Recent scanning tunneling microscopy measurements which indicate the formation of two-dimensional density modulations at some doping levels in cuprates were reviewed. A model of hard-core bosons which represent bound hole pairs in the two-dimensional doped antiferromagnet was discussed in the context of these experimental results. By means of an exact numerical diagonalization it was shown that the Coulomb repulsion between bosons brings about the formation of charge modulations.
In this paper we focus on the anomalous temperature dependence of the in-plane conductivity and symmetry mixing of the superconducting order parameter observed in various experiments on cuprates. We show that the one-band Hubbard model is not capable of describing the physics of cuprates because the kinetic energy is lowered in this model in the superconducting state, which contradicts experimental observations. The proper model to investigate doped, short-range antiferromagnets is the t-J model, for which our results agree with experiments. We analyze a spin polaron model, that is an effective model for a doped antiferromagnet. In the framework of this model we also study the superconducting order-parameter symmetry-mixing phenomenon. We show that the expected mixing of d-wave symmetry with p-wave symmetry takes place in the superconducting order-parameter at a finite value of the doping parameter. This symmetry mixing brakes the time-reversal symmetry.
The investigation of single-electron spectrum of the Hubbard model with local lattice anharmonicity is performed. The influence of the interaction with the vibrational subsystem on the effective exchange constant is considered. The static transverse dielectric susceptibility of the model is calculated. Analysis of the possible dielectric anomalies is performed on this basis.
We argue that three gaps observed in underdoped cuprates can be attributed to the formation of antiferromagnetic spin polarons and bipolarons. Within the spin polaron scenario the antinodal pseudogap at he high energy scale originates from the change of the Fermi surface topology, induced by antiferromagnetic correlations. That change gives rise to the diminishing of the spectral weight at the antinodal region near the Brillouin zone boundary. We demonstrate that effect by analyzing effective models of doped antiferromagnets. The second type of pseudogap appearing at the intermediate energy scale originates from the phenomena which are precursory to superconductivity and predominantly concern the portion of the Fermi surface near the nodal region. In order to analyze the latter phenomenon we use the negative U Hubbard model, in which many details typical to spin polaron physics are neglected, but which contains the essential ingredient of it, that is the strong short range attraction. The lowest energy scale is related to the true superconducting gap which develops with doping, although both types of pseudogap diminish with doping. This behavior can be explained by the fact that the spin polaron band is empty in the undoped system and therefore the formation of the superconducting state in the system is forbidden. Due to a pedagogical character of this report, we present in the introduction a short overview of mostly recent experimental results which are related to the gap-pseudogap physics.
We apply the concept of statistical spin liquid, in which the doubly occupied quasimomentum configurations {|k⇅⟩} for quasiparticles are excluded from the Fock space, to a planar superconductor with real space pairing. The results compare very well with experimental data for the cuprates, namely (i) the condensed state appears only for the number of holes 0 < δ < 0.15-0.25; (ii) the temperature dependence of the gap is close to the BCS result, but the gap has systematically lower value and is of an extended s-wave form.
The three-band Emery model, describing the holes in the CuO_{2} planes of the high-temperature superconducting oxides, is considered. The model includes the direct oxygen-oxygen hopping integral t_{pp}. The exact Bogolyubov transformation is used to exclude one oxygen band and obtain a two-dimensional Anderson model. Afterward, the effective Hamiltonian is obtained by eliminating the second oxygen band with the use of two approximate canonical transformations. The effective Hamiltonian describes the spins residing on the copper sites and interacting through an indirect interaction J_{SX}(R), where R is the distance between two copper ions. J_{SX}(R) depends on the doping rate δ and is a decaying function of R. Numerical results for J_{SX}(R) are given for different doping rates δ for the case of parabolic bands. The obtained interaction J_{SX}(R), when added to the original antiferromagnetic interaction (present in oxides at δ = 0), might lead to a frustration of the long-range antiferromagnetic ordering upon doping.
High T_{c} cuprate superconductors are characterized by two robust features: their strong electronic correlations and their intrinsic dynamical local lattice instabilities. Focusing on exclusively that latter, we picture their parent state in form of a quantum vacuum representing an electronic magma in which bound diamagnetic spin-singlet pairs pop in and out of existence in a Fermi sea of itinerant electrons. The mechanism behind that resides in the structural incompatibility of two stereo-chemical configurations Cu^{II}O₄ and Cu^{III}O₄ which compose the CuO₂ planes. It leads to spontaneously fluctuating Cu-O-Cu valence bonds which establish a local Feshbach resonance exchange coupling between bound and unbound electron pairs. The coupling, being the only free parameter in this scenario, the hole doping of the parent state is monitored by varying the total number of unpaired and paired electrons, in chemical equilibrium with each other. Upon lowering the temperature to below a certain T*, bound and unbound electron pairs lock together in a local quantum superposition, generating transient localized bound electron pairs and a concomitant opening of a pseudo-gap in the single-particle density of states. At low temperature, this pseudo-gap state transits via a first order hole doping induced phase transition into a superconducting state in which the localized transient bound electron pairs get spatially phase correlated. The mechanism driving that transition is a phase separation between two phases having different relative densities of bound and unbound electron pairs, which is reminiscent of the physics of ⁴He-³He mixtures.
We study the peculiarities of coherency in the superconductivity of two-orbital system. The superconducting phase transition is caused here by the on-site intra-orbital attractions (negative-U Hubbard model) and inter-orbital pair-transfer interaction. The dependencies of critical and non-critical correlation lengths on interaction channels and band fillings are analyzed.
We consider precursor effects of the superconducting order which possibly show up in the normal state of high temperature superconducting materials. The local pairs of electrons or holes are formed there well above the transition temperature T_c. Due to strong quantum fluctuations the single particle density of states can be partly depleted near the Fermi energy leading to the pseudogap. We claim that this feature should go hand in hand with emergence of the Bogoliubov-type quasiparticles. In the normal state they are expected to be damped and acquire the long lifetime upon passing T_c. These Bogoliubov-type quasiparticles may nevertheless become correlated on a finite spatial and temporal scale. We discuss how such short-range pair correlations can be detected experimentally.
The mechanism of superconductivity generation by spin fluctuations in the electron doped canted antiferromagnet on the triangular lattice was analyzed. The underlying assumption is that the formation of the bound state is the prerequisite of pairing. The outcome of this analysis is also valid if an additional isotropic attraction is active but the anisotropic spin-fluctuation mediated force decides on the symmetry of the two-particle bound state. When the canted antiferromagnetic state is generated, the symmetry of the point group C_{6v} for the triangular lattice is lowered to the symmetry of C_{3v}. It is demonstrated that spin fluctuations definitely favor the p-wave bound state, which transforms according to the E representation of C_{3v}. Since the inversion is not an element of C_{3v}, the parity is not a good quantum number and thus the predicted paired state will be a mixture of singlet and triplet. Such a scenario may be relevant to physics of superconducting triangular cobaltates or organics.
We study the extended Hubbard model with on-site density-density U and intersite pair hopping J interactions, i.e. the Penson-Kolb-Hubbard model. This report focuses mainly on the properties of the model at T ≥q 0 in the case of repulsive J (J < 0) which may stabilize superconductivity with η-pairing. The analysis is performed within the (broken symmetry) Hartree-Fock approximation for arbitrary interaction parameters (J < 0 and U) and electron concentration (0 < n < 2) on the d = 2 square lattice. The phase diagrams of the model at T=0 and at finite temperatures are examined taking into account magnetic and charge-ordered phases and superconducting states with η- and s-wave pairing.
The electron photoemission spectra of valence bands and core-level states of manganese perovskite La_{0.67}Pb_{0.33}(Mn_{1-x}Fe_{x})O_{3} with x = 0, 0.01, 0.03, 0.06, 0.10 and 0.15 were measured by the X-ray and Ultraviolet Photoemission Spectroscopy (XPS and UPS) below and above the metal-insulator transition. From analysis of the Mn 2p core-level spectra the ratio Mn^{3+}/Mn^{4+} was calculated as a function of the iron content. Comparison of the valence band spectrum with band structure calculations and with the high-resolution spectra measured at synchrotron radiation for Ca-, Ba- and Ce- substituted manganites revealed the strong hybridisation of Mn 3d and of O 2p states between -3 eV and -7 eV, and no estimated oxygen states between 0 eV and -2 eV where the Mn-3d states play a predominant role. The composition dependent insulating energy gaps were measured at room temperature. Reasons for the behaviour were discussed taking into account previous analysis of XPS/UPS spectra of other manganese perovskites.
Starting from a uniform d-wave superconducting phase we study the energy cost due to imposed unidirectional defects with a vanishing pairing amplitude. Both renormalized mean-field theory and variational Monte Carlo calculations within the t-J model yield that the energies of inhomogeneous and uniform phases are very close to each other. This suggests that small perturbations in the microscopic Hamiltonian might lead to inhomogeneous superconducting phases in real materials as observed in recent scanning tunneling microscopy on Ca_{2-x}Na_xCuO_2Cl_2.
Motivated by the difference between the experimental phase diagram of cuprates and expectations of the t-J model, we analyze the influence of the electronic structure on superconducting state generation for small levels of doping. Following some theoretical studies of the Fermi surface for hole doped superconducting cuprates we base our calculations on the t-t'-t''-J model. We construct the spin polaron model, which is an effective model for the t-J model, and we expand it by adding the new terms related to the next neighbor hopping integrals t' and t''. In the framework of this model we study evolutions of superconducting correlation functions with doping. As a result of numerical calculations we find out that superconducting state vanishes for small levels of doping and finite values of t' and t''. This is in qualitative agreement with experimental results.
The variational canonical transformation method has been applied to the Holstein model to obtain an effective polaronic Hamiltonian, which is subsequently analyzed in the limit of a weak effective electron-electron interaction. A competition between the superconducting and charge-density wave phases has been studied in the light of strong polaronic effects. The phase diagrams illustrating the system evolution from adiabatic to anti-adiabatic limit are presented.
In the lecture the theory of spin polarons is reviewed on the basis of its analogy with the theory of lattice polarons. The energy dispersion curve for a single polaron in a two-dimensional antiferromagnetic square lattice is calculated in the self-consistent Born approximation. Also in self-consistent Born approximation the energy of a pair of interacting spin polarons is calculated. The results of calculations for realistic values of parameters of the model lead to the conclusion that pairing of spin polarons is not a likely mechanism of superconductivity in cuprates.
The purpose of this work is twofold. In the first part we describe superfluidity/superconductivity as an emergent phenomenon resulting from two-body correlations in presence of the Bose-Einstein condensation of particles. We briefly discuss the underlying mechanism for bosons as well as fermion pairs and illustrate various realizations of superfluidity emphasizing the recent examples. In the second part we study the glassy liquid of incoherent pairs which might exist above the transition temperature T_{c} in the underdoped regime of cuprate superconductors. In particular, we explore the angular variation of pseudogap within two-dimensional version of the boson-fermion model using for a quantitative analysis the projective method. We find that above T_{c} the pseudogap closes first near the nodal areas restoring there pieces (arcs) of the Fermi surface whereas remaining parts of the large Fermi surface around the antinodal points are still absent due to incoherent pairs. Upon increasing temperature the length of the Fermi arcs enlarges because the superconducting correlations are gradually suppressed. An intriguing death of Fermi surface can thus be closely related to the Bogoliubov quasiparticles whose existence in the pseudogap state has been predicted by us and confirmed recently by the angle resolved photoemission spectroscopy measurements on Bi_2Sr_2CaCu_2O_8 and La_{1.895}Sr_{0.105}CuO_4 compounds.
We study the superconducting properties of a model of coexisting itinerant carriers and local pairs with finite binding energy, taking into account the effects of Coulomb (density-density) and direct pair hopping interactions. The evolution of the phase diagrams and superfluid characteristics with electron concentration, interaction parameters and the relative position of the bands is examined. The model is found to exhibit several kinds of superconducting behaviors ranging from the BCS-like to the local-pair-like. The relevance of the obtained results to the interpretation of experimental data for the doped bismuthates (Ba_{1-x}K_xBiO_3 and BaPb_{1-x}BiO_3) is pointed out.
We use quantum billiard with many scattering centers to describe conducting electrons properties in A_{n}C_{60} crystals, where A denotes alkali metal. We focus our attention on the A_{3}C_{60} crystal, for which we calculate the band structure, density of states, and conductivity for normal electrons. Conductivity shows linear dependence on temperature in this model, which agrees well with experimental data. We also discuss consequences of our results for superconductivity mechanism in A_{3}C_{60} and possibilities of analogous approach to describe electron properties in fused fullerenes and multiply connected carbon clusters.
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