Coherent motion of a hole in the copper-oxygen planes of high-temperature superconductors

The dispersion relation for the coherent propagation of a hole moving in a two-dimensional (CuO₂) _N system is discussed. The (CuO_2)N planes constitute the most important structural element in the high-T _c superconducting materials. The system is described by the Kondo-Heisenberg Hamiltonian, which is a simplified version of the extended Hubbard or Emery model. The calculations are based on the introduction of a trial wave function in the unitary space of the Cu spins and the O degrees of freedom. They generalize an approach recently proposed for the coherent motion of a hole in thet-J model. The propagation is mainly determined by the spin-fluctuation part of the superexchange between the copper spins. Minor contributions to the coherent hole motion are due to an effective tunneling of the hole to second and third nearest neighbors along spiral paths in the (CuO₂) _N plane. This mechanism can be considered as the analogue of a mechanism for coherent hole motion in thet-J model first discussed by Trugman. For the dispersion relation a cosine-band-like form is found similar to that for thet-J model. The band width, however, is somewhat increased. Except for this difference, our results seem to support the point of view of Zhang and Rice, who have claimed that there exists a one-to-one mapping between the low-lying states of the two-band model and the effectivet-J model.     

Unitary transformation treatment of a single hole in an Ising antiferromagnet

The behavior of a single hole in a two-dimensional Ising antiferromagnet (t-J ^z model), is studied in the generalized Dyson-Maleev representation, where the spins are mapped on boson operators and the hole is described as a spinless fermion. The formal similarity with Fröhlich's polaron Hamiltonian suggests that thet-J ^z model can be approximately diagonalized by means of two successive unitary transformations, analogous to those used by Lee, Low, and Pines in their intermediate-coupling treatment of the polaron. Our approach yields an upper bound to the exact ground state energy, as well as the corresponding ground state eigenvector. Fork=0 our energy bound is remarkably close to the result of the self-consistent Born approximation over a wide range of the coupling parameter, which includes the range typically assumed for the high-T _c materials. The ground state eigenvector is used to calculate the spatial distribution of bosons (spin deviations) surrounding the hole. Here our results are qualitatively very similar to those obtained in previous work, showing that our ground state eigenvector accounts quite well for the small size of the “spin polaron” in thet-J ^z model.     

Physical manifestations of valence-bond structures in correlated systems

Using the Hubbard model and the corresponding t-J model, we study the properties of correlated states with valence-bond structures. Mixed states with such structures and with antiferromagnetic spin ordering can be constructed by means of local unitary transformations of uncorrelated states. The latter turn out to have lower energy than mean-field antiferromagnetic solutions. Spin correlations for various degrees of doping δ=n−1 are in good agreement with the results of exact calculations for finite systems. In contrast to mean-field solutions, allowance for valence-bond correlations leads to a reasonable value of the critical δ, at which long-range antiferromagnetic order disappears. A calculation of the spectral functions that describe photoemission reveals typical behavior in two bands of effective hole (and electron) excitations, and energy transport in bands as the quasimomentum varies from (0,0) to (π,π), consistent with calculations in finite systems. We construct a homogeneous correlated state of fluctuating valence bonds (the band-model analog of states of fluctuating valence bonds), and demonstrate that its energy is lower than that of valence-bond alternant structures. Zh. éksp. Teor. Fiz. 112, 1409–1429 (October 1997)     

Effective Hubbard model for Zn-doped CuO2 plane

In the framework of the cell-perturbation method for the original p-d model an effective two-band Hubbard model for the CuO₂ plane with Zn impurities is derived. Zn impurities are modelled by Wannir oxygen one-hole states at vacant Cu sites. The model is based on the results of band structure calculations carried out within the local-density approximation. Further reduction to an extended t-J model shows a large ferromagnetic superexchange interaction between the Cu spin with the nearest virtual oxygen spin in the Zn cell. Received 17 November 1998     

Theory of the electronic structure and spin susceptibility of La2−x SrxCuO4

We solve the problem of the effect of strong electron correlations on the homogeneous spin susceptibility of current carriers in CuO₂ planes. We show that the dependence of the spin susceptibility χ(T) of high-T _c superconductors of the La_2−x Sr_xCuO₄ type on temperature and the doping index x can be explained fairly well by the two-band model suggested earlier (the singlet-correlated oxygen band plus the lower Hubbard band of copper). The model has features in common with the phenomenological t-J model but cannot be reduced to the latter completely. In contrast to the t-J model, the density of states of the oxygen holes has a peak near the bottom of the band. It is the presence of this peak together with the non-Fermi-liquid properties that explain the unusual behavior of the spin susceptibility of La_2−x Sr_xCuO₄. Zh. éksp. Teor. Fiz. 112, 1763–1777 (November 1997)     

Influence of spin fluctuations in the ground state on the coherent motion of holes in high-T c superconductors

The coherent two-dimensional motion of a hole generated in a high-T _c superconductor at half-filling is discussed. The system is described by thet-J model which reduces to the Heisenberg antiferromagnet (HAF) at half-filling. Special attention is payed to the influence of spin fluctuations in the ground state on the hole motion. Spin fluctuations can be considered as deviations of the true ground state of the Heisenberg antiferromagnet from the Néel state. The calculations are based on the introduction of a new trial wave function. It generalizes a wave function which was originally proposed by Shraiman and Siggia for the hole motion in the Néel state. As a result, we find that the excitation energy for the hole has a bandwidth which is reduced by a factor 0.7 as compared to the case without spin fluctuations. Moreover, the dispersion relation contains cubic harmonics which are due to effective hopping processes to more distant than second-or third-nearest neighbors. For larger values of the ratiot/J the band is substantially deformed. We compare our theory with results obtained from the exact diagonalization of finite clusters and find good agreement.     

Exchange and spin-fluctuation mechanisms of superconductivity in cuprates

A microscopic theory of superconductivity is considered in the framework of the Hubbard p-d model for the CuO₂ plane. The Dyson equation is derived in the nonintersecting diagram approximation using the projection technique for the matrix Green function of the Hubbard operator. The solution of the equation for the superconducting gap shows that interband transitions for Hubbard subbands lead to antiferromagnetic exchange pairing as in the t-J model, while intraband transitions additionally lead to spin-fluctuation pairing of the d-wave type. The calculated dependences of the superconducting transition temperature on the hole concentration and of the gap on the wave vector are in qualitative agreement with experiments.     

Coherent motion of a hole in a two-dimensional quantum antiferromagnet

The dispersion relation for the coherent propagation of a hole moving in a two-dimensional quantum antiferromagnet is discussed. The system is described by two model Hamiltonians, thet-J model and thet-t-J model, which have been used frequently to discuss strong electron-correlation effects present in high-T _c superconductors. The calculations are based on the introduction of a new wave function which is constructed by use of equations derived by Shraiman and Siggia. The different mechanisms for the coherent propagation, which are due to the spin fluctuation and the hopping terms of the Hamiltonian, are treated on the same footing. As a result of the inclusion of an effective hopping mechanism along spiral paths-first discussed by Trugman-the minimum of the band is somewhat changed compared to results recently obtained in the literature. For large values of the ratiot/J an inversion of the whole dispersion relation occurs. The overall shapes of the dispersion within both models are found to agree quite well, though for small values oft/J the bandwidth within thet-J model becomes significantly smaller than that of thet-t-J model.     

Spin waves and static susceptibility in the weakly doped t-J model

We investigate the spin dynamics in weakly doped high-temperature superconductors. The system is described by the two-dimensional t-J model. Our focus is on the interaction between mobile holes and spin waves. The calculations are based on a recently introduced cumulant method for computing the ground state energy of correlated electronic systems. Contrary to previous works using dynamical quantities like correlation functions or spectral densities our approach contains a static view to the system. This new method treats spin and hole dynamics on the same basis and allows for the calculation of static and dynamical quantities. We present results for spin-wave energies and transverse static susceptibilities for small hole concentrations and various values of t/J. We find a strong renor-malization of the spin-wave energies due to the spin-hole interaction. In agreement with neutron scattering experiments the spin-wave velocity vanishes at a critical hole density of a few percent which is equivalent to the instability of the antiferromagnetic order.     

Perovskites in high dimensions

We study the (D+1) band Hubbard model on generalizedD-dimensional perovskite structures. We show that in the limit of high dimensions the possible scaling behaviour is uniquely determined via the bandstructure and that the model without direct oxygen-oxygen hopping necessarily scales to the cluster limit. A 1/dimension expansion then leads to at-J like Hamiltonian and the Zhang-Rice analysis becomes rigorous. The large dimension fixed point, in general, still remains the cluster model even when a hopping term between n.n. oxygensites is included. Only for a unique ratio of the oxygen onsite energies to the oxygen-oxygen hopping amplitude is a new fixed point possible, corresponding to a heavy-Fermion Hamiltonian.     

On the spectral function of a hole in a one-dimensional quantum antiferromagnet

We discuss the spectral function of a single hole moving in a one-dimensional quantum antiferromagnet. The latter is described by an anisotropic version of thet-J model, wheret is the hopping matrix element. We introduce two independent coupling parametersJ andJ for the Ising and the transverse part of the Heisenberg exchange. Strong electronic correlations which are incorporated in the model prevent the use of usual diagrammatic techniques for dynamic Green functions based on Wick's theorem. For that reason a new projection technique for general correlation functions in terms of cumulants is used. We consider the case of max. For the case of small transverse coupling relative to the Ising part, we give exact expressions for the one hole correlation function. In the limit of vanishing spin fluctuations our result reduces to earlier calculations of the motion of a hole in a one-dimensional Néel state. However, the inclusion of the spin fluctuations leads to drastic modifications of the spectral function.     

Properties of the t-J model in the dynamical mean field theory: One-particle properties in the antiferromagnetic phase

We study the one-particle properties of the t-J model within the framework of Vollhardt's dynamical mean field theory. By introducing an AB-sublattice structure we explicitly allow for a broken symmetry for the spin degrees of freedom and are thus able to calculate the one-particle spectral function in the antiferromagnetic phase. We observe surprisingly rich structures in the one-particle density of states for T < T _N at finite doping up to 15%. These structures can be related to the well known results for one single hole in the Néel background. We are thus able to establish the relevance of this at a first sight academic limit to physical properties of the t-J model with a finite density of holes in the thermodynamical limit.     

Antiferromagnetism in the Hubbard model

The energy spectrum of the two-sublattice Hubbard model is obtained in the static-fluctuation approximation. It is shown how the structure of the energy spectrum is modified as the parameters of the Hubbard model are varied. The ground state of the simple Hubbard model of dimension d=2 is the dielectric antiferromagnetic state. The author derives a consistency equation for the magnetization, which has an antiferromagnetic solution. Fiz. Tverd. Tela (St. Petersburg) 39, 1594–1599 (September 1997)     

Filling dependence of correlation exponents and metal-Mott insulator transition in strongly correlated electron systems

Using a universal relation between electron filling factor and ground state energy,this paper studies the dependence of correlation exponents on the electron filling factor of one-dimensional extended Hubbard model in a strong coupling regime,and demonstrates that in contrast to the usual Hubbard model(gc = 1/2),the dimensionless coupling strength parameter g c heavily depends on the electron filling,and it has a "particle-hole" symmetry about electron quarter filling point.As increasing the nearest neighbouring repulsive interaction,the single particle spectral weight is transferred from low energy to high energy regimes.Moreover,at electron quarter filling,there is a metal-Mott insulator transition at the strong coupling point gc = 1/4,and this transition is a continuous phase transition.     

Anisotropic scattering rates and antiferromagnetic precursor effects in the t-t'-U Hubbard model

We have investigated the evolution of the electronic properties of the t-t'-U Hubbard model with hole doping and temperature. Due to the shape of the Fermi surface, scattering from short wavelength spin fluctuations leads to strongly anisotropic quasi-particle scattering rates at low temperatures near half-filling. As a consequence, significant variations with momenta near the Fermi surface emerge for the spectral functions and the corresponding ARPES signals. At low doping the inverse lifetime of quasiparticles on the Fermi surface is of order varying linearly in temperature from energies of order t down to a very low energy scale set by the spin fluctuation frequency while at intermediate doping a sub-linear T-dependence is observed. This behavior is possibly relevant for the interpretation of photoemission spectra in cuprate superconductors at different hole doping levels. Received 31 July 2000     

On the possibility of binding of two holes in an antiferromagnetic state

The energy of a pair of holes in a half-filled 2—d Hubbard model is studied assuming an antiferromagnetic spin configuration. By comparing with the energy of a single hole, we discuss the possibility of pairing of holes in connection with the recently discovered highT _c superconductivity.     

Pairing mechanism in the doped Hubbard antiferromagnet: the 4×4 model as a test case

We introduce a local formalism, in terms of eigenstates of number operators, having well defined point symmetry, to solve the Hubbard model at weak coupling on a N × N square lattice (for even N). The key concept is that of W = 0 states, that are the many-body eigenstates of the kinetic energy with vanishing Hubbard repulsion. At half filling, the wave function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. Further, we state a general theorem which allows to find all the W = 0 pairs (two-body W = 0 singlet states). We show that, in special cases, this assigns the ground state symmetries at least in the weak coupling regime. The N = 4 case is discussed in detail. To study the doped half filled system, we enhance the group theory analysis of the 4×4 Hubbard model introducing an Optimal Group which explains all the degeneracies in the one-body and many-body spectra. We use the Optimal Group to predict the possible ground state symmetries of the 4×4 doped antiferromagnet by means of our general theorem and the results are in agreement with exact diagonalization data. Then we create W = 0 electron pairs over the antiferromagnetic state. We show analitycally that the effective interaction between the electrons of the pairs is attractive and forms bound states. Computing the corresponding binding energy we are able to definitely predict the exact ground state symmetry. Received 24 October 2000     

Excitation spectrum of one-dimensional extended ionic Hubbard model

We use perturbative continuous unitary transformations (PCUT) to study the one dimensional extended ionic Hubbard model (EIHM) at half-filling in the band insulator region. The extended ionic Hubbard model, in addition to the usual ionic Hubbard model, includes an inter-site nearest-neighbor (n.n.) repulsion, V. We consider the ionic potential as unperturbed part of the Hamiltonian, while the hopping and interaction (quartic) terms are treated as perturbation. We calculate total energy and ionicity in the ground state. Above the ground state, (i) we calculate the single particle excitation spectrum by adding an electron or a hole to the system; (ii) the coherence-length and spectrum of electron-hole excitation are obtained. Our calculations reveal that for V = 0, there are two triplet bound state modes and three singlet modes, two anti-bound states and one bound state, while for finite values of V there are four excitonic bound states corresponding to two singlet and two triplet modes. The major role of on-site Coulomb repulsion U is to split singlet and triplet collective excitation branches, while V tends to pull the singlet branches below the continuum to make them bound states.     

Ferromagnetism in the Hubbard model: Spin waves and instability of the Nagaoka state

We discuss two single spin flip variational wave functions describing spin wave excitations which were proposed earlier by Shastry, Krishnamurthy and Anderson (SKA) and by Basile and Elser (BE), respectively, in order to investigate the instability of the fully polarized ferromagnetic state (Nagaoka state) in the infinite U Hubbard model. We calculate the energy of these variational states for the square lattice and for multiple chains. At the zone boundary in the vicinity of the point (0, π) the spin wave energy is reduced substantially by the binding of the spin up hole to the flipped down spin. For the square lattice this leads to a critical hole density of δ_cr = 0.407 for the SKA spin wave and of δ_cr = 0.322 for the BE spin wave which implies remarkable improvements in comparison to the corresponding scattering states investigated previously.     

Crystallization of electrons confined to a lattice

A necessary condition for electron crystallization is the dominance of the electronic Coulomb repulsion as compared with the kinetic energy. We show that 4f systems are good candidates for electron or hole crystallization to occur since the small radius of the 4f shell leads to small hybridizations and hence kinetic energy of the f electrons. Crystallization may take place in lattices with several equivalent 4f sites per unit cell when the electron or hole number is less than the number of sites. We give evidence that charge ordering in Yb₄As₃ is an example of the mechanism considered here. We also compare it with those considered by Wigner, Verwey, Mott and Hubbard.