Hisashi Hiramoto

ELECTRONIC SPECTRAL AND WAVEFUNCTION PROPERTIES OF ONE-DIMENSIONAL QUASIPERIODIC SYSTEMS: A SCALING APPROACH

We review the results of the scaling and multifractal analyses for the spectra and wave-functions of the finite-difference Schrodinger equation: Here V is a function of period 1 and ω is irrational. For the Fibonacci model, V takes only two values (it is constant except for discontinuities) and the spectrum is purely singular continuous (critical wavefunctions). When V is a smooth function, the spectrum is purely absolutely continuous (extended wavefunctions) for λ small and purely dense point (localized wavefunctions) for λ large. For an intermediate λ, the spectrum is a mixture of absolutely continuous parts and dense point parts which are separated by a finite number of mobility edges. There is no singular continuous part. (An exception is the Harper model V (x) = cos (2πx), where the spectrum is always pure and the singular continuous one appears at λ = 2.)

CRITICAL AND BICRITICAL PROPERTIES OF HARPER'S EQUATION WITH NEXT-NEAREST-NEIGHBOR COUPLING

We have exploited a variety of techniques to study the universality and stability of the scaling properties of Harpers equation, the equation for a particle moving on a tight-binding square lattice in the presence of a gauge field, when coupling to next-nearest sites is added. We find, from numerical and analytical studies, that the scaling behavior of the total width of the spectrum and the multifractal nature of the spectrum are unchanged, provided the next-nearest-neighbor coupling terms are below a certain threshold value. The full square symmetry of the Hamiltonian is not required for criticality, but the square diagonals should remain as reflection lines. A bicritical line is found at the boundary between the region in which the nearest-neighbor terms dominate and the region in which the next-nearest-neighbor terms dominate. On the bicritical line a different critical exponent for the width of the spectrum and different multifractal behavior are found. In the region in which the next-nearest-neighbor terms dominate, the behavior is still critical if the Hamiltonian is invariant under reflection in the directions parallel to the sides of the square, but a new length scale enters, and the behavior is no longer universal but shows strongly oscillatory behavior. For a flux per unit cell equal to 1/q the measure of the spectrum is proportional to 1/q in this region, but if it is a ratio of Fibonacci numbers the measure decreases with a rather higher inverse power of the denominator.

Inter-Polaron Interaction and Bipolaron Formation. I

The system of two electrons coupling with phonon fields is studied with the use of the path integral method. In particular, the condition of the formation of a bipolaron and its physical properties are investigated in detail. The deformation potential interaction with acoustic phonons (the coupling constant S ac ) and the Frohlich interaction with optical phonons ( S op ) act to help the bipolaron formation against the direct Coulomb repulsion which prevents it. Usually, S ac plays a dominant role. With e ∞ / e 0 ≪1 and the optical phonon energy not so large compared with the electron band width, however, the bipolaron can be formed at large values of S op even when S ac =0. The bipolaron always has an enormous effective mass; thus it is practically localized. The mean distance between two electrons in the bipolaron is usually of the order of the interatomic distance.

Dynamics of an Electron in Quasiperiodic Systems.I.Fibonacci Model

Dynamics of an electron in quasiperiodic systems is studied numerically. Calculations are carried out for the one-dimensional tight-binding model with diagonal or off-diagonal modulation obeying the Fibonacci sequence. The width of the wavepacket of an electron put on a single site at time t =0 exhibits such an overall time evolution as \(\sqrt{\langle\varDelta x^{2}\rangle}\sim t^{\alpha}\) (0<α<1). The dynamical index α decreases continuously with increasing the modulation strength. This anomalous power-law diffusion is successfully interpreted in terms of renormalization group arguments in both the strong and weak modulation limits.

Ab Initio Study of Elementary Processes in Silicon Homoepitaxy–Adsorption and Diffusion on Si(001)

Ab initio total-energy calculations of the reconstructed Si(001) with adatoms for various adsorption sites have been performed. The results are interpreted in terms of adatom-substrate interactions to understand microscopic mechanisms of the surface diffusion of Si adatoms. The spatial variation of the adsorption energy suggests strong anisotropy in the direction of the adatom diffusion on Si(001)–the most probable direction of diffusion is along the dimer rows. The surface dimer breaks when the adatom moves along the lateral projection of the dimer bond.

Dynamics of an Electron in Quasiperiodic Systems. II. Harper's Model

The dynamics of an electron in a one-dimensional tight-binding model with incommensurate sinusoidal modulation (Harpers model) is studied numerically. The width of a wavepacket of an electron put on a single site at the time t =0 exhibits such asymptotic time evolution as \(\sqrt{\langle\varDelta x^{2}\rangle}\sim t^{\alpha}\), where the dynamical index α takes only three values α=1 for V V c and α=α c (a value near 1/2) for V = V c , where V is the strength of modulation and V c is the critical value. This behavior is in a striking contrast with that in Fibonacci chains, in which α can take any value between 0 and 1 depending on the modulation strength as shown in our preceding paper [J. Phys. Soc. Jpn. 57 (1988) 230].

A New Self-Consistent Band Structure of C8K

The electronic structure of C 8 K is investigated by using the self-consistent numerical-basis-set LCAO method within the local-density-functional formalism. It is found that the graphite π * bands are split in C 8 K and some of them go down below the Fermi energy. As a result there exist three-dimensional Fermi surfaces originating from graphite π * bands in the center of the Brillouin zone. This is due to the charge unbalance between environmentally non-equivalent carbon atoms in a graphite layer, which is produced by the potassium atoms. The new band structure is shown consistent with recent experiments of optical spectra.

The Effect of an Interelectron Interaction on Electronic Properties in One-Dimensional Quasiperiodic Systems

The effect of an interelectron interaction ( U ) on electronic properties in one-dimensional quasiperiodic systems (the incommensurate Harper model and the Fibonacci model) is studied within the Hartree-Fock (HF) approximation. For the Fibonacci model, the HF one-body spectrum remains singular continuous (critical wave functions) for small | U |. For the Harper model, on the other hand, the singular continuous spectrum at critical coupling (λ c =2) disappears as soon as U is added.

Molecular Dynamics Study of Model System for C8K Type Compounds

By using the molecular dynamics method, structural and dynamical properties of a model system of C 8 K type compounds are studied. The model consists of one intercalant layer sandwiched by rigid graphite layers. The solid-liquid transition of intercalant ion system is observed, and the static and dynamical properties of the liquid state are investigated. The calculation of the pair distribution function clarifies the characteristic local structure of the “liquid”. The observation of traces of the ionic motions reveals that the motions of ions have a strong correlation. It is not the case that an individual ion jumps from a site to another one independently. The analysis of the activation energy of the calculated self-diffusion constant of the intercalant ions also leads to a conclusion consistent with this.

Screening of Coulomb Potential by 2-Dimensional Band Electrons in Intercalated Layered Materials

A model calculation is performed to investigate the effect of screening on the Coulomb potential of an intercalant ion in intercalated layered materials. The 2-dimensional conduction band electrons of the host material, which have transferred from intercalants, screen the Coulomb potential. The investigation is made by using the Thomas-Fermi approximation. The spatial behavior of the screened potential is classified into three clearly distinct regimes: the regime of 1/ r ( c ≪ r ), the rapid decreasing regime ( r ∼ c ) and the regime of 1/ r 3 ( r ≫ c ), where r is a distance from the intercalant and c is an interlayer distance of host materials. The existence of the rapid decreasing regime is one of the most remarkable features of our model system consisting of an intercalant and two sandwiching host layers.