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The d–p band model, a periodic array of strongly correlated d states with hopping to a p band, and in the presence of a uniform applied magnetic field is studied as a function of temperature using Roth's variational method. Expanding the σ spin electron occupation numbers of d and p states to first order in the magnetic field h, we calculate the linear term of the field induced magnetization and thus the susceptibility. This is given in terms of the number of holes for La_{2 - x}Sr_xCuO₄, in the limit of strongd–d correlations and we study the role of doping x and temperature "T" on the susceptibility.

Most of the proposed models of high-temperature superconductivity (HTSC) are based on the short-range electron-electron correlations or/and on a short-range electron-phonon interaction. However, in the cuprates the screening is poor due to a low carrier density, layered crystal structure, and high ionicity of the lattice. We develop further the bipolaron model of HTSC, which explicitly takes into account the long-range origin of all interactions. The long-range electron-phonon (Fröhlich) interaction binds carriers into real space pairs (small bipolarons) with surprisingly low mass but sufficient binding energy, while the long-range Coulomb repulsion keeps them from forming larger clusters. The model has explained many key features of cuprates. It is shown here that real-space pairing takes place in many cuprates at variance with some (incorrect) criteria of the BCS-BEC crossover.

Maximum-Entropy (ME) analysis is applied to muon-spin-rotation (μSR) data of RBa₂Cu₃O_y (RBCO; R = Ho, Eu) vortex states. Our focus is on the prospect of antiferromagnetism (AF) associated with the vortex core. The ME transforms are fitted by two μSR signals: the vortex signal and the grain-boundary (GB) signal. Below T_c, the GB signals are well fitted by Gaussians for both EuBCO (T_c = 94 K) and underdoped HoBCO (T_c = 66 K). Below 0.5T_c, EuBCO and HoBCO vortex signals are best fitted using Lorentzians, instead of expected Gaussians. An estimate for an effective Neél temperature of an AF vortex core is about 30 K. Our AF-core search results for RBCO vortex states are discussed considering a magnetic origin of cuprate superconductivity.

In this work the variational Roth's approach previously developed by the present authors to describe cuprate systems is extended to include the superconducting properties. We extend the Beenen and Edwards approach by including the d–p hybridization. The role of the d–p hybridization in modifying the values of superconducting order parameter is then studied in terms of the adopted values of the parameters defining the Hamiltonian of the system.

We consider the large Nernst signal discovered by Ong and collaborators in hole-doped cuprates, in particular in the pseudogap regime. Based on our previous quantitative calculations together with Huse [Phys. Rev. Lett.89, 287001 (2002)], we discuss the interpretation of the experimental observations as arising from superconducting fluctuations and its relation to the vortex scenario proposed by Ong. We also comment on the implications of the Nernst analysis for understanding the full range of pseudogap phenomena.

The bulge in the doping dependence of the basal plane area of cuprate superconductors is shown to be an effect of the particular inhomogenous electronic structure created by the dense packing of paired self-protected singlets (PSPS) in CuO₂ lattices.

Observed temperature-dependent heat capacity C (T) behavior of high-T_cYBa₂Cu₃O_7-δ cuprate superconductors has been theoretically analyzed in the temperature domain 70 ≤ T ≤ 110 K. Calculations of C (T) have been made within the two component scheme: one is the Fermionic term and the other the Bosonic (phonon) contribution. While estimating the electronic term, we use a mean field step and follow two-fluid model below and above T_c. Later on, the lattice heat capacity is estimated within harmonic approximation for high temperature expansion (T > θ/2π), the model has only one free parameter, the moments of phonon density of states. Within the two-fluid model for electronic specific heat along with reported γ value leads to a sharp discontinuity at T_c. The Coulomb correlations and electron-phonon coupling strength have significant implications on the γ. Henceforth, the present numerical analysis of specific heat from the present model shows similar results as those revealed from experiments. The accurate fitting of the specific heat data reveals that it is possible to decompose the documented specific heat into dominant lattice contribution and electronic channel. However, the specific heat from electronic term is only a fraction of lattice specific heat in YBa₂Cu₃O_7-δ high-T_c superconductors.

Strong finite-range electron-phonon interaction (EPI) bounds carriers into small mobile bipolarons. The Bogoliubov-de Gennes (BdG) equations are formulated and solved in the strong-coupling limit, when small bipolarons bose-condense with finite center-of-mass momentum, K ≠ 0. There are two energy scales in this regime, a temperature independent incoherent gap Δ_p and a temperature dependent coherent gap Δ_c(T, R) modulated in the real space, R. The order parameter has d-wave symmetry in R-space and the single-particle density of states (DOS) reveals checkerboard modulations similar to the checkerboard tunnelling DOS observed in cuprates.

A minimal model for the description of cuprate superconductor characteristics on doping scale (hole and electron) is developed. The leading interband pairing channel couples an itinerant band and defect states created by doping. Bare gaps between them are supposed and become closed by extended doping. Band overlap conditions determine special points in the phase diagram. Nodal and antinodal momentum regions are distinguished. Illustrative calculations have been made using a mean-field pair-transfer multiband Hamiltonian and corresponding free-energy expansions. The results are self-consistent and demonstrate that the elaborated approach is able to reproduce characteristic features of cuprate superconductors as, e.g., the doping dependence of T_c, superconducting gaps and pseudogaps, supercarrier density and effective mass, coherence length and penetration depth, critical magnetic fields and some other properties. Interband pairing scheme is suggested to be an essential aspect of cuprate superconductivity.

High temperature superconductivity in the cuprates remains one of the most widely investigated, constantly surprising and poorly understood phenomena in physics. Here, we describe briefly a new phenomenological theory inspired by the celebrated description of superconductivity due to Ginzburg and Landau and believed to describe its essence. This posits a free energy functional for the superconductor in terms of a complex order parameter characterizing it. We propose that there is, for superconducting cuprates, a similar functional of the complex, in plane, nearest neighbor spin singlet bond (or Cooper) pair amplitude ψ_ij. Further, we suggest that a crucial part of it is a (short range) positive interaction between nearest neighbor bond pairs, of strength J′. Such an interaction leads to nonzero long wavelength phase stiffness or superconductive long range order, with the observed d-wave symmetry, below a temperature T_c~z J′ where z is the number of nearest neighbors; d-wave superconductivity is thus an emergent, collective consequence. Using the functional, we calculate a large range of properties, e.g., the pseudogap transition temperature T* as a function of hole doping x, the transition curve T_c(x), the superfluid stiffness ρ_s(x, T), the specific heat (without and with a magnetic field) due to the fluctuating pair degrees of freedom and the zero temperature vortex structure. We find remarkable agreement with experiment. We also calculate the self-energy of electrons hopping on the square cuprate lattice and coupled to electrons of nearly opposite momenta via inevitable long wavelength Cooper pair fluctuations formed of these electrons. The ensuing results for electron spectral density are successfully compared with recent experimental results for angle resolved photo emission spectroscopy (ARPES), and comprehensively explain strange features such as temperature dependent Fermi arcs above T_c and the "bending" of the superconducting gap below T_c.

Having accepted a more generalized form for density-displacement type electron–phonon interaction (EPI) force we studied the simultaneous effect of uniaxial strains and EPI’s screening on the temperature of Bose–Einstein condensation $(T_{\mathrm{\text{BEC}}})$ of the ideal gas of intersite bipolarons. $T_{\mathrm{\text{BEC}}}$ of the ideal gas of intersite bipolarons is calculated as a function of both strain and screening radius for a one-dimensional chain model of cuprates within the framework of Extended Holstein–Hubbard model. It is shown that the chain model lattice comprises the essential features of cuprates regarding of strain and screening effects on transition temperature $(T_c)$ of superconductivity. The obtained values of strain derivatives of $\partial T_{\mathrm{\text{BEC}}}/\partial {𝜀}_i$$(i=a,c)$ are in qualitative agreement with the experimental values of $\partial T_c/\partial {𝜀}_i$$(i=a,b,c)$ of La${}_{2-x}$Sr${}_x$CuO₄ under moderate screening regimes.

We examine the effect of core-hole lifetime on the spectral weight of resonant inelastic X-ray scattering (RIXS) in hole-doped cuprates. We calculate the spectral weight by using the exact diagonalization technique for a 4 × 4 doped Hubbard lattice and find that the spin-flip channel detecting single-magnon excitation is less sensitive to the core-hole lifetime while in the non-spin-flip channel the spectral weight is strongly dependent on the lifetime. In the latter, charge and two-magnon excitations predominately contribute to RIXS for short and long core-hole lifetimes, respectively. For a realistic value of the core-hole lifetime in cuprates, both the charge and two-magnon excitations are expected to contribute to the non-spin-flip channel in RIXS when the incident-photon energy is tuned to the main peak of X-ray absorption spectrum.

In the correlated electron system with the pseudogap, full-gapped domains and Fermi-arced domains coexist. These domains are created by the quantum-fluctuated antiferromagnetic correlation that generates the short-ranged attractive potential to produce the Fermi arcs and the superconductivity. In the full-gapped domains, s-wave or $(d_{x^2-y^2}\pm i{d}_{xy})$-wave symmetry of the electron pairs is favored. In the Fermi-arced domains, only $d_{x^2-y^2}$-wave symmetry of pairs is stable. Superconductivity of different pairing symmetry coexists in different domains as well. Different from the Cooper pairs, the correlated electrons pair up in the real space with an energy gap. Gapless states, on the contrary, hinder the development of superconductivity.

For decades, the difficulty of tackling a strong coupling model with a perturbative approach remained despite numerous inquiries. In this work, a typical mean field theory procedure transforms a strong coupling Hamiltonian into a weak one, which can be solved with a perturbative approach. The Hamiltonian of two-dimensional free electron gas with Hubbard on-site interaction is calculated as a test of the new procedure. Consequently, the spectral characteristics of the cuprates “peak-dip-hump” are reproduced. The result is compared with the past theoretical investigations, e.g., quantum Monte Carlo method, density matrix renormalization group, tensor network methods, etc. which agree well with the spectral curve.

The main purpose of this brief review is to present a sketch of the mechanism of high-T_c superconductivity based mainly on tunneling measurements in cuprates. In the review, we shall mostly discuss tunneling spectroscopy in Bi₂Sr₂CaCu₂O₈. Analysis of the data shows that the Cooper pairs in cuprates are topological excitations (e.g. quasi-one-dimensional bisolitons, discrete breathers etc.), and the phase coherence among the Cooper pairs appears due to spin fluctuations.

Spin density waves (SDWs) may be thought of as comprising charge density waves (CDWs) in pairs, with one CDW composed of up-spin electrons and the other composed of down-spin electrons. The superconductivity in cuprates may then be said to be caused by the BCS-type pairing of these SDWs. This is no longer a simple Cooper pairing of singlet electrons but one that involves a collection of Cooper pairs. Transport in normal metallic states is then governed by CDW pinning, as in a quantum well that is characterized by linear temperature dependence. The pseudo-gap may be understood as originating from this BCS-type gap with SDW, where the parameters used are from those of the original BCS scheme except that the electron–electron interaction is multiplied by N_CDW, which is the number of electrons that have the same spin direction belonging to one CDW branch of the pair that comprises the SDW.

In this paper, the renormalized frequency spectrum and one-particle spectral function of a high temperature superconductor (HTS) is studied using double time thermodynamic Green's function approach via a newly formulated Hamiltonian (without considering BCS type Hamiltonian) which includes the effects of electron–phonon interactions, anharmonicities and that of isotopic impurities. It is investigated that the renormalized frequency further invokes the appearance of energy gap and functional dependence of d_x²-y² wave pairing in the superconducting state in cuprates. The salient feature of the present theory is the electron–phonon interaction in the vicinity of the impurity atoms reveals four-fold symmetric quasiparticle "cloud" aligned with the nodes of d-wave superconducting gap, which is believed to characterize superconductivity in high temperature superconducting materials. It has been further inferred that, a modest contribution of anharmonicity can also induce superconductivity.

In this work, thermal conductivity of high temperature superconductors (HTS) has been analyzed on the basis of modified Callaway model. In the new formulation, the relaxation times of various contributing processes have been observed in newer perspectives of electron and phonon line widths. To obtain line widths, the quantum dynamics of electron and phonon is carried out by using double time thermodynamic Green’s functions method via a general Hamiltonian. The outcome of this heuristic approach is utilized to successfully explain the spectacular behavior of thermal conductivity of HTS, and particularly in the vicinity of transition temperature.

Strong finite-range electron-phonon interaction (EPI) bounds carriers into small mobile bipolarons. The Bogoliubov-de Gennes (BdG) equations are formulated and solved in the strong-coupling limit, when small bipolarons bose-condense with finite center-of-mass momentum, K ≠ 0. There are two energy scales in this regime, a temperature independent incoherent gap Δ_p and a temperature dependent coherent gap Δ_c(T,R), modulated in the real space, R. The order parameter has d-wave symmetry in R-space and the single-particle density of states (DOS) reveals checkerboard modulations similar to the checkerboard tunnelling DOS observed in cuprates.

Charge stripes can be traced back to the 1990s or even earlier.^[1] Stripes are a special case of the general phenomenon of electronic phase separation in strongly correlated transition metal oxide systems wherein regions with a high concentration of mobile carriers are separated from those with a low concentration due to Coulomb interactions. The carrier-rich regions are generally metallic and/or ferromagnetic, while the carrier-poor regions are antiferromagnetic and insulating. Such phase separation manifests itself in the form of metallic droplets in an antiferromagnetic insulating matrix or self-organization, for example, in one dimension as stripes.^{[1, 2]} The phase-separated regions tend to be of nanometric dimensions…