.4 K, γ=750 mJ/molK²), and CeRhIn₅ (P_c=16 kbar, T_c=2.1 K, γ=400 mJ/molK²) in terms of crystalline-electrical-field effects(CEF). We suggest the possibility that the interplay between the symmetry of the CEF ground-state (or low-T CEF scheme of levels) and the f–s hybridization could generate spin fluctuations relevant to the superconducting pairing mechanism in these materials. This hypothesis may provide insight into the fact that some crystal structures appear to favor superconductivity. Further, CeMIn₅ (M=Co, Ir, Rh) appear to be structural relatives of the cubic heavy Fermion superconductor CeIn₃, but with much higher T_c's. We argue that structural layering inherent in the tetragonal CeMIn₅ crystal structure determines the magnetic and electronic anisotropy responsible for the enhanced T_c's. We also describe similarities and differences between these compounds and the high-T_c cuprates.     

Plane-chain coupling in YBa2Cu3O7: temperature dependence of the penetration depth

We have studied the penetration depth for a model of YBa₂Cu₃O₇ involving pairing, both in the CuO₂ planes and in the CuO chains. In this model pairing in the planes is due to an attractive interaction, while Coulomb repulsion induces in the chains an order parameter with opposite sign. Due to the anti-crossing produced by hybridization between planes and chains, one obtains a d-wave like order parameter which changes sign on a single sheet of the Fermi surface and has nodes in the gap. We find that our model accounts quite well for the anisotropy of the penetration depth and for the absolute values. We reproduce fairly well the whole temperature dependence for both the a- and the b-directions, including the linear dependence at low temperature. We use a set of parameters which are all quite reasonable physically. Our results for the c-direction are also satisfactory, although the situation is less clear both experimentally and theoretically.     

Superconductivity in the cuprates: Deduction of mechanism for d-wave pairing through analysis of ARPES

In the Eliashberg integral equations for d-wave superconductivity, two different functions (α²F)_n(ω, θ) and (α²F)_p,d(ω) determine, respectively, the “normal” self-energy and the “pairing” self-energy. ω is the frequency of fluctuations scattering the fermions whose momentum is near the Fermi-surface and makes an angle θ to a chosen axis. We present a quantitative analysis of the high-resolution laser based Angle Resolved Photoemission Spectroscopy (ARPES) data on a slightly under doped cuprate compound Bi2212 and use the Eliashberg equations to deduce the ω and θ dependence of (α²F)_n(ω, θ) for T just above T_c and below T_c. Besides its detailed ω dependence, we find the remarkable result that this function is nearly independent of θ between the (π; π)-direction and 25 degrees from it, except for the dependence of the cut-off energy on θ. Assuming that the same fluctuations determine both the normal and the pairing self-energy, we ask what theories give the function (α²F)_p,d(ω) required for the d-wave pairing instability at high temperatures as well as the deduced (α²F)_n(θ, ω). We show that the deduced (α²F)_n(θ, ω) can only be obtained from antiferromagnetic (AFM) fluctuations if their correlation length is smaller than a lattice constant. Using (α²F)_p,d(ω) consistent with such a correlation length and the symmetry of matrix-elements scattering fermions by AFM fluctuations, we calculate T_c and show that AFM fluctuations are excluded as the pairing mechanism for d-wave superconductivity in cuprates. We also consider the quantumcritical fluctuations derived microscopically as the fluctuations of the observed loop–current order discovered in the under-doped cuprates, and which lead to the marginal Fermi–liquid properties in the normal state. We show that their frequency dependence and the momentum dependence of their matrix-elements to scatter fermions are consistent with the θ and ω dependence of the deduced (α²F)_n(ω, θ). The pairing kernel (α²F)_p,d(ω) calculated using the experimental values in the Eliashberg equation gives d-wave instability at T_c comparable to the experiments.     

Superconductivity mechanism of Ba1−xKxBiO3

Based on the singly occupied a_iσ picture and the mechanism of charge fluctuation, the effective Hamiltonian of the two-band Hubbard model is derived by using the degeneracy perturbation theory for the noncuprate compound Ba_1−xK_xBiO₃. By considering the next-neighbour pairing of two opposite spin holes in coordinate space, the Green's function equation of motion and the superconductivity equation are obtained. Furthermore, how the superexchange interaction and the hopping energy affect the next-neighbour pairing has been reasonably explained, and the superconductivity window is due to the Cooper pairing in coordinate space.     

The case for dx − y pairing in the cuprate superconductors

The nature of the orbital structure of the pairs in the superconducting phase of the high-temperature superconducting cuprates remains one of the central questions in this field. Here we examine the possibility that the superconducting state of these materials is characterized by d_{x² − y²} pairing. We begin by looking theoretically at why this type of pairing might be favored in a strongly correlated system with a short-range Coulomb interaction. Then we turn to the experimental question of how one would know if d_{x² − y²} pairing were present.     

New gap equation for strongly correlated metals

Assuming a phenomenological self-energy ImΣ(ω)|ω|^β, (β=1), which becomes gapped below T_c, we derived a new gap equation. The new gap equation contains the effect of the kinetic energy gain upon developing a superconducting order parameter. However, this new kinetic energy gain mechanism works only for a repulsive pairing potential leading to a s-wave state. In this case, compared to the usual potential energy gain in the superconducting state as in the BCS gap equation, the kinetic energy gain is more effective to easily achieve a high critical temperature T_c, since it is naturally Fermi energy scale. In view of the experimental evidences of a d-wave pairing state in the hole-doped copper-oxide high-T_c superconductors, we discuss the implications of our results.     

Josephson current in an irradiated Weyl semimetal junction

The influence of the off-resonant circularly polarized light on the Josephson current in the time-reversal broken superconducting Weyl semimetal junctions is investigated by using the Bogoliubov–de Gennes equation and the transfer matrix approach. Both the zero momentum BCS pairing states and the finite momentum Fulde–Ferrell–Larkin–Ovchinnikov(FFLO) pairing states are considered for the Weyl superconductors. When a circularly polarized light is applied, it is shown that the current phase relation remains unchanged for the BCS pairing with the increasing of incident radiation intensity A_0. For FFLO pairing, the Josephson current exhibits the 0–π transition and periodic oscillation as a function of A_0. The dependence of free energy and critical current on A_0 are also investigated.     

Comparison of band structure and superconductivity in FeSe_(0.5)Te_(0.5) and FeS

The isovalent iron chalcogenides,FeSe_(0.5)Te_(0.5) and FeS,share similar lattice structures but behave very differently in superconducting properties.We study the underlying mechanism theoretically.By first principle calculations and tightbinding fitting,we find the spectral weight of the d_(X~2-Y~2) orbital changes remarkably in these compounds.While there are both electron and hole pockets in FeSe_(0.5)Te_(0.5) and Fe S,a small hole pocket with a mainly d_(X~2-Y~2) character is absent in FeS.We find the spectral weights of d_(X~2-Y~2) orbital change remarkably,which contribute to electron and hole pockets in FeSe_(0.5)Te_(0.5) but only to electron pockets in FeS.We then perform random-phase-approximation and unbiased singular-mode functional renormalization group calculations to investigate possible superconducting instabilities that may be triggered by electron-electron interactions on top of such bare band structures.For FeSe_(0.5)Te_(0.5) ,we find a fully gapped s~±-wave pairing that can be associated with spin fluctuations connecting electron and hole pockets.For Fe S,however,a nodal dxy(or d_(x~2-y~2) in an unfolded Broullin zone)is favorable and can be related to spin fluctuations connecting the electron pockets around the corner of the Brillouin zone.Apart from the difference in chacogenide elements,we propose the main source of the difference is from the d_(X~2-Y~2) orbital,which tunes the Fermi surface nesting vector and then influences the dominant pairing symmetry.     

Superconductivity in Bilayer Cuprates

We calculate the stability of d_x²-y² wave superconducting state in bilayer cuprates within the antiferromagnetic and van Hove scenario. We find an increment ~10 K of T_c^max with the growth from one plane to a bilayer when the hole pairing induced by the spin-wave exchange is included.