草部 浩一

Magnetic structure is studied for several pi-networks of graphite-like structures with edge and/or topological defects using the tight-binding model (the Huckel model). Zigzag-edged graphite bare edge states, which form a partly flat band at the Fermi energy. Short range repulsion (the Hubbard U) is enough to induce huge magnetic moments coming from spin polarization of localized electrons on the edge. While, introduction of azupyrene defect (two pentagons and two heptagons instead of four hesagons) in graphite modifies the band structure, some of which have a flat lon-est excitation band. We propose a series of one-dimensional polymers with a flat band, which is exactly shown to be ferromagnetic for electron doping up to the half-filling of this band, so long as the system is well described by the Hubbard model.

Isotope effects in diffusion of hydrogen atoms are investigated theoretically. It is shown that isotope effect is reduced by a nonadiabatic effect of the heat bath so that the classical-quantum crossover temperature and quantum tunneling rate lose their mass dependence. On the other hand, isotope effect is reversed in classical hopping rate under strong spatial confinement at the barrier top. These results indicate that isotope effects can be the means of observing influences of many degrees of freedom characterizing environment in diffusion process.

We have investigated the activation barriers and the intermediate paths of the transformation to cubic diamond and that to hexagonal diamond from graphite under pressure, allowing both atomic geometry and unit-cell shape lo vary, in order to clarify the difference of the microscopic mechanisms between them. For this investigation, we have developed a method, of finding a saddle point of the potential surface automatically on the basis of constant-pressure first-principles molecular dynamics. At the transition states, the length of the interlayer bonding is universal irrespective of the transformations and pressures, while there is a difference in the lateral displacement of atoms on the paths. It is found that the activation barrier from graphite to cubic diamond is lower than that to hexagonal diamond by similar to 70 meV/atom. These results suggest that, whenever collective slide of graphite planes is allowed, the transformation to cubic diamond is favored, and that hexagonal diamond can be obtained only when such slide is prohibited.

Inspired by Sutherland's work [Phys. Rev. Lett. 74 (1995) 816] on the detection of bound spin waves, we propose that bound electron states can he detected from the dependence of interacting electron systems on the Aharonov-Bohm flux in the 'extended zone' scheme. where the electron pairing halves the original period of N-alpha flux quanta in a system of linear size N-alpha. Along with the Bethe ansatz analysis, a numerical implementation for keeping track of the adiabatic flow of energy levels is applied to the attractive/repulsive Hubbard model and the t-J ladder.

The inverse isotope effect in hydrogen diffusion at metal surfaces has been investigated with the Quantum Transition State Theory using a two-dimensional model potential with confinement orthogonal to the diffusion path. It is clarified by quantum Monte Carlo simulation that a decrease in the hopping rate by confinement, competing with an increase by tunneling, induces the inverse isotope effect within a certain temperature range above a classical-quantum crossover temperature. We also show that, at high temperature, the confinement effect can be included in the potential barrier for diffusion and that the inverse isotope effect can be described with a reduced one-dimensional model within Feynman's variational method.

We study the electronic states of graphite ribbons with edges of two typical shapes, armchair and zigzag, by performing tight binding band calculations; and find that the graphite ribbons shaw striking contrast in the electronic states depending on the edge shape. In particular, a zigzag ribbon shows a remarkably sharp peak of density of states at the Fermi level, which does not originate from infinite graphite. We find that the singular electronic states arise from the partly flat bands at the Fermi level, whose nave functions are mainly localized on the zigzag edge. We reveal the puzzle for the emergence of the peculiar edge state by deriving the analytic form in the case of semi-infinite graphite with a zigzag edge. Applying the Hubbard model within the mean-field approximation, we discuss the possible magnetic structure in nanometer-scale micrographite.

We have investigated the activation barriers and the intermediate paths of the transformation to cubic diamond and that to hexagonal diamond from graphite under pressure, allowing both atomic geometry and unit-cell shape to vary, in order to clarify the difference of the microscopic mechanisms between them. For this investigation, we have developed a method of finding a saddle point of the potential surface automatically on the basis of constant-pressure first-principles molecular dynamics. At the transition states, the length of the interlayer bonding is universal irrespective of the transformations and pressures, while there is a difference in the lateral displacement of atoms on the paths. It is found that the activation barrier from graphite to cubic diamond is lower than that to hexagonal diamond by ∼70 meV/atom. These results suggest that, whenever collective slide of graphite planes is allowed, the transformation to cubic diamond is favored, and that hexagonal diamond can be obtained only when such slide is prohibited. © 1996 The American Physical Society.

The extended Aharonov-Bohm period test, recently proposed by the present authors, is used to study the electron pairing transition in the t-J ladders. The critical point is detected as a gap opening in the extended spectral flow. The result suggests a pairing prior to the onset of a phase separation, which is consistent with a recent Tomonaga-Luttinger analysis. © 1996 Plenum Publishing Corporation.

The simplest topological defect in a graphite sheet can be introduced by switching one bond with the movement of two carbon atoms, which transforms four hexagons to two pentagons and two heptagons. Putting the topological defects periodically in a graphite sheet, we study how the electronic state changes based on the tight binding model. Depending on the combination of geometrical parameters which specify the arrangement of the defects, we find that the electronic states can be classified into the zero-gap semiconducting, semi-metallic and metallic cases. The localized charge density states at the defect sites emerge just above the Fermi level. Curious states having a flat band at the Fermi level appear in some particular geometrical arrangements of the defects. In addition, we propose to design a series of graphitic polymers with a fiat lowest-unoccupied band.

Examining the band structure of graphite ribbons with a typical edge shapes of armchair or zigzag, we find that minute graphite in a nanometer scale shows a striking contrast in the ir electronic states depending on tile edge shape. A wide armchair ribbon can reproduces the electronic state of graphite, but a zigzag ribbon shows a pair of partly flat bands which gives a remarkable peak of density of states at the Fermi level. We derive the analytic solution of this peculiar Edge State, disclosing the puzzle of its emergence.

A noble mechanism of spin polarization is proposed for finite graphite sheet with edge. For graphite ribbon with zigzag edge, there appear peculiar Ledge states'. These localized states comprise nearly flat band at the Fermi level, which easily causes magnetic instability. Magnetic structure is suggested from Hartree-Fock analysis of the Hubbard model, where huge magnetic moments are induced at around both of edges by weak Hubbard U and are coupled antiferromagnetically with each other.

A persistent current, coupled with the spin state, of purely many-body origin is shown to exist in Nagaoka's ferromagnetic state in two dimensions (2D). This we regard as a manifestation of a gauge field, which comes from the surrounding spin configuration and acts on the hole motion, being coupled to the Aharonov-Bohm flux. This provides an example where the electron-electron interaction exerts a profound effect involving the spins in clean two-dimensional lattice systems in sharp contrast to continuum or spinless fermion systems.

Phase diagram of the extended Hubbard model with on-site repulsion and nearest-neighbor attraction is obtained for various band fillings, covering the strong-correlation regime, in one dimension by mapping the system to the Tomonaga-Luttinger model with use of exact diagonalization of finite systems. We find that the strong electron correlation makes the superconducting region, which is sandwiched between spin-density wave and phase-separation regions, significantly wider than expected from the weak-coupling g-ology.

The peculiar effect of electron correlation in multiband systems is illustrated for the recently proposed ferromagnetism in a Hubbard model having flat bands. Despite the flatness of the band, an acoustic spin-wave mode with a finite stiffness exists along with optical modes below a Stoner gap. The relevant energy (gap and stiffness) transmutes from the Hubbard U in the weak-coupling limit to t (transfer integral) in the strong-coupling limit. This implies a stable itinerant ferromagnetism with finite band widths.

Magnetic phase diagram for the two-band Hubbard model in one dimension is explored. In the parameter space of direct and exchange interactions, the insulating ferromagnetism with an orbital superstructure transforms into metallic ferromagnetism as the strength of Hund's coupling is increased. When the orbital degeneracy is lifted, the ferromagnetic state is destabilized except in the region where metallic ferromagnetism appears.

The occurrence of high-spin ground states in the strongly correlated electron system is clarified in one and two dimensions. Even for infinitestimal Hubbard U, the ground state with a spin-polarized Fermi surface periodically arises as the number of electrons is varied due to a 'k-space Hund's coupling'. A non-perturbative crossover to strong U regime, which is accompanied by a series of level crossings and involves the stability of the Nagaoka state, is also demonstrated.

Occurence of high-spin ground states in strongly-correlated electron systems is explored. In the single-band Hubbard model, high-spin states arise even for small U due to a 'k-space Hund's coupling', which cross over to strong-U states including Nagaoka's state around the half filling. The magnetic phase diagram for the two-band Hubbard model with interband interactions is also revealed. © 1991.

Dispersions and wave functions of all the low-lying excitations are studied numerically along with the Bethe-ansatz analysis for the finite-U one-dimensional Hubbard model for U = 0 --> U = infinity. We find the following. (i) In addition to conventional charge or spin excitations such as des Cloizeaux-Pearson modes, there are classes of excitations involving both spin and charge degrees of freedom. These include the heavy-mass modes arising from the Doucot-Wen gauge potentials. (ii) As U is increased, some level crossings take place at a crossover region of U approximately 10t in which low-lying spin- and charge-excitation bands become separated and the antiferromagnetic spin correlation becomes significant. (iii) For systems doped with more than one hole, the heavy-mass modes split into branches.

We propose non-orthogonal spin 1/2 functions of N spins with the total spin S(tot) = S, and its z components of S(z)tot = M, which are generated by the standard tableaus of Young's diagrams of the symmetric group. The proof that the spin functions form a complete set of the space of {S(tot) = S, S(z)tot = M} is presented in terms of permutation operators of the symmetric group.