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A theory of the underlying metallic state of large-U$_d$ high-Tc cuprates is presented starting from the covalent Cu-2O 3-band model associated with a sufficiently small copper occupancy. U$_d=\infty$ is dealt by the slave fermion approach. Diagrammatic low order NCA theory in terms of the Cu-O hopping is supplemented with two independent slave particle chemical potentials which implement the U(1) local gauge invariance "at average", thus avoiding the mean-field approximations. The resulting hole spectra consist of itinerant and localized states. The itinerant states close to the Fermi level are coherent. They exhibit dichotomies, the copper/oxygen in real and the nodal/antinodal in reciprocal space. The localized states, related to random Cu-O "mixed valence" fluctuations within the CuO$_2$ unit cells, are incoherent and fall well away from the Fermi level. Consequently, Luttinger's band sum rule for the conduction band is broken. Comparison with IPES, ARPES and NQR data on NCCO, LSCO, Bi2201 and Bi2212 - in order of increasing correlations - leads to remarkable agreements considering that only three bare band parameters are involved., Comment: 5 pages, 4 figures

We report on the interplay of localized and extended degrees of freedom in the metallic state of high-temperature superconductors in a multiband setting. Various ways in which the bare magnetic response may become incommensurate are measured against both phenomenological and theoretical requirements. In particular, the pseudogap temperature is typically much higher than the incommensurability temperature. When microscopic strong-coupling effects with real-time dynamics between copper and oxygen sites are included, they tend to restore commensurability. Quantum transport equations for low-dimensional multiband electronic systems are used to explain the linear doping dependence of the dc conductivity and the doping and temperature dependence of the Hall number in the underdoped LSCO compounds. Coulomb effects of dopands are inferred from the doping evolution of the Hartree-Fock model parameters., Comment: 8 pages, 7 figures, invited talk at Superstripes-2013, Ischia, to appear in the Journal of Superconductivity and Novel Magnetism

A systematic method of calculating the dynamical conductivity tensor in a general multiband electronic model with strong boson-mediated electron-electron interactions is described. The theory is based on the exact semiclassical expression for the coupling between valence electrons and electromagnetic fields and on the self-consistent Bethe--Salpeter equations for the electron-hole propagators. The general diagrammatic perturbation expressions for the intraband and interband single-particle conductivity are determined. The relations between the intraband Bethe--Salpeter equation, the quantum transport equation and the ordinary transport equation are briefly discussed within the memory-function approximation. The effects of the Lorentz dipole-dipole interactions on the dynamical conductivity of low-dimensional $sp_\alpha$ models are described in the same approximation. Such formalism proves useful in studies of different (pseudo)gapped states of quasi-one-dimensional systems with the metal-to-insulator phase transitions and can be easily extended to underdoped two-dimensional high-$T_c$ superconductors., Comment: 13 pages, 10 figures

The role of the oxygen degree of freedom in the cuprates' superconducting planes is analyzed in detail. Structural and photoemission results are reviewed to show that the most sparse description of the in-plane electronic states requires explicit control of the oxygens. For metallic states, the relative contributions of oxygen and copper vary along the Fermi surface, with the arc metallicity dominantly oxygen-derived. For the magnetic responses, we find that the observed incommensurability arises naturally if one keeps separate the roles of the two sites. For the charge order in LBCO, we propose a scenario, based on magnetic interactions in the plane. We stress the need for further experimental investigations of the evolution of the intracell charge distribution with doping, and for a better theoretical understanding of the large particle-hole-symmetry breaking required for successful phenomenologies, but difficult to reconcile with ab initio calculations., Comment: Invited talk at Superstripes-2012, Erice, final version as accepted by the Journal of Superconductivity and Novel Magnetism - some references corrected

A large-Ud theory is constructed for the metallic state of high-Tc cuprates. The Emery three-band model, extended with Ox-Oy hopping tpp, and with Ud tending to infinity, is mapped on slave fermions. The Dyson time-dependent diagrammatic theory in terms of the Cu-O hopping tpd, which starts from the nondegenerate unperturbed ground state, is translationally and asymptotically locally gauge invariant. The small parameter of the theory is nd. The lowest order of the theory generates the single particle propagators of the hybridized pdp- and dpd-fermions with the exact three band structure. The leading many-body effect is band narrowing, obtained without mean-field slave particle approximations. Damping found in the single particle propagation is related to incoherent Cu-O2 intracell "mixed valence" fluctuations. The corresponding continuum falls below the Fermi level. The conventional Luttinger sum rule for coherent bands is thus broken. Due to local gauge invariance, these results are insensitive to the replacement of the Cu-O anticommutations by commutations. This replacement affects the effective local kinematic repulsion Ud\mu\ between the hybridized pdp hole propagators. The a posteriori antisymmetrization of Ud\mu\ removes the repulsion between the pdp particles in the triplet configuration, keeping their singlet repulsion intact. Such a Ud\mu\ is moderate, and close to optimal doping favors the coherent, antinodal, low energy SDW correlations. Resonant valence bonds which involve Jpd appear as incoherent perturbative corrections to these correlations. In function of doping and/or frequency, the incoherent "mixed valence" fluctuations compete with magnetic coherence. This dichotomy, between properties local in the direct and reciprocal space, is the fundamental feature of the Emery model in the large Ud metallic limit., Comment: 29 pages, 18 figures

The single bipolaron problem is examined in the context of the 1D Holstein-Hubbard model, emphasizing analogies and differences with respect to the complementary single polaron physics. The bipolaron band structure below the phonon threshold is revealed, showing a complex relationship between numerous excited bands as the adiabatic limit is approached. Light bipolarons with significant binding energy, the stability of large bipolarons, the small to large bipolaron crossover as a function of the Hubbard repulsion, as well as the bipolaron dissociation, are investigated in detail, disentangling adiabatic, nonadiabatic and lattice coarsening effects. It is emphasized that condensation of bipolarons occurs in the dilute limit only at very low temperatures., Comment: 12 pages, 7 figures

The large U_d theory, based on the Emery three band model extended with the Ox-Oy hopping t_pp, is constructed for the metallic state of high-Tc cuprates, using the mapping on the slave fermion theory. The time-dependent diagrammatic theory in terms of the Cu-O hopping t_pd starts from the locally gauge invariant state with vanishing occupation of the Cu state and builds a finite n_d in higher orders. This theory is locally gauge invariant asymptotically, but replaces the d-p anticommutation between the Cu and O sites by the commutation and is antisymmetrized a posteriori. Rather than t_pd, the small parameter of the theory is n_d less or equal to 1/2. The leading many body effect is band narrowing, different from the mean-field one. It is accompanied by the d10-d9 intracell charge transfer disorder, which breaks the Luttinger sum rule for the conduction band. The corresponding damping of the single particle propagation is situated well below the Fermi level. The effective local repulsions between the hybridized pdp propagators show up beyond the third order. The a posteriori antisymmetrization removes the triplet repulsion between the pdp particles but keeps the singlet repulsion which favors incommensurate SDW correlations at low energy. Such repulsion is the metallic counterpart of the superexchange J_pd between the dpd propagators. Resonant valence bonds thus appear as perturbative corrections. The resulting theory is shown to compare favorably with numerous experiments, emphasizing the physical importance of the oxygen degrees of freedom., Comment: 31 pages, 14 figures

Atomic repulsion $U_d$ on the Cu site in high T$_c$ cuprates is large but, surprisingly, some important properties are consistent with moderate couplings. The time dependent perturbation theory with slave particles is therefore formulated in the $U_d\to\infty$ limit for the metallic phase in the physically relevant regime of the three-band Emery model. The basic theory possesses the local gauge invariance asymptotically but its convergence is fast when the average occupation of the Cu-site is small. The leading orders exhibit the band narrowing and the dynamic Cu/O$_2$ charge transfer disorder. The effective local repulsion between particles on oxygen sites is shown to be moderate in the physical regime under consideration. It enhances the coherent incommensurate SDW correlations. The latter compete with the Cu/O$_2$ charge transfer disorder, in agreement with basic observations in high T$_c$ cuprates., Comment: 4 pages, 2 figures

The behavior of the 1D Holstein polaron is described, with emphasis on lattice coarsening effects, by distinguishing between adiabatic and nonadiabatic contributions to the local correlations and dispersion properties. The original and unifying systematization of the crossovers between the different polaron behaviors, usually considered in the literature, is obtained in terms of quantum to classical, weak coupling to strong coupling, adiabatic to nonadiabatic, itinerant to self-trapped polarons and large to small polarons. It is argued that the relationship between various aspects of polaron states can be specified by five regimes: the weak-coupling regime, the regime of large adiabatic polarons, the regime of small adiabatic polarons, the regime of small nonadiabatic (Lang-Firsov) polarons, and the transitory regime of small pinned polarons for which the adiabatic and nonadiabatic contributions are inextricably mixed in the polaron dispersion properties. The crossovers between these five regimes are positioned in the parameter space of the Holstein Hamiltonian., Comment: 19 pages, 9 figures

The translationally invariant diagrammatic quantum perturbation theory (TPT) is applied to the polaron problem on the 1D lattice, modeled through the Holstein Hamiltonian with the phonon frequency omega0, the electron hopping t and the electron-phonon coupling constant g. The self-energy diagrams of the fourth-order in g are calculated exactly for an intermittently added electron, in addition to the previously known second-order term. The corresponding quadratic and quartic corrections to the polaron ground state energy become comparable at t/omega0>1 for g/omega0~(t/omega0)^{1/4} when the electron self-trapping and translation become adiabatic. The corresponding non adiabatic/adiabatic crossover occurs while the polaron width is large, i.e. the lattice coarsening negligible. This result is extended to the range (t/omega0)^{1/2}>g/omega0>(t/omega0)^{1/4}>1 by considering the scaling properties of the high-order self-energy diagrams. It is shown that the polaron ground state energy, its width and the effective mass agree with the results found traditionally from the broken symmetry side, kinematic corrections included. The Landau self trapping of the electron in the classic self-consistent, localized displacement potential, the restoration of the translational symmetry by the classic translational Goldstone mode and the quantization of the polaronic translational coordinate are thus all encompassed by a quantum theory which is translationally invariant from the outset., Comment: 10 pages, 5 figures

We study the effect of antiferromagnetic correlations in the three-band Emery model, in comparison with the experimental angle-resolved photoemission (ARPES) spectra in optimally doped NCCO. The same calculation, formerly used to describe BSCCO, is relevant here, but in contrast to BSCCO, where quantum paramagnon fluctuations are important, the characteristic energy of the dispersive paramagnons in NCCO is of the order of Tc. The wide dispersing features of the single-electron spectrum in NCCO are analogous to the BSCCO hump. The Fermi surface is pseudogapped in both the nodal and antinodal directions, although the detailed features differ, being dominated by loss of intensity in the nodal direction, and loss of coherence in the antinodal one. Direct oxygen-oxygen hopping is important in NCCO as well as in BSCCO, in order to obtain overall agreement with the measured ARPES spectra., Comment: Final version as accepted in PRB(RC), one paragraph added, 4 pages, 3 figures

We study the effect of antiferromagnetic (AF) correlations in the three-band Emery model, with respect to the experimental situation in weakly underdoped and optimally doped BSCCO. In the vicinity of the vH singularity of the conduction band there appears a central peak in the middle of a pseudogap, which is in an antiadiabatic regime, insensitive to the time scale of the mechanism responsible for the pseudogap. We find a quantum low-temperature regime corresponding to experiment, in which the pseudogap is created by zero-point motion of the magnons, as opposed to the usual semiclassical derivation, where it is due to a divergence of the magnon occupation number. Detailed analysis of the spectral functions along the (pi,0)-(pi,pi) line show significant agreement with experiment, both qualitative and, in the principal scales, quantitative. The observed slight approaching-then-receding of both the wide and narrow peaks with respect to the Fermi energy is also reproduced. We conclude that optimally doped BSCCO has a well-developed pseudogap of the order of 1000 K. This is only masked by the narrow antiadiabatic peak, which provides a small energy scale, unrelated to the AF scale, and primarily controlled by the position of the chemical potential., Comment: Final version as accepted in EPJ B, 13 pages, 8 figures

The effect of antiferromagnetic (AF) correlations is studied in the framework of the three-band (Emery) model, with respect to experiments in BSCCO. We study the pseudogap regime with a central peak. Detailed dispersions of quasiparticle peaks show that one can simultaneously fit Fermi surfaces and ARPES leading-edge energy scales. The band parameter regime is a strong-coupling one: marked renormalization of the copper-oxygen overlap, making it smaller than the oxygen-oxygen overlap, while the copper-oxygen energy splitting is the largest of the three. The same regime was found previously in a zeroth-order fit of Fermi surfaces. The inclusion of AF correlations in a weak-coupling approach resolves the only qualitative discrepancy of the zeroth-order mean-field slave-boson calculation with experiment: it is argued that the observed large flat region of the dispersion around the vH point is due to the very non-dispersive central peak in the X-M direction. The sudden increase of the experimental one-particle dispersion in the X-M direction is explained by the quasiparticle strength shifting to the upper wing of the magnetic pseudogap, as one moves further away from the X (van Hove) point. Near it, the lower wing is predicted to be observed in the X-M direction, in addition to the narrow central peak, giving rise to a two-peaked structure below the Fermi level, as found experimentally., Comment: Contribution to M2S-HTSC in Rio, May 2003

The solution to the long standing problem of the cohesion of organic chain compounds is proposed. We consider the tight-binding dielectric matrix with two electronic bands per chain, determine the corresponding hybridized collective modes, and show that three among them are considerably softened due to strong dipole-dipole and monopole-dipole interactions. By this we explain the unusual low frequency optical activity of TTF-TCNQ, including the observed 10meV anomaly. The softening of the modes also explains the cohesion of the mixed-stack lattice, the fractional charge transfer almost independent of the material, and the formation of the charged sheets in some compounds., Comment: 7 pages, 1 figure, to be published in Europhysics Letters

In this lecture we present some interesting issues that arise when the dynamics of the charge carriers in the CuO$_2$ planes of the high temperature superconductors is considered. Based on the qualitative picture of doping, set by experiments and some previous calculations, we consider the strength of various inter and intra-cell charge transfer susceptibilities, the question of Coulomb screening and charge collective modes. The starting point is the usual p-d model extended by the long range Coulomb (LRC) interaction. Within this model it is possible to examine the case in which the LRC forces frustrate the electronic phase separation, the instability which is present in the model without an LRC interaction. While the static dielectric function in such systems is negative down to arbitrarily small wavevectors, the system is not unstable. We consider the dominant electronic charge susceptibilities and possible consequences for the lattice properties., Comment: 14 pages, 15 figures, latex, to be published in "From Quantum Mechanics to Technology", Lecture Notes in Physics, Springer

Starting from the tight-binding dielectric matrix in the random phase approximation we examine the collective modes and electron-hole excitations in a two-band electronic system. For long wavelengths (${\bf q}\rightarrow0$), for which most of the analysis is carried out, the properties of the collective modes are closely related to the symmetry of the atomic orbitals involved in the tight-binding states. In insulators there are only inter-band charge oscillations. If atomic dipolar transitions are allowed, the corresponding collective modes reduce in the asymptotic limit of vanishing bandwidths to Frenkel excitons for an atomic insulator with weak on-site interactions. The finite bandwidths renormalize the dispersion of these modes and introduce a continuum of incoherent inter-band electron-hole excitations. The possible Landau damping of collective modes due to the presence of this continuum is discussed in detail., Comment: 25 pages, LaTeX, to appear in Z.Phys. B

The screened electron-electron interaction in a multi-band electron system is calculated within the random phase approximation and in the tight-binding representation. The obtained dielectric matrix contains, beside the usual site-site correlations, also the site-bond and bond-bond correlations, and thus includes all physically relevant polarization processes. The arguments are given that the bond contributions are negligible in the long wavelength limit. We analyse the system with two non-overlapping bands in this limit, and show that the corresponding dielectric matrix reduces to a $2\times2$ form. The intra-band and inter-band contributions are represented by diagonal matrix elements, while the off-diagonal elements contain the mixing between them. The latter is absent in insulators but may be finite in conductors. Performing the multipole expansion of the bare long-range interaction, we show that this mixing is directly related to the symmetry of the atomic orbitals participating in the tight-binding electronic states. In systems with forbidden atomic dipolar transitions, the intra-band and inter-band polarizations are separated. However, when the dipolar transitions are allowed, the off-diagonal elements of the dielectric matrix are of the same order as diagonal ones, due to a finite monopole-dipole interaction between the intra-band and inter-band charge fluctuations., Comment: 32 pages, LaTeX, to appear in Z.Phys. B

The effect of the charge fluctuations on the electronic spectrum and the Raman spectrum of high temperature superconductors is examined within the slave boson approach. Instead of using the saddle point approximation for slave bosons, we confine ourselves to the non-crossing approximation (NCA) in summing the diagrams for the Green functions, thus obtaining the renormalized hole spectrum and its lifetime on equal footing. The electronic Raman spectrum is calculated, showing the characteristic featureless behaviour up to the frequency of the order of renormalized $\Delta_{pd}$ parameter. The dependence on the polarization of the incident and the scattered light agrees with experiments., Comment: 4 pages plus 3 compressed & uuencoded eps figures, LATEX 2.09, published in Physica C 235-240 (1994) 2265-2266, proceedings from the M2S-HTSC IV conference

The effect of the charge fluctuations on the electronic and Raman spectrum of high temperature superconductors is examined, using the slave boson approach to the large Coulomb repulsion $U_d$ on the copper site. Instead of the saddle point approximation $\srv{b}\ne 0$ for the slave boson, characteristic for various $N\ide\infty$ approaches, we confine ourselves to the non-crossing approximation (NCA) diagrams for the Green functions. In this way the effects of charge fluctuations and of the constraint of no double occupancy on the copper site on the shape of the electronic spectrum are studied primarily, while the slave boson diagrams responsible for copper-copper spin correlations are intentionally not included. The novel feature of the charge fluctuation dynamics shows up in the slave boson spectrum as the plateau extending over the range of 1eV below $\omega=0$. This is further reflected in the electronic Raman spectrum that we calculate for various combinations of the polarization of the incoming and scattered light. The Raman spectrum shows the characteristic featureless behaviour up to frequencies of the order of 1eV while the polarization dependence is also in qualitative agreement with experiment., Comment: 20 pages plus 9 compressed & uuencoded ps figures, LATEX 2.09, published in Physica C 241 (3-4, JAN 15 1995)

Starting from the random phase approximation for the weakly coupled multiband tightly-bounded electron systems, we calculate the dielectric matrix in terms of intraband and interband transitions. The advantages of this representation with respect to the usual plane-wave decomposition are pointed out. The analysis becomes particularly transparent in the long wavelength limit, after performing the multipole expansion of bare Coulomb matrix elements. For illustration, the collective modes and the macroscopic dielectric function for a general cubic lattice are derived. It is shown that the dielectric instability in conducting narrow band systems proceeds by a common softening of one transverse and one longitudinal mode. Furthermore, the self-polarization corrections which appear in the macroscopic dielectric function for finite band systems, are identified as a combined effect of intra-atomic exchange interactions between electrons sitting in different orbitals and a finite inter-atomic tunneling., Comment: 20 pages, LaTeX, no figures