Intrinsic Inhomogeneity of the Cuprates: Pseudogap, Resistive vs. Diamagnetic Transitions

The pseudogap phenomenon in the cuprates can be explained by an intrinsic inhomogeneity of the samples. At temperatures above the superconducting resistive transition but below the temperature at which the pseudogap disappears, the sample contains superconducting islands embedded in a normal matrix. As a result, the normal resistance coexists with the gap structure, and there is a splitting of the resistive and Meissner transitions.     

Thermodynamic Properties of High-Temperature Superconductors in the Pseudogap Regime

Experimental data extracted from thermodynamic measurements in underdoped high-temperature superconductors show significant deviations from the results predicted by the BCS theory. In these particular compounds, the anomalies observed in the superconducting phase are associated also to the presence of a pseudogap in their normal state. On the basis of a simple model, which treats the pseudogap phenomenologically, we performed a Ginzburg–Landau expansion to extract the main properties of the superconducting phase. Our results for the specific-heat-coefficient jump at the transition point, (T _c), coherence length, T(T), and penetration depth, (T), qualitatively recover the experimental data.     

Doping and Isotope Dependence of the Pseudogap in High-Tc Cuprates Observed by Neutron Crystal-Field Spectroscopy: A Fast Local Probe

The temperature dependence of the relaxation rate of crystal-field excitations in the high-T _c superconductors HoBa₂Cu₄O₈ and HoBa₂Cu₃O _x (6.4 < x < 7) was investigated by inelastic neutron scattering techniques. The data show clear evidence for the opening of an electronic gap in the normal state at T* > T _c in the underdoped regime as well as for slightly overdoped samples. For HoBa₂Cu₄O₈ T* increases from 170 to 220 K upon oxygen isotope substitution (¹⁶O vs ¹⁸O). This huge isotope shift (which is absent in NMR and NQR experiments) suggests that the mechanism leading to an isotope effect on the pseudogap has to involve a time scale in the range 10^–8 > 10^–13 s.     

Lattice Distortions and Charge Carriers in Cuprates

A phenomenological model with itinerant bands and local states trapped by thelattice on the Cu-sites, is discussed to describe global features ofcuprates. Relative energy positions of localized and itinerant states beingtuned (thermodynamically or by doping), the system must undergo first-orderMott metal-insulator transition. Decreasing the local level (from themetallic end of a stoichiometric compound), charge separation instabilityoccurs first before the Mott transition. Crossing and hybridization betweenlocal (flat) and itinerant bands introduce a structure in density of stateswhich may account for pseudogap features in cuprates. Modelresults in polaronic lattice effects and is rich enough to serve as aphenomenology of cuprates.     

On the Pseudogap State in Y- and La-Type High-Temperature Superconductors: Doping Dependence, Isotope Effects, and Electronic Properties Studied by Neutron Spectroscopy

The doping dependence as well as the oxygen and copper isotope effects on the pseudogap temperature T* were investigated by neutron spectroscopic experiments of the relaxation rate of crystal-field excitations in rare-earth based Y- and La-type high-temperature superconductors. We found three essential results from our truly bulk-sensitive experiments: (1) For all doping levels we had T* > T _c, even in the optimally doped and overdoped regimes. (2) In bilayer high-T _c compounds we observed huge oxygen and copper isotope effects on T*, which give evidence that the pseudogap formation is governed by lattice modes involving both the oxygen and copper ions. In single layer high-T _c compounds, on the other hand, no shift of T* was found for the copper isotope substitution. (3) Our results obtained for all doping levels support the unusual temperature dependence of the gap function in the pseudogap region reported for underdoped Bi-type compounds, i.e., a breakup of the Fermi surface into disconnected arcs in the temperature range T _c < T < T*.     

Pseudogap and Transport in HTS

Perpendicular transport is one of the key factors to HTS superconductivity, sampling the quasi-insulating blocking layer, separating the conducting CuO-planes, and driving the metal–insulator transition (MIT) that is induced by disorder and underdoping. Various measurements have been carried out to study the transport, the MIT, and the in-plane Fermi surface especially by surface methods via the blocking layer, and these depend sensitively on surface quality. ARXPS results on UHV cleaving show that at 300 K and 10^–10 Torr, a Bi hydroxide layer occurs in 30 min, followed by H₂O or C_y H_x OH chemisorption. Consequences of this result on STS, ARPES, perpendicular transport, Coulomb charging, and pseudogap are analyzed, yielding scenario for HTS superconductivity, where static and dynamic charge exchange via and with the blocking layer initiates plaques of preformed pairs of d-wave symmetry weakening the inplane Coulomb repulsion yielding by this plasmonic mechanism, finally, HTS. Consequences of this scenario on anisotropic transport with its strong Fermi velocity v_F anisotropy and its strong in-plane scattering rate (T) const. at (, 0) in k-space with pseudo gap kT^* _{_P}/3 and superconducting gap _S 3 kT_c maxima and the strongly decreasing rate (T) T at 0.4 (, ) with pseudo gap _{_p} (k) node and superconducting gap _s (k node are given.     

An Analytical Approach for the Pseudogap in the Spin Fluctuations Model

The electronic self-energy due to the electron–spin fluctuation interaction is calculated using the one loop approximation for a two-dimensional system and quasi-two-dimensional (anisotropic) model. We analyzed the relevance of the diffusive modes and the temperature dependence of the magnetic correlation length for a possible temperature dependence of the pseudogap.     

Pseudogap Phenomenon in Single Phase Hg-1223 Cuprate Superconductors

The single phase Hg-1223 cuprate superconductors have been successfully fabricated. The postannealing treatment under oxygen (O₂) gas and argon (Ar) gas with different annealing time was performed in order to obtain various hole density samples. These samples were used to study the pseudogap phenomenon in the normal phase. With the plot of ln[1/(T) – 1/_N(T)] against 1/T, three characteristic temperatures T*, T _S, and T _F were obtained, which describe the role of the pseudogap phenomenon. The magnitudes of the pseudogap were extracted from the slope of the stated plots. It is found that the three characteristic temperatures T*, T _S, and T _F change with the hole density linearly. The relationship between T* and T _C goes within T* = T*_op+₀ (1–T_C/T^max _C) , where T*_op and T _C ^max are the pseudogap opening temperature and the critical temperature for the optimal sample. It is also found that the pseudogap phenomenon only exists below the optimal regime in the hole doping phase diagram.     

Pseudogap in Boron-Doped Diamond and Cuprates

The Marcus model, well known as a general model for electron transfer, is applied to electron pair formation and transfer in systems characterized by neighboring superconducting and local phases, particularly boron-doped diamond and cuprates. Hubbard-U is identified with the adiabatic free energy difference between charged and spin-coupled configurations. Typical for the Marcus model is the coupling of electronic and nuclear coordinates due to structural changes with number of electrons during electron transfer or excitation.     

Analysis of the Pairing Interaction in the Cuprates

Thermal difference reflectance (TDR) spectra taken on a large number of superconducting cuprates has enabled us to determine the energy dependence and strength of the pairing interaction in each. All show strong contributions from the phonons and a smaller, but significant contribution from an electronic transition near 1.7 eV. Recent improvements in the signal-to-noise ratio have revealed that the electronic excitation is accompanied in all cases by a weaker companion about 0.5 eV lower in energy. No other contributions are found. We identify these transitions as the d _z2 to d _x2–y2 excitations of the Cu ion in the 3d ⁹ and 3d ⁸ states, respectively, and have calculated the coupling strength mediated by each. The calculated values agree in order of magnitude with the observed strengths. We find that, in addition to the direct electronic coupling that corresponds to an electron–phonon-like term, the overlap between the oxygen and the copper orbitals leads to an exchange term. The direct term couples only to an s-wave gap, as for phonons, while the exchange term couples s-wave to d-wave, and vice versa. We discuss the consequences of this result.     

Superconductivity in Cuprates, the van Hove Scenario

We review the consequences of the presence of van Hove singularities close to the Fermi level in the HTCS cuprates. We show that it may explain the properties of these materials such as the high T _c, anomalous isotope effect, marginal Fermi liquid properties, gap anisotropy, etc. We show that the pseudogap observed in the normal state can be attributed to the Coulomb interaction between carriers in these disordered compounds.     

Oscillator-Strength Sum Rule in the Cuprates

The oscillator-strength sum rule played an important role in the firstwork on the energy gap of superconductors by Tinkham. Recently, asmall but measurable depletion in the sum rule integral has beenobserved at optical frequencies in the cuprates. It has been suggestedthat this behavior contradicts what is expected of traditional modelsof superconductivity. We disagree with this conclusion. We show thatthis depletion is consistent with earlier Thermal DifferenceReflectance (TDR) measurements and their interpretation within thestrong coupling extension of the BCS theory, as evidence of anelectronic contribution to the pairing interaction at energies between1.0 and 2.0 eV for these materials. We show quantitative agreementwith the magnitude of the depletion and agreement with recent workwith ARPES on the dispersion and lifetime of quasiparticles from thesame model. We have located the two transitions responsible for theelectronic contribution from TDR measurements of the thermalderivative of the dielectric function.     

Pseudogap and Quantum-Transition Phenomenology in HTS Cuprates

The low-energy excitation spectrum of HTS cuprates is examined in the light of thermodynamic, transport, quasiparticle and spin properties. Changes in the thermodynamic spectrum associated with the normal-state pseudogap disappear abruptly at a critical doping state, p _crit=0.19 holes per Cu. Moreover, ARPES data at 100K show that heavily damped quasiparticles (QP) near (,0) suddenly recover long lifetimes at p _crit, reflecting an abrupt loss of scattering from AF spin fluctuations. This picture is confirmed by SR zero-field relaxation measurements which indicate the presence of a novel quantum glass transition at pcrit. Consistent with this picture resistivity studies on thin films of Y_0.7Ca_0.3Ba₂Cu₃O_7– reveal linear behavior confined to a V-shaped domain focussed on pcrit at T=0. The generic phase behavior of the cuprates may be governed by quantum critical fluctuations above p _crit and the pseudogap appears to be caused by short-range AF correlations.     

A New Model of Pseudogap Physics in the Cuprates

We discuss a short-range order mechanism for understanding pseudogap physics of cuprates in which the competition between a variety of magnetic orders frustrates the development of the long-range order. We show in particular that the competition between the effects of Van Hove singularity nesting and conventional Fermi surface nesting leads to a material-dependent transition between Mott and Slater physics, and the emergence of a spin-frustrated state in the crossover region.     

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.     

NMR Evidence for Spatial Modulations in the Cuprates

Nuclear magnetic resonance (NMR) data on Cu, apical and planar O in La_1.85Sr_0.15CuO₄ are presented. Spin echo double resonance shows that the large Cu magnetic shift distribution is of short-length scale. Analysis of the O data reveals static modulations of the spin susceptibility with a spin–spin correlation function near zero. The Cu shift distribution is found to be of orbital origin. The full planar oxygen spectra show a correlated modulation of the electric field gradient with the spin susceptibility. Similar results on other cuprates indicate universality of these phenomena.     

Estimation of the Surface-d to Bulk-s Crossover in the Macroscopic Superconducting Wavefunction in Cuprates

The concept of a surface d- and bulk s-symmetry in cuprate superconductors is applied to recent small-angle neutron-scattering results. These show a change of hexagonal to square vortex lattice as a function of the magnetic field along the c-axis. Identifying the hexagonal lattice with s- and the square with d-symmetry, the crossover distance from the surface d to the bulk s perpendicular to the c-axis is estimated to be 35 nm for LSCO and roughly 7 nm for YBCO, both at optimum doping. The crossover along the c-axis has to be of only a few layers distance to reconcile tunneling, photoemission, and pulsed femtosecond reflectivity experiments. These estimates are compatible with -rotation, NMR, and other experiments.     

From Friedel Oscillations and Kondo Effect to the Pseudogap in Cuprates

One of the great achievements performed by Jacques Friedel in France has been to promote experimental activities on the electronic properties in condensed matter physics, which has led him, among others, to be an active promoter of the up-rise of the “Laboratoire de Physique des Solides” (LPS). I have had the chance to be involved in this process in the early days and to create a Nuclear Magnetic Resonance (NMR) group which remains active nowadays. Among various other scientific activities, I have performed some work on Kondo effect in the 1970s which has allowed me to enlighten the real interest of the NMR probe as a local experimental technique to visualize the perturbation brought by impurities in normal metals. These experiments were of course driven by my strong exposure to J. Friedel’s education on charge and spin density oscillations in metals. This work has been also my first personal contact with correlated electron physics, a field in which I have been involved for years particularly since the discovery of high T _c cuprates (HTSC). I recall that the early NMR experiments done in these systems have given evidence for the existence of strong electronic correlations and established the occurrence of the “pseudogap”, on which I have initially had some exchanges with J. Friedel. The pseudogap, occurring below a temperature T ^∗, has during the last twenty years raised endless discussions about the incidence of correlations on superconductivity. Many researchers are still advocating today that the pseudogap is due to the existence of preformed pairs above T _c. I shall show that its robustness to impurities and disorder that we evidenced from the early days rather suggested that it results from a competing order of the correlated state. This is apparently better accepted nowadays, although various distinct ordered states detected below T ^∗ are not yet understood. The short reviews of the work done on Kondo effect and on the cuprates in Orsay allow me to enlighten the importance of the initial choices done by J. Friedel for the LPS. I also underline the large contrast between the scientific behaviours which prevailed between these two periods of scientific activity. This is not only ascribed to the discovery of the HTSC but also to the changes in publication policies and to the modification of evaluation procedures, all this being driven by the advent of information technologies. I suggest that these changes might have a negative incidence, in my opinion, on the research and education system, at least in our field of science.