太田 幸則

Motivated by recent experimental studies on the effects of Zn and Ni impurities on transport and magnetic properties of cuprate superconductors, we examine how the electronic states of doped two-dimensional t-J model are affected by the presence of various types of an impurity site. We use an exact-diagonalization technique on small clusters to calculate the ground state properties, single-particle excitation spectra, and spin excitation spectra, where the impurity is introduced as either an immobile vacancy site simulating Zn2+ or a localized spin site with S=1/2 or 1 simulating Ni2+. Possible experimental relevance of the calculated states of doping holes is considered.

The one-particle excitation spectra and the momentum distribution functions for the periodic Anderson and Kondo Lattices in one and two dimensions and their dependence on the electron density are studied by using the exact diagonalization method with twisted boundary conditions on clusters with six and eight unit cells. We find the following: in the insulating state there exist more low-energy excitations than expected for a non-interacting system with the mixing gap, and in the metallic state the heavy fermion band is formed by reconstructing the low-energy excitations in the insulating state upon doping of carriers but not by simply shifting the Fermi level. As a result, the momentum distribution function has two characteristic momenta.

The electronic structure and excitation spectra in high-T-c superconducting cuprates are examined by using the exact diagonalization method on finite-size clusters. The low-energy electronic states are mapped onto the two-dimensional tJ model. Several excitation spectra in the tJ model are derived as functions of electron concentration and parameter (J/t) value where J is the antiferromagnetic exchange interaction between Cu spins and t is the hopping parameter of charge carriers introduced into the cuprates. The spectra are found to be in accord with those calculated in BCS theory with d(x(2) - y(2))-wave pairing.

An exact-diagonalization technique on small clusters is used to study low-lying excitations and superconductivity in the two-dimensional negative-U Hubbard model. We first calculate the Bogoliubov-quasiparticle spectrum, condensation amplitude, and coherence length as functions of the coupling strength U/t, thereby working out how the picture of Bogoliubov quasiparticles in the BCS superconductors is affected by increasing the attraction. We then define the Cooper-pair operator as a spatially extended composite boson and make a variational evaluation of its internal structure. We thereby calculate the single-particle spectral function of the Cooper pair and obtain the dispersion relation for its translational motion. The dynamical density correlation function of the pairs is also calculated. We thus demonstrate the applicability of our numerical method for gaining insight into low-lying excitations of models for the intermediate coupling superconductivity relevant to cuprate materials. © 1995 The American Physical Society.

We present an exact diagonalization study of bilayer clusters of the t-J model. Our results indicate a crossover between two markedly different regimes which occurs when the ratio J/J between interlayer and intralayer exchange constants increases: for small J/J the data suggest the development of three-dimensional antiferromagnetic correlations without appreciable degradation of the intralayer spin order and the dx2-y2 hole pairs within the planes persist. For larger values of J/J local singlets along the interlayer bonds dominate, leading to an almost complete suppression of the intralayer spin correlation and the breaking of the intralayer hole pairs. The ground state with two holes in this regime has s-like symmetry. We present data for static spin correlation function, magnetic structure factor, and spin gap. We calculate the momentum distribution and electronic spectral function of the local singlet state realized for large J/J, and show that it deviates markedly from that of a single layer, making it an implausible candidate for modeling high-temperature superconductors. © 1995 The American Physical Society.

We present an exact diagonalization study of the dynamical spin and density correlation functions in small clusters of 2D t-J model for hole dopings ≤25%. Both correlation functions show a remarkably regular, but very different, scaling with both hole density ρh and parameters t and J. The density correlation function is most consistent with that of condensed bosons in a band of width ∼t, the spin correlation function with that of fermions in a band of width ∼J. We show that the familiar spin bag scenario explains these results in a natural way. © 1995 The American Physical Society.

We report a numerical study of a bilayer t-J model, i.e., two layers of the two-dimensional t-J model weakly coupled by hopping and exchange terms and present results for the single-particle spectral function, and the optical conductivity for in-plane and out-of-plane current. The results indicate renormalized free particle behavior in the z direction, i.e., the effective z-axis hopping integral is renormalized by the in-plane quasiparticle weight. The spectral weight of the z-axis conductivity is concentrated in a dominant low-energy peak, the current correlation function can be obtained from the convolution of the single-particle Green function. © 1995 The American Physical Society.

Using a proposed numerical technique for calculating anomalous Green's functions characteristic of superconductivity, we show that the low-lying excitations in a wide parameter and doping region of the two-dimensional t-J model are well described by the picture of dressed Bogoliubov quasiparticles in the BCS pairing theory. The pairing occurs predominantly in the dx2-y2-wave channel and the energy gap has a size DELTAd congruent-to 15J-0.27J between quarter and half fillings. Opening of the superconducting gap in the photoemission and inverse-photoemission spectra is demonstrated.

Using a proposed numerical technique for calculating anomalous Green's functions characteristic of superconductivity, we show that the low-lying excitations in a wide parameter and doping region of the two-dimensional t-J model are well described by the picture of dressed Bogoliubov quasiparticles in the BCS pairing theory. The pairing occurs predominantly in the dx2-y2-wave channel and the energy gap has a size DELTAd congruent-to 15J-0.27J between quarter and half fillings. Opening of the superconducting gap in the photoemission and inverse-photoemission spectra is demonstrated.

The effective Hamiltonian which describes the magnetic properties of La2CuO4-type crystals is derived by taking into account the spin-orbit interaction. It is shown that the weak ferromagnetism is caused by the superexchange interaction through the multi-orbitals on the ligand ions. The Hamiltonian is applied to the analysis of the magnetic properties of La2CuO4-type crystals.

An exact diagonalization technique for small clusters is used to study the electronic structure of the Hubbard model with nearest-neighbor repulsive interaction. The phase diagram of the model is extracted from the calculated charge and spin correlation functions and single-particle excitation spectra. It is shown that the small Fermi surface is realized in a parameter and doping region, which may provide a complementary understanding of the large Fermi surface believed to exist in the Hubbard model.

A Comment on the Letter by W. Stephan and P. Horsch, Phys. Rev. Lett. 66, 2258 (1991). © 1994 The American Physical Society.

Effects of long-range Coulomb interaction in one-dimensional electron systems are studied. By using a quantum Monte Carlo method, we obtain that the zero-frequency wave-number dependent charge susceptibility at quarter-filling shows both 2kF and 4kF singularities, kF being the Fermi wave number, in contrast with the Hubbard model with the on-site and nearest-neighbor interactions. The results are in accord with the X-ray experiments in (NMP)x(Phen)1-x(TCNQ). The power-law exponent α in the spectral function ρ{variant}(ω) ∼ |ω|α observed in the high-resolution photoemission experiments is calculated by using the exact diagonalization method and found to increase with increasing the range of the interaction. © 1994.

An exact-diagonalization technique on small clusters is used to study excitation spectra and superconductivity in the two-dimensional t-J model. We demonstrate that the low-lying excitations in a wide parameter (J/t) and doping regions of the model are described well by the picture of dressed Bogoliubov quasiparticles within the BCS pairing theory. The pairing occurs predominantly in dx2-y2-wave channel and the energy gap has a size Δd{reversed tilde equals}0.15J-0.27J between quarter and half fillings. © 1994.

An exact-diagonalization technique on small clusters is used to study excitations and superconductivity in the two-dimensional negative-U Hubbard model. We calculate the Bogoliubov-quasiparticle spectrum, condensation amplitude, and coherence length as a function of the coupling strength ( U t), thereby working out how the picture of Bogoliubov quasiparticles in the BCS superconductors is affected by increasing the attraction U t. © 1994.

The effective spin Hamiltonians for the distorted NiO2 and CuO2 planes with low-temperature orthorhombic (LTO) and low-temperature tetragonal (LTT) structures are derived by taking into account the spin-orbit coupling and structural distortion as perturbations. We explain why the weak ferromagnetism occurs in both LTO and LTT phases for cuprates whereas it does only in the LTT phase for nickelates. The spin-wave gaps observed by neutron scattering experiments are analyzed. We find that the gaps of the in-plane and out-of-plane modes in La1.65Nd0.35CuO4 are caused, respectively, by anisotropic superexchange and direct-exchange interactions. © 1994.

Moriya's perturbation theory is applied to the distorted NiO2 and CuO2 planes, and the effective spin Hamiltonians are derived. Spin-wave theory is explored for the Hamiltonians, and the spin-wave excitations are studied for nickelates and cuprates with low-temperature orthorhombic and low-temperature tetragonal (LTT) structures. It is shown that in the cuprates the origin of the anisotropy responsible for the spin-wave gaps is different for in-plane and out-of-plane modes: i.e., anisotropic superexchange for the in-plane mode, and anisotropic direct exchange for the out-of-plane mode. This difference explains the observed structural dependence of the spin-wave gaps in La1.65Nd0.35CuO4. In nickelates, the single-ion anisotropy is solely responsible for the spin-wave gaps, which are observed in La2NiO4. We discuss the mechanism of the weak ferromagnetism; in the nickelates the Dzyaloshinski-Moriya (DM) interaction causes the weak ferromagnetism in the LTT phase where an appropriate spin configuration is prepared by the single-ion anisotropy. In the cuprates, where the single-ion anisotropy for preparing the spin configuration is absent, the DM and pseudodipolar interactions themselves determine the spin configuration: the weak ferromagnetism originates only from the competition between these two interactions. It is proposed that a multiorbital effect is essential to explain the observed weak ferromagnetism in the LTT phase of La1.65Nd0.35CuO4. © 1994 The American Physical Society.

An exact-diagonalization technique on small clusters is used to calculate the single-particle spectral function for the one-band and three-band Hubbard models. We show that the strongly momentum-dependent spectral-weight transfer induced by carrier doping leads to the evolution of the dispersion of low-energy states. The quasiparticle-like band narrowing is examined.

The dispersive electronic state emerging upon carrier-doping in cuprates, i.e., the so-called ingap state, is derived in the three-band and one-band Hubbard models by means of the exact diagonalization of finite-size clusters. The dispersive state near the charge transfer gap at half filling undergoes a strongly momentum-dependent transfer of the spectral weight by carrier doping, and evolves into the new ingap state at the edge of the gap with a free-electron-like dispersion characteristic of a large Fermi surface consistent with Luttinger's sum rule. It is shown that the extended Hubbard model with strong nearest-neighbor repulsive interaction, on the other hand, forms a small Fermi surface by carrier doping and provides a counter-example of the doped cuprates. © 1993.

The effective Hamiltonian for the CuO2 plane of high-Tc cuprates is derived by taking into account the spin-orbit interaction. A finite-size exact-diagonalization technique is applied to the Hamiltonian, and the magnetic and electronic structures of the CuO2 plane in the low-temperature orthorhombic (LTO) and low-temperature tetragonal (LTT) phases of the La2CuO4-type crystals are examined. It is shown that the contribution from the in-plane oxygen 2pz orbital perpendicular to the plane is essential for the emergence of the weak ferromagnetism in the LTO-phase La2CuO4. In the LTT phase, either the uniaxial antiferromagnetism or the weak ferromagnetism is induced, depending on how the 2pz orbital contributes to the anisotropic superexchange interaction of the single Cu-O-Cu bond. We study the dynamics of a hole in an extended t-J model, and show that the lattice distortion works to change the symmetry of the electronic ground state via the spin-orbit coupling. The effect is, however, small and seems irrelevant to the anomalous properties of La1.88Ba0.12CuO4. © 1993 The American Physical Society.

An exact diagonalization technique on small lattices is used to calculate the single-particle spectral function A (k,omega) for one- and three-band Hubbard models at various parameter values and doping rates, thereby examining the low-energy electronic structure (or in-gap state) of the doped CuO2 plane in high-T(c) superconducting cuprates. It is illustrated that, by carrier doping, the dispersive state of the charge excitation gap at half filling undergoes a strongly momentum-dependent spectral-weight transfer, and evolves into the new state with a free-electron-like dispersion that forms the in-gap state characteristic of a large Fermi surface consistent with Luttinger's sum rule. The quasiparticlelike band narrowing observed is shown to depend sensitively on the parameter values and doping rate.

An exact diagonalization technique on small lattices is used to calculate the single-particle spectral function A (k,omega) for one- and three-band Hubbard models at various parameter values and doping rates, thereby examining the low-energy electronic structure (or in-gap state) of the doped CuO2 plane in high-T(c) superconducting cuprates. It is illustrated that, by carrier doping, the dispersive state of the charge excitation gap at half filling undergoes a strongly momentum-dependent spectral-weight transfer, and evolves into the new state with a free-electron-like dispersion that forms the in-gap state characteristic of a large Fermi surface consistent with Luttinger's sum rule. The quasiparticlelike band narrowing observed is shown to depend sensitively on the parameter values and doping rate.