Thermodynamics and phase diagram of high temperature superconductors

Thermodynamic quantities are derived for superconducting and pseudogap regimes by taking into account both amplitude and phase fluctuations of the pairing field. In the normal (pseudogap) state of the underdoped cuprates, two domains have to be distinguished: near the superconducting region, phase correlations are important up to temperature T(phi). Above T(phi), the pseudogap region is determined only by amplitudes, and phases are uncorrelated. Our calculations show excellent quantitative agreement with specific heat and magnetic susceptibility experiments on cuprates. We find that the mean field temperature T0 has a similar doping dependence as the pseudogap temperature T(*), whereas the pseudogap energy scale is given by the average amplitude above T(c).     

Nodal superconductivity and antinodal pseudogap in cuprate superconductors

According to recent experimental findings the leading pairing resides in the nodal (FS arcs) momentum region of hole doped cuprates. The pseudogap is an antinodal feature. A corresponding multiband model of the electronic background evolving with doping serves the usually presented phase diagram. The pairing is due by the pair-transfer between overlapping nodal defect (polaron) band and the itinerant band. A bare gap vanishing with extended doping between the antinodal defect subband and the itinerant band top leads to the formation of the pseudogap as a perturbative band-structure effect. The calculated behaviour of two superconducting gaps and of the pseudogap on the whole doping scale is in qualitative agreement with the observations. Arguments to include cuprates into the class of multiband-multigap superconductors are given by these results.     

Mechanism of Pseudogap Detected by Electronic Raman Scattering： Phase Fluctuation or Hidden Order？

We study the electronic Raman scattering in the cuprates to distinguish the two possible scenarios of the pseudogap normal state. In one scenario, the pseudogap is assumed to be caused by phase fluctuations of the preformed Cooper pairs. We find that pair-breaking peaks appear in both the B1g and B2g Raman channels, and they axe smeared and tend to shift to the same energy with the increasing strength of phase fluctuations. Thus both channels reflect the same pairing energy scale, irrespectively of the doping level. In another scenario, the pseudogap is assumed to be caused by a hidden order that competes with the superconducting order. As an example, we assume that the hidden order is the d-density-wave （DDW） order. We find analytically and numerically that in the DDW normal state there is no Raman peak in the B2g channel in a tight-binding model up to the second nearest-neighbor hopping, while the Raman peak in the Big channel reflects the energy gap caused by the DDW order. This behavior is in agreement with experiments in the pseudogap normal state. To gain further insights, we also calculate the Raman spectra in the DDW＋SC state. We study the doping and temperature dependence of the peak energy in both channels and find a two-gap behavior, which is in agreement with recent Raman experiments. Therefore, our results shed light on the hidden order scenario for the pseudogap.     

Charge confinement effect in cuprate superconductors: an explanation for the normal-state resistivity and pseudogap

The fact that the stripe phase and pseudogap in the cuprate superconductors occur in the same doping regime is emphasized. A model based on charge confinement in self-organized nanometer-scale stripe fragments is proposed to understand various generic features of the normal-state energy gap including the magnitude of the gap, its anti-correlation with the superconducting gap, and the d-wave symmetry in its -dependence. This model also provides a basis for understanding other anomalous normal-state properties such as the linear temperature dependence of electrical resistivity. Received 7 December 1998     

Manifestations of the pseudogap and superconducting gap of cuprates in photoemission

The degree to which the interpretation of the existence of a pseudogap and a superconducting gap in cuprates on the basis t-t′-U the Hubbard-model corresponds to the data obtained from the photoemission spectra is discussed. The pseudogap in the model is interpreted as the work function of electrons from the insulating parts of the Brillouin zone boundary. On this basis one can explain the angle dependence of the gap measured in the photoemission spectra and its evolution on changes in doping and temperature. In particular, an explanation is found for the decline in the ratio of the angle derivative of the gap near the site, v _Δ = (1/2)dΔ(?)/d?, to the maximum value of the gap, Δ_max, with decreasing doping. That behavior and the different temperature dependence of the gap Δ(?) for different angles are due to the presence of two contributions to Δ with different anisotropies—from the pseudogap and from the superconducting gap. The calculation of the spectral functions confirms the sharp Fermi boundary observed in the direction and the smeared edge of the distribution along the path Γ(0, 0)-M(π, 0)-Y(π, π).     

Strong correlation, electron-phonon interaction and critical fluctuations: isotope effect, pseudogap formation, and phase diagram of the cuprates

Within the Hubbard-Holstein model with long-range Coulomb forces, we revisit the charge-ordering (CO) scenario for the superconducting cuprates and account for the presence or the absence of a formed stripe phase in different classes of cuprates. We also evaluate the mean-field and the fluctuation-corrected critical lines for CO and we relate them with the various pseudogap crossover lines occurring in the cuprates and we discuss a mechanism for their peculiar isotopic dependence. Considering the dynamical nature of the CO transition, we explain the spread of T∗ and of its isotopic shift, obtained with experimental probes with different characteristic time scales.     

Pseudogaps in an incoherent metal

How are the properties of a metal changed by strong inelastic scattering? We investigate this question within the two-dimensional t-J model using extended dynamical mean field theory and a generalized noncrossing approximation. Short-ranged antiferromagnetic fluctuations lead to a strongly incoherent single particle dynamics, large entropy, and resistance. Close to the Mott transition at low hole doping a pseudogap opens, accompanied by a drop in resistivity and an increase in the Hall constant for both lower temperatures T and doping levels. The behavior obtained bears surprising similarity to properties of the cuprates.     

Temperature dependence of the gap size near the brillouin-zone nodes of HgBa2CuO4+delta superconductors

Although more than 20 years have passed, the identification of the superconducting order parameter in cuprates is still under debate. Here, we show that the gap size near the nodes is a good candidate for the order parameter: it scales with the critical temperature Tc over a wide doping range and displays a significant temperature dependence below Tc in both the underdoped and the overdoped regimes. In contrast, the gap size at the antinodes does not scale with Tc in the underdoped regime and appears to be controlled by the pseudogap which persists below Tc.     

Correlation effects obtained from optical spectra of Fe-pnictides using an extended Drude-Lorentz model analysis

We introduce an analysis model, an extended Drude–Lorentz model, and apply it to Fe-pnictide systems to extract their electron–boson spectral density functions (or correlation spectra). The extended Drude–Lorentz model consists of an extended Drude mode for describing correlated charge carriers and Lorentz modes for interband transitions. The extended Drude mode can be obtained by a reverse process starting from the electron–boson spectral density function and extending to the optical self-energy and, eventually, to the optical conductivity. Using the extended Drude–Lorentz model, we obtained the electron–boson spectral density functions of K-doped BaFe₂As₂ (Ba-122) at four different doping levels. We discuss the doping-dependent properties of the electron–boson spectral density function of K-doped Ba-122. We also can include pseudogap effects in the model using this approach. Therefore, this approach is very helpful for understanding and analyzing measured optical spectra of strongly correlated electron systems, including high-temperature superconductors (cuprates and Fe-pnictides).     

The short-range correlations of a doped Mott insulator

This paper presents numerical studies of the single hole model that address the interplay between the kinetic energy of itinerant electrons and the exchange energy of local moments as of interest to doped Mott insulators. Due to this interplay, two different spin correlations coexist around a mobile vacancy. These local correlations provide an effective two-band picture that explains the two-band structure observed in various theoretical and experimental studies, the doping dependence of the momentum space anisotropic pseudogap phenomena and the asymmetry between hole and electron doped cuprates.     

Non-Fermi-liquid behavior and d-wave superconductivity near the charge-density-wave quantum critical point

A scenario is presented, in which the presence of a quantum critical point due to formation of incommensurate charge density waves accounts for the basic features of the high temperature superconducting cuprates, both in the normal and in the superconducting states. Specifically, the singular interaction arising close to this charge-driven quantum critical point gives rise to the non-Fermi liquid behavior universally found at optimal doping. This interaction is also responsible for d-wave Cooper pair formation with a superconducting critical temperature strongly dependent on doping in the overdoped region and with a plateau in the optimally doped region. In the underdoped region a temperature dependent pairing potential favors local pair formation without superconducting coherence, with a peculiar temperature dependence of the pseudogap and a non-trivial relation between the pairing temperature and the gap itself. This last property is in good qualitative agreement with so far unexplained features of the experiments.     

Electron spectrum in high-temperature cuprate superconductors

A microscopic theory for the electron spectrum of the CuO₂ plane within an effective p-d Hubbard model is proposed. The Dyson equation for the single-electron Green’s function in terms of the Hubbard operators is derived and solved self-consistently for the self-energy evaluated in the noncrossing approximation. Electron scattering on spin fluctuations induced by the kinematic interaction is described by a dynamical spin susceptibility with a continuous spectrum. The doping and temperature dependence of electron dispersions, spectral functions, the Fermi surface, and the coupling constant λ are studied in the hole-doped case. At low doping, an arc-type Fermi surface and a pseudogap in the spectral function close to the Brillouin zone boundary are observed. The text was submitted by the authors in English.     

Pseudogap in doped Mott insulators is the near-neighbor analogue of the Mott gap

We show that the strong-coupling physics inherent to the insulating Mott state in 2D leads to a jump in the chemical potential upon doping and the emergence of a pseudogap in the single-particle spectrum below a characteristic temperature. The pseudogap arises because any singly occupied site not immediately neighboring a hole experiences a maximum energy barrier for transport equal to t(2)/U, t the nearest-neighbor hopping integral and U the on-site repulsion. The resultant pseudogap cannot vanish before each lattice site, on average, has at least one hole as a near neighbor. The ubiquity of this effect in all doped Mott insulators suggests that the pseudogap in the cuprates has a simple origin.     

Anomalous thermodynamics of the doped Mott-Hubbard insulators

The concentration dependence of the entropy of doped Mott-Hubbard insulators has been considered within the t-J model. It has been shown that a change in the type and statistics of charge carriers as compared to the Fermi gas leads to a radical change in the entropy s, in particular, to the giant growth of the entropy upon doping. The quantity ∂s/∂x ≈ k _B is approximately consistent with the experimental data for HTSC cuprates in the pseudogap phase.     

Nematic order of spin structures of clusters in the hubbard model

The possibility of interpreting the normal pseudogap state of cuprates as a result of the formation of spin and charge structures is investigated for solutions of the Hubbard model of a finite 2D cluster based on the mean field method. The iterative self-consistency procedure reduces the initial uncorrelated spin distributions to stable structures. The Fourier components of the charge and spin distributions in such structures have peaks for characteristic incommensurate quasi-momenta depending on the doping. It is shown that for any doping, the density of states of the system has a sharp minimum (pseudogap) at the Fermi level. This emergence of the gap just at the Fermi level is a property typical of not only the superconducting state, but also the normal state of spin glasses. The characteristics of the Fermi surface averaged over the implemented structures and the properties of quasiparticles in the nodal and antinodal regions of the quasi-momentum are considered.     

Doping-dependent evolution of low-energy excitations and quantum phase transitions within an effective model for high-T<Subscript>c</Subscript> copper oxides

In this paper a mean-field theory for the spin-liquid paramagnetic non-superconducting phase of the p- and n-type high-T_c cuprates is developed. This theory applied to the effective t-t'-t′′-J^* model with the ab initio calculated parameters and with the three-site correlated hoppings. The static spin-spin and kinematic correlation functions beyond Hubbard-I approximation are calculated self-consistently. The evolution of the Fermi surface and band dispersion is obtained for the wide range of doping concentrations x. For p-type systems the three different types of behavior are found and the transitions between these types are accompanied by the changes in the Fermi surface topology. Thus a quantum phase transitions take place at x = 0.15 and at x = 0.23.Due to the different Fermi surface topology we found for n-type cuprates only one quantum critical concentration, x = 0.2. The calculated doping dependence of the nodal Fermi velocity and the effective mass are in good agreement with the experimental data.     

Fluctuation-exchange study of antiferromagnetism in disordered electron-doped cuprate superconductors

On the basis of the Hubbard model, we extend the fluctuation-exchange (FLEX) approach to investigating the properties of the antiferromagnetic (AF) phase in electron-doped cuprate superconductors. Furthermore, by incorporating the effect of scatterings due to the disordered dopant atoms into the FLEX formalism, our numerical results show that the antiferromagnetic transition temperature, the onset temperature of pseudogap due to spin fluctuations, the spectral density of the single particle near the Fermi surface, and the staggered magnetization in the AF phase as a function of electron doping can consistently account for the experimental measurements.