Origin of Superconductivity and Construction of Doping Curves for Cuprates on an Elasticity-Exchange Competition Model

Superconducting T _c is modeled over the doping range for the three prototype cuprate families (with respect to apical coordination). The model is based on a competition of elastic and exchange energies (ExEl model). Data for these energies are taken from direct observation such as T _c and the pseudo-gap T _p. An additional penalty for charge concentration in pairs is introduced for the low pair concentration region. These energies are internally calibrated. The rather different observed curve shapes and quantitative features in the doping curves of different materials can be related to the relative magnitude of T _c and T _p. Both linear and parabolic curve shapes near the T _c optimum can be explained on the ExEl model. The basis of the relevant phenomenology is indicated in bond ordering effects, for which new concepts, e.g. for resonating pair kernels, are developed. Accordingly, stripes of single holes are dimerized into pair strands through super-exchange. Conclusions are drawn about the limits of phenomenology for cuprates and other high T _c materials.     

Superconductivity in a Binary Boson-Fermion Mixture with Weak Interaction

A concept describing the origin of the pseudogap phase of high-T _c superconducting cuprates is discussed. Based on the idea about electron-composite boson mixture, existing below some value T _p in cuprates, first, an analytical expression for T _p is obtained. It is shown that T _p depends on interaction parameter responsible for two electron-composite boson transformation, as well on the boson formation energy. Second, the composite boson condensation temperature T _c, determined as a one below which the density of condensed bosons just ceases to be zero, is found. The reason why the behaviors of T _p and T _c in dependence on the interaction parameter may be so different is addressed.     

Role of Interlayer and Intersite Interactions in Superconducting State in High-Tc Layered Cuprates

We studied the role of interlayer and intersite interactions on transition temperature and specific heat of layered high-T _c cuprates. We used double-time Green's function technique in the spirit of mean field approximation in order to obtain the expressions for hole density, transition temperature, and specific heat. These expressions are found to be dependent on the carrier concentration and intersite and interlayer interactions. The numerical analysis shows that the effect of intersite interaction on transition temperature and specific heat is qualitatively similar to that of interlayer interactions and provides favorable conditions to establish long-range order in the superconducting state.     

Evidence for Dielectric (e–h) and Superconducting (e–e) Pairing in Cuprates

It is demonstrated that anomalous behavior of cuprates can be described in a natural way by the model with partial dielectrization of conduction electron energy spectra (EES). In such a model, near the Fermi surface (FS), there are formed the fours of charged particles (FCP) rather than independent electron–hole (e–h)- and electron–electron (e–e)-pairs. Since the bonding energies are the same for Cooper (e–e)- and dielectric (e–h)-pairs, then the temperature of SC transition T _c due to the Bose-condensation of FCP can be much more than the temperature of Bose-condensation of Cooper pairs only. The dielectric (e–h)-transition is connected with structural phase transformation in the cuprate system, formation of stripe structure, etc. The model successfully describes the presence of maximum at T _c (x)-curve, T-dependence of pseudogap (PG) and SC-gap, effect of nonmagnetic impurities to T _c , STM and ARPES spectra and other properties of cuprates.     

Cuprate superconductors: Universal properties and trends; evidence for Bose-Einstein condensation?

We explore the compatibility of empirical trends in various thermodynamic properties of cuprate superconductors with the Bose-Einstein condensation scenario. These trends include the relations between transition temperature, hole concentration and condensate density, the rise and the upper limit of the transition temperature, the dependence of pressure and isotope coefficients on transition temperature, as well as the observed critical behavior, which is reminiscent of three-dimensional systems with a scalar complex order parameter and short-range interactions. For this purpose we consider an interacting charged Bose gas. Due to the high polarizability of the cuprates, the Coulomb interaction is strongly screened. For this reason, the problem of calculating thermodynamic properties becomes essentially equivalent to that of the uncharged gas with short-range interactions. This problem, however, has not been solved either. Nevertheless, in the dilute limit the problem reduces to the ideal Bose gas treated by Schafroth, while in the dense regime condensation and superfluidity are suppressed because bosons of finite extension fill the available volume. This limiting behavior provides an interpolation scheme for the dependence of both transition temperature and zero temperature superfluid density on boson density. On this basis, and relating the hole concentration in the cuprates which corresponds to the boson density and the superfluid density to the square of the inverse London penetration depth, the compatibility of the empirical trends in the cuprates with the Bose gas behavior can be verified. Our analysis reveals remarkable agreement between these trends and the corresponding Bose gas behavior. There is even strong evidence of the most striking implication of this scenario, the dependence of the transition temperature on the zero-temperature superfluid density, which resembles the outline of a fly's wing. This evidence emerges from recentSR data for Tl₂Ba₂CuO₆₊ and kinetic inductance measurements for La_2–xSr_xCuO₄ films, revealing that the penetration depths of underdoped and overdoped samples atT _c do not differ significantly. In view of this we found considerable evidence of the nature of the superconducting transition in the cuprates, without invoking any specific pairing mechanism.The authors are grateful to J. G. Bednorz, D. Baeriswyl, H. Beck, J. I. Budnick, H. Keller, K. A. Müller, Ch. Niedermeier, and J. J. Rodriguez for valuable discussions.     

Upper limit ofTc for the copper oxides

The value of the critical temperature of the cuprates correlates with the doping level and is affected by the interplay of two competing factors: (1) the increase in carrier concentration, and (2) the pair-breaking effect of magnetic impurities. An analysis of the temperature dependence of the critical field leads to the conclusion that magnetic impurities are present even in a sample with the maximum observed value ofT _c.A new parameter, intrinsicT _c (T _cintr), which is its value in the absence of magnetic impurities, is introduced. The maximum value ofT _cintr, which corresponds to the maximum doping level, appears to be similar for different cuprates and to be equal to 160–170 K. This is the upper limit ofT _c in the cuprates.     

Absence of a Competition Between Magnetism and Superconductivity in Layered Nickel Borocarbides: Common Correlations of Tc with Crystal Chemical Parameters for Magnetic and Nonmagnetic Compounds

In the present work, an analysis of the crystal chemical parameters of nickel borocarbides RNi₂B₂C (R = rare earth) is given. The reasons for the dependence of superconducting transition temperature (T _c) on crystal chemical parameters by two separate curves for magnetic and nonmagnetic R are considered. For all R, a common pattern of dependence of T _c on crystal chemical parameters similar to that existing in layered quasi two-dimensional systems (HTSC cuprates and diborides) is established. The absence of the influence on the T _c of borocarbides of magnetic properties R is also established. On the basis of the correlations found, the radii of a number of rare earths are more precisely defined, and T _c of compounds at various substitutions R are calculated.     

Questioning the Assumptions of the Parabolic Model for Superconductive Cuprates

The assumptions of the parabolic model are questioned. These assumptions pertain to an expectation of universal T _c optima for cuprates at an experimental hole concentration of p = 0.16n, where n is the number of CuO₂ planes. This model was developed based on the T _c maximum for La_{2 – x} Sr _x CuO₄ at x = 0.16. However, a variety of cases are presented for higher optimal hole concentrations, including La₂CuO_4.16, where it is twice as high. Also, the success of a charge order model in universally predicting optimal T _c at formal stoichiometric holes, h = 0.5n, suggests a need for expansion of the parabolic model. By quantitatively taking into account the deleterious effect of the blocking layer, optimal T _c can be absolutely calibrated at a uniform optimal charge order with alternate holes.     

Lattice Effects Across the Phase Diagram of Pnictides

We have studied by Raman spectroscopy the effect of doping, temperature, and hydrostatic pressure on selected Fe pnictides of the 1111 series. Two sets of RFeAsO_1?x F _x compounds have been examined (R=Sm and Nd) with a varying amount of doping and transition temperature. The doping dependence of the Raman active modes reveals that the rare earth phonon is correlated with the transition temperature (T _c) and not with the amount of doping. As in the case of several other pnictides, the low temperature measurements indicate phonon modifications at much higher temperatures than T _c even in the superconducting compounds. The application of hydrostatic pressure indicates a nonlinear behavior of the rare earth phonon, which increases with doping and in the superconducting compounds correlates with modifications in T _c. The results are similar with those of the cuprates, where hydrostatic pressure has induced phonon and structure modifications at characteristic pressures where the T _c dependence on pressure is also modified. All results point to some role of the lattice for superconductivity in the pnictides.     

Superconductivity and the Van Hove Scenario

We give a review of the role of the Van Hove singularities in superconductivity. Van Hove singularities (VHs) are a general feature of low-dimensional systems. They appear as divergences of the electronic density of states (DOS). Jacques Friedel and Jacques Labbé were the first to propose this scenario for the A15 compounds. In NbTi, for example, Nb chains give a quasi-1D electronic structure for the d-band, leading to a VHs. They developed this model and explained the high T _C and the many structural transformations occurring in these compounds. This model was later applied by Jacques Labbé and Julien Bok to the cuprates and developed by Jacqueline Bouvier and Julien Bok. The high T _C superconductors cuprates are quasi-bidimensional (2D) and thus lead to the existence of Van Hove singularities in the band structure. The presence of VHs near the Fermi level in the cuprates is now well established. In this context we show that many physical properties of these materials can be explained, in particular the high critical temperature T _C, the anomalous isotope effect, the superconducting gap and its anisotropy, and the marginal Fermi liquid properties, they studied these properties in the optimum and overdoped regime. These compounds present a topological transition for a critical hole doping p≈0.21 hole per CuO₂ plane.     

Copper oxycarbonates and mercury-based cuprates: Promising high-Tc superconductors

A short overview of two recently discovered series of high-T _c superconductors is given. The first one deals with copper oxycarbonates which exhibit _c 's up to 82 K. Their structural principle is based on the fact that rows of CO₃ groups can assure the connection between either octahedral or pyramidal copper layers forming new intergrowths withT _c 's superior to those of the mother structures. The second family concerns the mercury-based cuprates, characterized byT _c 's ranging from 27 to 132 K. The structure of the mercury compounds is closely related to those of the thallium cuprates TlBa₂Ca_m–1Cu _m O_2m+3 which exhibit thallium monolayers; they differ from the Tl cuprates by a high oxygen deficiency at the level of the mercury layers due to the preference of this cation for two-fold coordination.     

Pair breaking, “intrinsic”Tc, and the upper limit ofTc in the cuprates

The presence of magnetic impurities leads to a drastic decrease inT _c in the overdoped region, gaplessness, and the usual temperature dependence ofH _c2. The magnetic moments are localized on the apical oxygen site, and this allows us to explain the increase inT _c with the increase in the number of Cu-O planes in the unit cell. Applied pressure can raiseT _c above the usual value at optimum doping, toward the intrinsicT _c. The cuprates as a class of compounds have an upper limit ofT _c in the rangeT _c,upp=160–170 K.     

Non-in situ pressure effects on the superconducting characteristics and microstructure in Bi-Ca-Sr-Cu-O systems

Results on the pressure dependence of the transition temperatureT _c and the resistancetemperature behaviour of Bi₂Ca₁ Sr₂Cu₂O_x compound are presented. Both the onsetT _c and theT _c (R = O) are found to decrease with increasing pressure in the 0 to 50 kbar (1 bar = 10⁵Pa) range. Up to 20 k bar, the normal state resistivity is seen to be metallic beyond which it becomes semiconducting. The pressure is found to reduce theT _c at a rate of 0.2 K kbar^–1. The scanning electron micrographs of the starting bismuth cuprates showed characteristic needle-like structure, whereas the pressurized samples were found to be particularly different, consisting of small grains.     

Upper limit ofT c for the copper oxides

The value of the critical temperature of the cuprates correlates with the doping level and is affected by the interplay of two competing factors: (1) the increase in carrier concentration, and (2) the pair-breaking effect of magnetic impurities. An analysis of the temperature dependence of the critical field leads to the conclusion that magnetic impurities are present even in a sample with the maximum observed value ofT _c. A new parameter, “intrinsic”T _c (T _cintr), which is its value in the absence of magnetic impurities, is introduced. The maximum value ofT _cintr, which corresponds to the maximum doping level, appears to be similar for different cuprates and to be equal to 160–170 K. This is the upper limit ofT _c in the cuprates.     

Doping Dependence of the Effects of In-Plane Disorder on T c and the Pseudogap in Single Layer La214 and Double Layer Y123: a Comparative Study

High-T _c emerges from an strongly electronically correlated normal state in hole doped cuprates. In this paper, the comparative effect of Zn on the superconducting transition temperature, T _c , was studied for the La_2?x Sr _x Cu_1?y Zn _y O₄ (Zn-La214) and YBa₂(Cu_1?y Zn _y )₃O_7?δ (Zn-Y123) compounds as a function of hole concentration, p, and Zn content (y) in order to explore the interplay among different electronic ground states in different cuprate systems. Zn induced rate of suppression of T _c , dT _c (p)/dy, for Zn-La214 was found to be strongly p-dependent and showed a monotonic variation, except in the vicinity of p～0.125 (i.e., near the 1/8th anomaly where the charge/spin stripe correlations are at their strongest). Magnitude of dT _c (p)/dy decreased markedly around p～0.125. The same feature, at a somewhat reduced scale, was also observed for Zn-Y123. We have also reviewed the p-dependent pseudogap energy scale, ε _g (p), which shows a quasilinear decrease with increasing p, without any noticeable feature at p～0.125. The magnitude and the evolution of ε _g (p) are quite similar for both Zn-La214 and Zn-Y123 compounds even though T _c and structural and electronic anisotropies are significantly different.     

Effect of oxygen deficiency (δ) on transition temperature of yttrium cuprate superconductors

The nature of pairing mechanism as well as transition temperature of yttrium cuprates is discussed using the strong coupling theory. An interaction potential has been developed for the layered structure with two conducting CuO₂(a–b) layers in a unit cell. The interaction potential properly takes care of electron-electron, electron-phonon and electron-plasmon interactions. Furthermore, the electron-phonon coupling parameter (λ), the modified Coulomb repulsive parameter (μ*) and the 2D acoustic phonon (plasmon) energy as a function of oxygen deficiency is worked out. Finally, the superconducting transition temperature (T _c) is then evaluated by using these coupling parameters and obtainedT _c = 95(92)K for Y(Yb)Ba₂Cu₃O_7−δ superconductors withδ = 0·0. The model parameters estimated from the layered structure approach are consistent with the strong coupling theory. The result deduced on the variation ofT _c withδ are in fair agreement with the earlier reported data on yttrium cuprates. The analysis of the above results are discussed.     

Upper Critical Field and Specific Heat of Cuprates

A representative set of magnetotransport measurements in novel superconductors is analyzed. The resistive upper critical field, H _c2 (T) of many cuprates, of superconducting spin-ladders, and organic (TMTSF)2X systems has a universal nonlinear temperature dependence H _c2 (T_c – T)^3/2 in a wide temperature interval near T _c, while its low-temperature behavior depends on the chemical formula and sample quality. The unusual H _c2(T) is described as the Bose–Einstein condensation field of preformed pairs. Its universal temperature dependence follows from the scaling arguments. Controversy in the determination of H _c2 (T) from the resistivity and specific heat measurements is resolved in the framework of the charged Bose-gas model with the impurity scattering. It is shown that specific heat shows two anomalies. The high-temperature anomaly is strong and shows only weak shift with applied field. The low-temperature anomaly corresponds to resistive transition and is very weak in agreement with the experiments. Both anomalies coincide at H = 0.     

Pair breaking, “intrinsic”T c,and the upper limit ofT c in the cuprates

The presence of magnetic impurities leads to a drastic decrease inT _c in the overdoped region, gaplessness, and the usual temperature dependence ofH _c2. The magnetic moments are localized on the apical oxygen site, and this allows us to explain the increase inT _c with the increase in the number of Cu-O planes in the unit cell. Applied pressure can raiseT _c above the usual value at optimum doping, toward the “intrinsic”T _c. The cuprates as a class of compounds have an upper limit ofT _c in the rangeT _c,upp=160–170 K.     

Tc-Variation of (Y1−yCay)Ba2Cu3Ox single crystals under hydrostatic pressure

Former pressure experiments on YBa₂Cu₃O_x single crystals showed only small dT_c/dp values at high oxygen contents (6.9x7.0), which corresponds to an almost optimal hole-doping n_h. By Ca-doping these investigations can be extended to the heavily overdoped region. Reducing then the oxygen content allows to return to the optimal hole concentration n_h,opp which gives the maximum transition temperature T_c,max for this Ca-content. Oxygen and Ca-doping of YBa₂Cu₃O_x single crystals are used to determine the parabolic T_c(n_h) dependency by ac-susceptibility measurements under hydrostatic pressure conditions up to 0.6 GPa. In order to avoid pressure induced oxygen ordering processes the samples were held below 100 K during the experiment including all pressure changes. The Ca-doped highly oxygenated single crystals show large negative dT_c/dp values. Reducing the oxygen content increases dT_c/dp to zero, as expected. A further reduction of the oxygen content increases the dT_c/dp values much faster than expected from the overdoped region. These findings are interpreted to arise from the anisotropic pressure effect on T_c with a pressure effect in c-axis direction that is mainly due to hole doping and with additional structural effects when pressure is applied in a- and b-axis direction.     

Oxygen deficiency dependence of transition temperature in (Sm, Er) Ba2Cu3O7−δ superconductors

We have investigated the effects of oxygen deficiency (δ) on the transition temperature (T _c) of (Sm, Er)Ba₂Cu₃O₇₋ δ superconductors by incorporating the effects of the two dimensional (2D) acoustic phonons and plasmons in the framework of strong coupling theory. The proposed approach for yttrium cuprates properly takes care of the double CuO₂ plane in a unit cell and has been found earlier to be successful in describing the pairing mechanism as well as the variation ofT _c withδ in Y Ba₂Cu₃O₇₋ δ system. The coupling strength (λ), the screening parameter (μ*) and the two dimensional acoustic phonon (plasmon) energyħω ₋(ω₊) as a function of oxygen deficiency is worked out. Finally, the transition temperature is evaluated and is found to be consistent with the earlier experimental data on yttrium cuprates. Thus, coupled phonon-plasmon mechanism is adequate to understand the nature of pairing mechanism and oxygen deficiency dependence of transition temperature in 90 K (Sm, Er)Ba₂Cu₃O₇₋ δ superconductors.