Superconducting Bands Stabilizing Superconductivity in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7</Subscript> and MgB<Subscript>2</Subscript>

It is shown that the ceramic superconductor YBa₂Cu₃O₇ as well as the superconducting intermetallic compound MgB₂ possesses a narrow, partly filled “superconducting band” with Wannier functions of special symmetry in their band structures. This result corroborates previous observations about the band structures of numerous superconductors and non-superconductors showing that evidently superconductivity is always connected with such superconducting bands. These findings are interpreted in the framework of a nonadiabatic extension of the Heisenberg model. Within this new group-theoretical model of correlated systems, Cooper pairs are stabilized by a nonadiabatic mechanism of constraining forces effective in narrow superconducting bands. The formation of Cooper pairs in a superconducting band is mediated by the energetically lowest boson excitations in the considered material that carry the crystal-spin angular momentum 1⋅ℏ. These crystal-spin-1 bosons are proposed to determine whether the material is a conventional low-T _c or a high-T _c superconductor. This interpretation provides the electron–phonon mechanism that enters the BCS theory in conventional superconductors.     

Modified BCS Mechanism of Cooper Pair Formation in Narrow Energy Bands of Special Symmetry I. Band Structure of Niobium

The superconductor niobium possesses a narrow, roughly half-filled energy band with Bloch functions, which can be unitarily transformed into optimally localized spin-dependent Wannier functions belonging to a double-valued representation of the space group O ⁹ _h of Nb. The special symmetry of this superconducting band can be interpreted within a nonadiabatic extension of the Heisenberg model of magnetism. While the original Heisenberg model assumes that there is exactly one electron at each atom, the nonadiabatic model postulates that the Coulomb repulsion energy in narrow, partly filled energy bands is minimum when the balance between the bandlike and atomiclike behavior is shifted as far as possible toward the atomiclike behavior. Within this nonadiabatic Heisenberg model, the electrons of the superconducting band form Cooper pairs at zero temperature. Just as in the BCS theory of superconductivity, this formation of Cooper pairs is mediated by phonons. However, there is an important difference: within the nonadiabatic Heisenberg model, the electrons in a narrow superconducting band are constrained to form Cooper pairs because the conservation of spin angular momentum would be violated in any normal conducting state. There is great evidence that these constraining forces are responsible for superconducting eigenstates. This means that an attractive electron–electron interaction alone is not able to produce stable Cooper pairs. In addition, the constraining forces established within the nonadiabatic Heisenberg model must exist in a superconductor.     

Anisotropic superconductivity in the Emery model

We have investigated anisotropic superconductivity originating from intersite pairing between holes in nearest and next nearest neighboring sites in the Emery model. Strong local Coulomb correlations among holes in copper orbitals have been taken into account within the Hubbard I approximation scheme. The superconducting transition temperature has been evaluated as a function of the hole concentration. It has been shown that with the onset of superconductivity, pairing among oxygen-like quasiparticles in the mixeds-wave+d-wave channel plays the dominating role, being replaced by pairing in the extendeds-wave channel for higher concentration of holes. Superconducting correlations are mostly effective for a rather narrow range of the model parameter values, close to values derived from band structure calculations. Therefore, the coupling betweens-wave andd-wave channels seems to be a general feature of superconductivity in CuO₂ planes.     

Superconductivity in Itinerant Ferromagnetic Systems

We studied the possible superconducting state in an electronic itinerant ferromagnetic system characterized by a density of states that presents a moderately strong peak that is controlled by a specific parameter a and is positioned near the band edge. Specifically, we investigated the superconducting critical temperature, T _c , and the zero-temperature superconducting gap, ??₀. The analysis is done in a self-consistent way, the BCS mean-field equation being solved together with the electron density equation to trace possible changes in the system??s chemical potential due to the strong correlations between the component electrons. We discussed the density dependence of the superconducting critical temperature and zero-temperature superconducting gap for various values of the control parameter a and of the electron?Celectron attractive interaction. In the zero temperature limit we derive the system??s phase diagram and discuss the possible fermionic and bosonic regimes of the diagram as function of the strength of the attractive interaction.     

Superconducting Phase Diagram of Rh17S15

We report on measurements of the magnetization up to 7 T, of the specific heat and electrical resistivity in fields up to 14 T, and of the magnetic susceptibility in fields up to 20 T of a polycrystalline sample of Rh₁₇S₁₅. Our data allow us to complement the superconducting phase diagram. The existence of narrow 4d-band states (and thus of strong electronic correlations that seem not to provide magnetic correlations) is supported by the moderately high electronic contribution to the specific heat of about 107 mJ/molK², favoring the existence of a strong superconducting interaction. This fact, and the remarkably high upper critical field (exceeding the simple Pauli limit by a factor of two), give evidence of the uncommon nature of the superconductivity in Rh₁₇S₁₅.     

Modified BCS Mechanism of Cooper Pair Formation in Narrow Energy Bands of Special Symmetry II. Matthias Rule Reconsidered

In part I of this paper a modified BCS mechanism of Cooper pair formation of electrons was proposed. This mechanism is connected with the existence of a narrow, roughly half-filled superconducting energy band of given symmetry. The special symmetry of the superconducting band was interpreted within a nonadiabatic extension of the Heisenberg model of magnetism. Within this nonadiabatic Heisenberg model, the electrons of the superconducting band are constrained to form Cooper pairs at zero temperature because in any normal conducting state the conservation of crystal-spin angular momentum would be violated. Except for this participation of the angular momentum, the pair formation is mediated in the familiar way by phonons. Superconducting bands can be identified even within a free-electron band structure. Therefore, in this paper the band structures of the bcc and hcp solid solution alloys composed of transition elements are approximated by appropriate free-electron band structures with s–d symmetry. From the free-electron bands, the number n of valence electrons per atom related to the maxima of the superconducting transition temperature T _c in these solid solutions is calculated within the nonadiabatic Heisenberg model. The two observed maxima of T _c are reproduced without any adjustable parameter at valence numbers n approximately equal to 4.9 and 6.5 in bcc and 4.7 and 6.7 in hcp solid solutions. This result is in good agreement with the measured values of 4.7 and 6.4 of Hulm and Blaugher. The upper maximum is predicted not to exist in bcc transition elements but to occur in several ordered structures of bcc solid solution alloys.     

An Effective Interaction Approach to Anisotropic Superconductors Beyond the Weak Coupling Theory—An Origin of the d-wave Symmetry in High-T c Cuprate

We propose an effective interaction approach to superconducting systems which is adapted to periodic systems and intermediate net coupling between charge carriers by phonon mediated and Coulomb repulsive interactions. A coupling function of effective interaction is given for homogeneous field beyond the weak coupling approximation by using a generalized intermediate coupling method. Adequate kernel for the periodic systems is also reduced to that coupling function in homogeneous field and the Fourier coefficients relevant to the Bloch function. Within the present approach we discuss the symmetry of the superconducting gap in cuprate under the assumption that a nonbonding band filled by 2p_σ electrons exists in an undoped system and that doped holes occupy orbitals in this band. Those orbitals are represented by linear combinations of p _x and p _y functions. It is argued, in the tetragonal limit, that the symmetry of the gap function is d-wave-like on account of the products of orbital functions in combination of singlet spin-pair in the kernel.     

Effect of interlayer interaction in high-Tc cuprate superconductors

We have studied the role of interlayer attractive interaction in a high-T _c system having two layers per unit cell. The single band two-layer tight binding model Hamiltonian is considered and the double time Green's function technique is applied within the mean field approximation. The expressions for the hole density, transition temperature, and intra- and interlayer order parameters are obtained which are found to be dependent on the interlayer interaction and other parameters appearing in the Hamiltonian. The numerical analysis shows that the coupling of the charge carriers (holes) between the layers provides better conditions for the stabilization of long-range order and high superconducting transition temperature in layered superconductors. It is also observed that superconductivity is confined to a narrow region of hole concentration and the single particle tunneling suppresses the transition temperature.     

Polarons and strong electron-phonon coupling in the optical response of La{2-x}SrxCuO4SrxCuO4

A multiliquid approach, based on free carriers with strong electron-phonon interaction, localized polaronic states near 0.15 eV, and a mid-infrared band at 0.5 eV, is applied to model the optical response of La_{2-x}Sr_xCuO₄. The normal state reflectance and absorbance of La_1.83Sr_0.17CuO₄ are investigated and their temperature dependence is explained. Both the ac and dc response are recovered, and the quasilinear behavior of the optical scattering rate up to 3000–4000 cm^-1 is found to be consistent with strong electron-phonon interaction, which also accounts for the value ofT _c . In the superconducting state a comparison with optical data indicates the presence of additional carriers in the conduction band. Model calculations suggest the 0.5 eV mid-infrared band as the source of these carriers and indicate a bipolaronic origin of this band.     

Quasiparticle spectrum in copper oxides

The results of electronic structure calculations of the CuO₂ layer, performed by the generalized tight-binding method, are presented. The strong electron correlations on both the Cu and O ions are included explicitly. The resulting quasiparticle band structure contains an insulator gap for undoped compounds like La₂CuO₄. The valence band consists of a large number of narrow Hubbard quasiparticle bands. The dispersion law of quasiparticles at the top of the valence band has a minimum at the point, indicating the existence of the multivalley Fermi surface in the doped La_2-x Sr _x CuO₄. The origin of the Fermi liquid behavior in the narrow quasiparticle bands is discussed.     

Coupling to Phonons in the Migdal–Eliashberg Approach

The relevance of the strong correlations in the high critical temperature superconductors (HTSC) is well experimentally documented. However, if the properties of the normal and superconducting state in HTSC oxides are interpreted in terms of the standard Eliashberg theory, which holds in low temperature superconductor systems, the Migdal–Eliashberg approach implies serious limitations in the reproduction of experimental spectroscopies whose contributions are inter-band and not intra-band. Recent angle-resolved photoemission spectroscopy (ARPES) measurements on HTSC oxides whose contributions are intra-band show a kink in the quasiparticle spectrum at characteristic phonon frequencies in the normal and superconducting state. In contrast with our theoretical discussion, we include our theoretical results for the renormalized energy E _k as a function of the bare band energy ε _k obtained from ARPES in a Pb sample and in a Bi₂Sr₂CaCu₂O_8+δ optimally doped sample (Bi2212). This is clear evidence that electron-phonon is strong and involved in pairing.      

Superconductivity in Hydrogen-rich Material: GeH<Subscript>4</Subscript>

The electronic properties, lattice dynamics, and electron–phonon coupling of the Cmmm phase of GeH₄ have been studied by first-principle calculations using density functional perturbation theory. The electronic band structure shows the Cmmm phase metallic nature. It is found strong electron phonon interaction, and the superconducting critical temperature, predicted by Allen–Dynes modified McMillan equation, is about 40 K at 20 GPa.     

Electronic and Phonon Contributions to the Pairing in the Cuprates

Thermal Difference Reflectance (TDR) Spectroscopy has been used to determinethe superconducting gap parameter for several of the superconducting cupratesover a wide range of energies, extending from the infrared (0.3 eV)to the ultraviolet (5.3 eV). A contribution to the pairing is found in eachcase from the phonons, and from an electronic excitation with energy thatranges from 1.6 eV and 2.3 eV for the different compounds attributed to thed ⁹–d ¹⁰ L charge-transfer excitation between Cu and O. In every case thereflectance ratio between the superconducting and normal state, Rs/Rnplotted as a function of photon energy can be well described using theEliashberg theory. The theory also predicted a characteristic shape for thelow energy part of such spectra due to the phonons. We report theobservation of this feature in measurements on films of Tl₂Ba₂CaCu₂O₈. Wediscuss the significance of the success of the Eliashberg theory inexplaining these results and successfully predicting new effects in thelight of the correlations that had been thought to invalidate such atheoretical approach.     

Influence of La and Gd Impurities on the Two Phase Transitions in U0.97Th0.03Be13

The phase diagram of U _1–x Th _x Be ₁₃ exhibits two irregular points at x _C1=1.9 at.% and x _C2=4.55 at.% which mark the endpoints of the concentration range where two phase transitions in specific heat measurements are observed. While it is clear that the upper one belongs to a superconducting phase transition, there are different interpretations for the lower one. It has been suggested that the lower transition involves magnetic correlations which coexist with a single superconducting state or that the lower transition separates two different superconducting states (one or both are probably non-s-wave like). In this scenario the onset of local magnetic order is discussed as being due to an accompanied antiferromagnetic transition or as a product of broken time reversal symmetry. To get more information about the nature of the two superconducting phases, substitution experiments with non-magnetic La and magnetic Gd on the U sites in U _0.97 Th _0.03 Be ₁₃ were performed. From specific heat measurements we argue that the upper transition behaves with La/Gd doping like a conventional s-wave superconductor, whereas the lower transition cannot be brought in line with common pictures of superconducting transitions. Also at the     

Superconducting and non-superconducting PrBa2Cu3O7

Superconducting properties of Pr123 and microscopic structural differences between the superconducting and non-superconducting Pr123 crystals are reviewed. It is shown that the variety of physical properties of Pr123 is closely related to Cu deficiency at the chain site and our experimental results are consistently explained with a model that the Pr 4f-O 2p hybridization forms a narrow band and carriers are localized by a kind of atomic disorder in non-superconducting crystals.     

Anisotropic Upper Critical Field in Single Crystal MgB2

Recent experiments on MgB₂ single crystals appear to indicate that superconductivity in this material is described not only by two superconducting order parameters attached to the band and the band, respectively, but also these two order parameters have different anisotropy. More explicitly the anisotropy of H _c2(t) requires an oblate order parameter in momentum space attached to the a band while H _c1(t) is described by a prolate order parameter, attached to the band. Therefore the vortex state in MgB₂ should be described by an interplay of these two superconducting order parameters.     

c-axis phonons and the enhancement of pairing correlations in high-temperature superconductors

We consider the two-dimensional Hubbard model including electron-phonon interaction. Strong local correlations (U limit) are taken into account within the mean-field approximation for auxiliary boson fields. Phonon-assisted transitions between intraand interlayer states are introduced as the source of coupling between two-dimensional CuO₂ layers. This type of processes effectively leads to the nonlinear (quadratic) interaction of intralayer electrons withc-axis phonons. We construct the Eliashberg equations for the resulting Hamiltonian and evaluate the superconducting transition temperatureT _c. Our model calculation demonstrates that a pronounced enhancement ofT _c in thed-wave channel is possible. The largest enhancement ofT _c tends to take place for small hole concentrations. This means that the coupling toc-axis phonons could compete with two-dimensional correlations responsible for the onset of antiferromagnetic order. It is remarkable that the two-dimensional features in the normal state are hardly affected by this specific interlayer interaction. Therefore,c-axis two-phonon-mediated interlayer coupling can cooperate with interlayer pair tunneling and substantially contribute to an increased pairing.     

Periodic Oscillations of Josephson-Vortex Flow Voltage in Stacked Intrinsic Josephson Junctions

Using the coupled sine-Gordon equations, we study the magnetic oscillation behavior of the Josephson-vortex flow voltage (JVFV) in stacked intrinsic Josephson junctions (IJJs). It is found that the periodic oscillations of the JVFV with the magnetic field are determined by the lattice structure. In narrow IJJs with a high density of vortices, the boundary interaction is favorable for forming a rectangular lattice structure and inducing H ₀ oscillations. The oscillation period is equal to the magnitude of the field needed to add one vortex quantum per one intrinsic Josephson junction. In wide IJJs, the shearing inter-layered interaction is favorable for forming a triangular lattice structure and inducing H ₀/2 oscillations. In this case, with increasing magnetic field, a transformation from the triangular (with period H ₀/2) to rectangular (with period H ₀) configurations is also obtained in a long lateral size. Besides, from the magnetic oscillation characteristics of the JVFV in wide IJJs, the oscillating inversions have also been obtained.     

Superconductivity in the cuprates as a consequence of antiferromagnetism and a large hole density of states

We briefly review a theory for the cuprates that has been recently proposed based on the movement and interaction of holes in antiferromagnetic (AF) backgrounds. A robust peak in the hole density of states (DOS) is crucial to produce a large critical temperature once a source of hole attraction is identified. The predictions of this scenario are compared with experiments. The stability of the calculations after modifying some of the original assumptions is addressed. We find that if the dispersion is changed from an antiferromagnetic band at half-filling to a tight-binding cosk _x+cosk _y narrow band at n=0.87, the main conclusions of the approach remain basically the same i.e., superconductivity appears in the -channel andT _c is enhanced by a large DOS. The main features distinguishing these ideas from more standard theories based on antiferromagnetic correlations are here discussed.