Fusayoshi J. Ohkawa

Ordered States in Periodic Anderson Hamiltonian with Orbital Degeneracy and with Large Coulomb Correlation

Ordered states of a periodic Anderson Hamiltonian with large Coulomb correlation and with orbital degeneracy of localized levels are theoretically investigated. When the number of f electrons is nearly one per site, and when the exchange interaction is antiferromagnetic as a whole, it is predicted that an antiferromagnetic type ordering occurs in the orbital order of localized levels at a certain low temperature accompanied by the lattice distortion due to the Jahn-Teller effect, and that a ferromagnetic or an antiferromagnetic ordering of spin, if it occurs, occurs at a lower temperature. One of the most characteristic features of this orbital ordered state is a strong coupling between orbital antiferromagnetic moments and spin ferromagnetic ones. It is tried to explain the experimental data of CeB 6 with a model that a quartet is the ground multiplet of localized levels.

Anisotropic Superconductivity in the Kondo Lattice

Various types of anisotropic superconductivity have been investigated near its transition temperature in the periodic Anderson Hamiltonian with a weak attractive interaction between the nearest neighbor f electrons. The superconductivity with the s -, p - or d γ-symmetry is possible in a model where the f sites form a simple cubic lattice. Due to the finite range of the interaction, even the s -symmetry Cooper pairs can be anisotropic. This anisotropic s -wave superconductivity has many different properties from the ordinary BCS superconductivity if the Fermi wave vector is large; the transition temperature T c can be significantly reduced by nonmagnetic impurities, the specific heat jump can be smaller than the BCS value, and the energy gap near T c can vanish along lines on the Fermi surface. The competition among different symmetries is discussed.

Copper Pairs of dγ-Symmetry in Simple Square Lattices

Physical properties of d γ-symmetry Cooper pairs were theoretically investigated by assuming the dispersion relation of a simple square lattice with the nearest neighbor transfer integral and attractive interactions between the nearest neighbors. Calculated properties such as the energy gap, the density of states and the NMR relaxation time show highly anisotropic features. A possibility is discussed that d γ-symmetry super-conductivity realized by the nearest neighbor exchange interactions can explain the properties of high- T c ceramic superconductors recently discovered. It is also shown that exchange interactions determined in insulating phases can explain high superconducting transition temperatures in metallic phases.

Theory of Valley Splitting in an N-Channel (100) Inversion Layer of Si. : I. Formulation by Extended Zone Effective Mass Theory

The theories based upon the multi-valley effective mass equation proposed by Twose are criticized and it is concluded that they can not explain the observed valley splittings. In order to treat valley splittings correctly, a formulation based upon the extended zone scheme is presented with the main interest in the valley splitting in an n -channel (100) inversion layer of Si.

Orbital Antiferromagnetism in CeB6

It is definite from recent theoretical and experimnental works that a quartet \(\varGamma_{8}\) is the ground multiplet of f levels in CeB 6 . Because the degeneracy of the quartet is composed of the orbital degeneracy as well as the Kramers degeneracy, its degree of freedom can be expressed by two kinds of Pauli matrices, which are called orbital spins and magnetic spins, respectively. It is proposed that the low temperature phase II is an antiferromagnetic state of orbital spins caused by the exchange interaction. Our model can explain various mysterious experimental results of phase II such as the increase of the transition temperature with increasing magnetic fields and the appearance of antiferromagnetic motments in the presence of fields, which vanish in the absence of fields. Therefore it can be concluded that the ordering in phase II of CeB 6 is the first example of the orbital ordering realized by the exchange interaction.

Theory of Valley Splitting in an N-Channel (100) Inversion Layer of Si II. Electric Break Through

The extended zone effective mass equation as proposed in the preceding paper is applied to the vally splitting in an n -channel (100) inversion layer of Si, and the valley splitting is explained theoretically for the first time. The splitting turns out to be about Δ E =0.15×( N inv +32/11 N depl ) meV for the carrier concentrations N inv and N depl of the inversion and depletion layers which are in 10 12 cm -2 unit. The mechanism of the splitting is the electric break through, and two kinds of break through play a role in this system. The estimated splitting is too small to be observed, and it is suggested that the splitting will be greatly enhanced by many-body effects under a high magnetic field. However the appearance of the characteristic cusps in the measured line shapes of the Schubnikov-de Haas oscillation confirms that the theory gives the correct magnitude of the valley splitting without the enhancement by many-body effects.

Valley splitting in an n-channel (100) inversion layer on p-type silicon

Abstract The extended zone effective mass theory is proposed and is applied to the investigation of the valley splitting in an n-channel (100)Si inversion layer. The splitting is due to a tunnelling effect in k -space, and is given approximately as ΔE ≈ 0.15 ( N inv + g −1 N depl ) meV ( N inv and N depl in units of 10 12 cm −2 g = 11 32 ). When the strain exists, or when k x and k y are both non-zero, the splitting is a little larger than this value. The enhancements of the Zeeman splittings and the valley splittings caused by the many body effects under strong magnetic fields are taken into account. The theory predicts the structure and line shape of the transverse magnetoconductivity oscillations, and the results show a very good agreement with the experiment including the cusps at the peak of the Landau levels in the indices N ⩾ 3.

Electron Correlation in the Hubbard Model in d =∞ Dimension

The Hubbard model with strong correlation is examined. The mean-field approximation (MFA) based on the best single-site approximation (SSA) is rigorous in the limit of high dimension of d =+∞. The best SSA is reduced to solving the Anderson model. The ground state is a heavy-electron liquid, presumably superconducting, in the weak-coupling regime, which is approximately defined by g ≈ J ( Q )/4 T K 1, on the other hand, the ground state is a MFA-type antiferromagnetic state.

A Single-Site Picture of Valence Fluctuation in Periodic Anderson Hamiltonian with Large Coulomb Correlation

It is discussed that a competition between a formation of the singlet bound state at each site and an exchange interaction plays an important role in a periodic Anderson Hamiltonian with large Coulomb correlation. As the depth of f levels measured from the chemical potential is shallower, each f level site is more likely to behave independently; the depth is related with the number of f electrons per site ( n f ). Therefore the system can be classified into three regimes: i) The first one is the independent f level regime where n f is significantly less than one. ii) In the crossover regime where n f is nearly one, each f level site behaves independently at high temperatures. However a band-like coherent behavior, or magnetic orderings are expected at low temperatures. iii) In the RKKY regime where n f is very nearly one, magnetic orderings are expected at low temperatures.

Kondo Effect in Disordered Two-Dimensional Systems

Interplay between localization and the Kondo effect has been examined for a model two-dimensional system. Various physical quantities associated with localized spins are calculated perturbatively in terms of exchange coupling constant J and \(\lambda{=}\hbar/2\pi\varepsilon_{\text{F}}\tau_{0}\) where e F is the Fermi energy and τ 0 is the relaxation time of plane wave states; the susceptibility and the conductivity are shown to have quantum corrections proportional to λ J 2 ln 2 ( t ) and λ J 3 / t , respectively, where \(t{=}\hbar/2\pi\tau_{0}kT\). It is discussed that the ground states of localized spins are qualitatively the same as in pure systems because the ensemble average of local densities of states defined by ≪ρ( e 1 , r )ρ( e 2 , r )…ρ( e n , r )≫ appears to be non zero for any n in the limit of equal energies, e i → e F .