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.     

On the Possibility of s+d Wave Superconductivity Within a Two-Band Scenario for High T c Cuprates

A variety of different experimental results show substantial evidence that the order parameter in high-temperature superconducting copper oxides is not of pure d-wave symmetry, but that an s-wave component exists, which especially shows up in experiments that test the c-axis properties. These findings are modeled theoretically within a two-band model with interband interactions, where the superconducting order parameters in the two bands are allowed to differ in symmetry. It is found that the coupling of order parameters with different symmetries (s+d) leads to substantial enhancements of the superconducting transition temperature T _c as compared to order parameters with only s-wave symmetry. An additional enhancement factor of T _c is obtained from the coupling of the bands to the lattice where moderate couplings favor superconductivity while too strong couplings lead to electron (hole) localization and consequently suppress superconductivity.     

Effect of interlayer interaction in high-T c 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.     

Anisotropic uniaxial pressure effects in YBa2Cu3O7−δ

We present measurements of the uniaxial pressure dependence ofT _c of untwinned YBa₂Cu₃O_7?δ crystals with various oxygen stoichiometries. For all samples investigated,T _c decreases for pressure alonga, increases for pressure alongb, and, in oxygen deficient samples, increases strongly for pressure alongc. These results are compared to the behavior found in the La_2?x Sr _x CuO₄ and YBa₂Cu₄O₈ systems. Neither the model of pressure-induced charge transfer nor coupling to orthorhombic distortions can explain all the data. However, the presence of singularities in the electronic density of states close to the Fermi energy is a possible origin of the observed behavior. Our preliminary data on the pressure dependence of thec-axis and in-plane resistivities in twinned crystals are consistent with this view.     

Superconducting behavior of high-T c YBa2Cu3O7 thin films with BaO impurity produced by pulsed laser deposition

We have investigated the superconducting behavior of high-T _c YBa₂Cu₃O₇ (YBCO) thin films containing BaO impure phase produced by pulsed laser deposition. The thin films were characterized by the standard four-probe method, X-ray diffraction (XRD), and scanning electron microscopy (SEM). XRD showed that all these thin films contained BaO impurity, with thec-axis normal to the surface of the substrates. The presence of impurity existed from substrate temperatureT _s of 727 to 796°C. When these thin films with BaO impurity were measured under the magnetic fields, it was found that the critical current densityJ _c increased slightly with increase in magnetic fieldB within the range ofB≤500 G, in the case ofB perpendicular to thec-axis of the film.     

Influence of Electron–Phonon Interaction on Superconducting State Parameters of MgB2

A three-square well model is employed for the three interactions namely, electron–acoustic phonon, electron–optical phonon, and Coulomb in the calculation of superconducting transition temperature (T _c) for layered structure MgB₂. The analytical solutions for the energy gap equation allow us to understand the relative interplay of these interactions. The values of the coupling strength and of the Coulomb interaction parameter indicate that the test material is in the intermediate coupling regime. The superconducting transition temperature of MgB₂ is estimated as 41 K for λ_ac ≈ 0.3, λ_op ≈ 0.1, and μ* ≈ 0.07. We suggest from these results that both the acoustic and optical phonons within the framework of a three-square well scheme consistently explains the effective electron–electron interaction leading to superconductivity in layered structure MgB₂.     

Co-doping effects of Ca and Ce on the Superconducting Properties in Y1?x Ca x (Ba1?y Ce y )2Cu3O7?δ

A series of Y_1?x Ca _x (Ba_1?y Ce _y )₂Cu₃O_7??? (0??x??0.3, 0??y??0.3) polycrystalline superconductor samples were prepared using the solid-state reaction technique. The phase identification, crystal structure, and superconducting transition temperature (T _c ) were studied by means of X-ray diffraction (XRD) and resistivity measurements. The results indicted that the phase of samples changed from orthorhombic phase to tetragonal phase with increasing Ca concentration x and Ce concentration?y, and Ce did not form the superconducting structure. The lattice constants had a little change. The a-axis and c-axis lattice parameters increased. The b-axis lattice parameter decreased. The T _c and resistance had an obvious dropping tendency with increasing Ca and Ce concentrations. The transition width became sharper with the increase of x (=y). We drew a conclusion that the Ce-doping had an effect for strengthening the intergrain connectivity, and it counteracted the weakening effect of Ca-doping which introduced the hole causing a reduction in the interlayer coupling strength.     

Anisotropic superconductivity in the two-dimensional Hubbard model

We address the problem of anisotropic superconductivity in the two-dimensional Hubbard model. The Eliashberg equations have been generalized to the case which accounts for the anisotropy of the order parameter. Strong local correlations are treated within the mean field slave boson approximation. The superconducting transition temperatureT _c is evaluated as a function of the occupation number. Our results indicate that thed-wave state is the most likely channel for superconductivity for small concentration of holes. We have also derived an approximate analytical formula forT _c valid for any value of the occupation number. In addition, the influence of strong correlations on the electron-phonon coupling function is also discussed.     

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.     

Theory of superconductivity. 3. 2D conduction bands for high Tc. Bose-Einstein condensation transition of the third order

A general theory of superconductivity is developed, starting with a BCS Hamiltonian in which the interaction strengths (V ₁₁,V ₂₂,V ₁₂) among and between “electron” (1) and “hole” (2) Cooper pairs are differentiated, and identifying “electrons” (“holes”) with positive (negative) masses as those Bloch electrons moving on the empty (filled) side of the Fermi surface. The supercondensate is shown to be composed of equal numbers of “electron” and “hole” ground (zero-momentum) Cooper pairs with charges ±2e and different masses. This picture of a neutral supercondensate naturally explains the London rigidity and the meta-stability of the supercurrent ring. It is proposed that for a compound conductor the supercondensate is formed between “electron” and “hole” Fermi energy sheets with the aid of optical phonons having momenta greater than the minimum distance (momentum) between the two sheets. The proposed model can account for the relatively short coherence lengthsξ observed for the compound superconductors including intermetallic compound, organic, and cuprous superconductors. In particular, the model can explain why these compounds are type II superconductors in contrast with type I elemental superconductors whose condensate is mediated by acoustic phonons. A cuprous superconductor has 2D conduction bands due to its layered perovskite lattice structure. Excited (nonzero momentum) Cooper pairs (bound by the exchange of optical phonons) aboveT _c are shown to move like free bosons with the energy-momentum relation?=1/2v_Fq. They undergo a Bose-Einstein condensation atT _c = 0.977?v _F k _b ^?1 n ^1/2, wheren is the number density of the Cooper pairs. The relatively high value ofT _c (～100 K) arises from the fact that the densityn is high:n ^1/2～ξ^?1 ～10⁷ cm^?1. The phase transition is of the third order, and the heat capacity has a reversed lambda (λ)-like peak atT _c .     

High-pressure dc sputtering of High-T c BPSCCO thin films withT c(0) above 100 K

High-T _c Bi(Pb)-Sr-Ca-Cu-O thin films have been made on single-crystal MgO substrates using high-pressure dc sputtering technique. X-ray studies confirm the crystallinity and highly oriented structure withc-axis perpendicular to the substrate. By optimizing the annealing schedule the formation of the high-T _c phase is stabilized. The best film exhibited superconducting transition temperature with zero-resistance temperature,T _c(0), as high as 101 K. Temperature dependence ofJ _c indicates the presence of Josephson-type weak links.     

Pressure Dependence of T<Emphasis Type="Italic">c</Emphasis> in High Temperature Superconductors: Role of Interlayer Interactions

We have studied the role of interlayer interactions (W) in the pressure dependence of T _c of layered superconductors. The expressions for dT _c /dP are obtained by including the effects of layered structure within the framework of two different proposed models, namely the negative-U Hubbard model and the Hirsch model. We observe that the inclusion of interlayer interaction provides better explanation of pressure dependence of T _c . Our numerical results show that the systems having one CuO₂ layer per unit cell may be well described by small values of W while the larger values of W accounts for the systems having two or more superconducting layers in a unit cell. The calculated values of dT _c /dP vs. W are found to be in good agreement with those of experimental results obtained for various high T _c superconductors of cuprate family.     

On the Possibility of s+d Wave Superconductivity Within a Two-Band Scenario for High Tc Cuprates

A variety of different experimental results show substantial evidence that the order parameter in high-temperature superconducting copper oxides is not of pure d-wave symmetry, but that an s-wave component exists, which especially shows up in experiments that test the c-axis properties. These findings are modeled theoretically within a two-band model with interband interactions, where the superconducting order parameters in the two bands are allowed to differ in symmetry. It is found that the coupling of order parameters with different symmetries (s+d) leads to substantial enhancements of the superconducting transition temperature T _c as compared to order parameters with only s-wave symmetry. An additional enhancement factor of T _c is obtained from the coupling of the bands to the lattice where moderate couplings favor superconductivity while too strong couplings lead to electron (hole) localization and consequently suppress superconductivity.     

Toward 2D Magnets in the (MnBi2Te4)(Bi2Te3)n Bulk Crystal

2D magnets and their engineered magnetic heterostructures are intriguing materials for both fundamental physics and application prospects. On the basis of the recently discovered intrinsic magnetic topological insulators (MnBi₂Te₄)(Bi₂Te₃)_n, here, a new type of magnet, in which the magnetic layers are separated by a large number of non-magnetic layers and become magnetically independent, is proposed. This magnet is named as a single-layer magnet, regarding the vanishing interlayer exchange coupling. Theoretical calculations and magnetization measurements indicate that, the decoupling of the magnetic layers starts to emerge from n = 2 and 3, as revealed by a unique slow-relaxation behavior below a ferromagnetic-type transition at T_c = 12–14 K. Magnetization data analysis shows that the proposed new magnetic states have a strong uniaxial anisotropy along the c-axis, forming an Ising-type magnetic structure, where T_c is the ordering temperature for each magnetic layer. The characteristic slow relaxation, which exists only along the c-axis but is absent along the ab plane, can be ascribed to interlayer coherent spin rotation and/or intralayer domain wall movement. The present results will stimulate further theoretical and experimental investigations for the prototypical magnetic structures, and their combination with the topological surface states may lead to exotic physical properties.     

Superconductivity and electrical resistivity in alkali metal doped fullerides: Phonon mechanism

We consider a two- peak model for the phonon density of states to investigate the nature of electron pairing mechanism for superconducting state in fullerides. We first study the intercage interactions between the adjacent C₆₀ cages and expansion of lattice due to the intercalation of alkali atoms based on the spring model to estimate phonon frequencies from the dynamical matrix for the intermolecular alkali- C₆₀ phonons. Electronic parameter as repulsive parameter and the attractive coupling strength are obtained within the random phase approximation. Transition temperature,T _c, is obtained in a situation when the free electrons in lowest molecular orbital are coupled with alkali-C₆₀ phonons as 5 K, which is much lower as compared to reportedT _c (≈ 20 K). The superconducting pairing is mainly driven by the high frequency intramolecular phonons and their effects enhance it to 22 K. To illustrate the usefulness of the above approach, the carbon isotope exponent and the pressure effect are also estimated. Temperature dependence of electrical resistivity is then analysed within the same model phonon spectrum. It is inferred from the two- peak model for phonon density of states that high frequency intramolecular phonon modes play a major role in pairing mechanism with possibly some contribution from alkali-C₆₀ phonon to describe most of the superconducting and normal state properties of doped fullerides.     

Theoretical aspects of charge correlations in θ-(BEDT-TTF)2X

A review is given on the theoretical studies of charge correlations in θ-(BEDT-TTF)₂X. Various studies show that within a purely electronic model on the θ-type lattice with on-site U and nearest neighbor V_p and V_c interactions, the diagonal stripe, c-axis three-fold, and the vertical stripe charge correlations are favored in the regime V_p<V_c, V_p∼V_c, and V_p>V_c, respectively. In the realistic parameter regime of V_p∼V_c, there is competition between the c-axis three fold state and diagonal stripe state. Since these are different from the experimentally observed a-axis three fold and the horizontal stripe charge correlations, additional effects have to be included in order to understand the experiments. The electron–lattice coupling, which tends to distort the lattice into the θ_d-type, is found to favor the horizontal stripe state, suggesting that the occurrence of this stripe ordering in the actual materials may not be of purely electronic origin. On the other hand, distant electron–electron interactions have to be considered in order to understand the a-axis three fold correlation, whose wave vector is close to the nesting vector of the Fermi surface. These studies seem to suggest that the minimal model to understand the charge correlation in θ-(BEDT-TTF)₂X may be more complicated than expected. Future problems regarding the competition between different types of charge correlations are discussed.     

Effect of Biexciton on Cooper Pairing in High Tc Superconductors

In this paper, we have modified the Cooper theory by considering a biexcitonic attractive interaction for high T _c superconductors. We have developed an expression for (2Δ/K _B T _c) as a function of phonon and biexciton mediated coupling constants. For the sake of simplicity, we use a two-square-well potential model (electron–phonon and electron–biexciton). The calculated values of (2Δ/K _B T _c) show good agreement with experimental values.     

Synthesis and Para-conductivity Analyses of TlBa2(Ca 3 − y Mg y )Cu4 O 1 2 − δ Superconductors

TlBa ₂(Ca _3?yMg _y)Cu ₄ O _12?δ (y=0,0.5,1.0, 1.5,2) superconductors are synthesized at normal pressure, and the influence of doped Mg atoms on the superconductivity parameters at the microscopic level is investigated by carrying out para-conductivity analyses of conductivity data. The samples have shown tetragonal structure, and the unit cell volume decreases with increased Mg doping. The onset temperature of superconductivity [ T _c(onset)] and zero resistivity critical temperature [ T _c(R=0)] decreases with Mg. Maximum magnitude of diamagnetism is observed in the samples with Mg of y=2. The apical oxygen mode of the type Tl-O _A-Cu(2) and CuO ₂ planar oxygen modes are softened as observed in fourier transform infrared spectrometer (FTIR) absorption measurements. The fluctuation-induced conductivity (FIC) analyses of conductivity data have shown the enhancement of inter-plane coupling and coherence length along the c-axis. These analyses have shown an increase in the coherence length along the c-axis and the inter-layer coupling J. The enhancement of inter-plane may possibly be arising due to a small decrease in the value of the order parameter of the carriers from ∣ψ∣ ²=1 in the CuO ₂ planes in Mg-doped samples. The values of B _c0(T), B _c1(T), J _c(0) are suppressed with the increased incorporation of Mg, which most likely arises due to the weak coupling of the grains induced by Mg doping.     

Non-k-Diagonality in the Interlayer Pair-Tunneling Model of High-Temperature Superconductivity

We investigate the effect of k-space broadening of the interlayer pairing kernel on the critical temperature T_c and the k-dependence of the gap function in a one-dimensional version of the interlayer pair-tunneling model of high-T_c superconductivity. We consider constant as well as k-dependent intralayer pairing kernels. We find that the sensitivity to k-space broadening is larger the smaller the width of the peak of the Fermi-level gap calculated for zero broadening. This width increases with the overall magnitude of the interlayer tunneling matrix element, and decreases with the bandwidth of the single-electron intralayer excitation spectrum. The width also increases as the Fermi level is moved towards regions where the excitation spectrum flattens out. We argue that our qualitative conclusions are valid also for a two-dimensional model. This indicates that at or close to half-filling in two dimensions, when the Fermi-surface gap for zero broadening attains its peaks at (±/a, 0) and (0, ±/a) where the excitation spectrum is flat, these peaks should be fairly robust to moderate momentum broadening.