Masaki Goda

Flat Bands of a Tight-Binding Electronic System with Hexagonal Structure

A constructive method to find flat bands is demonstrated for a model describing tight-binding electrons on the hexagonal lattice in which each atomic site has three orbitals. The system may represent σ-electrons of an s p 2 -hybridized material but we assume transfer integrals between orbitals to be free parameters for general discussion. Finding highly degenerate eigenfunctions of each flat band is identified as finding a localized eigenfunction, which is determined as a basis function of an irreducible representation of, for example, a point group C 6 v . This approach yields not only flat bands on all over the k -space but also some partial flat bands only on a partial k -space. In the former case, if the flat band locates at the bottom (or the top) of a band structure, it is shown that Mielkes condition holds, allowing occurrence of the flat band ferromagnetism.

Transmission of electrons in a new type of disordered system

The distribution of transmission coefficients and Thouless numbers of electrons through a disordered system of finite size is studied both numerically and theoretically. The disordered system has a long-range structural correlation obeying an inverse-power law (generated by a modified Bernoulli map). The authors have found that: (i) the Lyapounov exponents of the transmission coefficient and the Thouless number are positive definite in an infinite system and (ii) in a case of strong structural correlation the distribution of Lyapounov exponents of the transmission coefficient of a finite system converges slowly with increasing system size, and it does not obeys the central-limit theorem.

Quantum diffusion in a coherently time-varying one-dimensional disordered system

Abstract Quantum diffusion of an electron in a coherently time-varying one-dimensional disordered system is studied numerically by means of the symplectic integrator method. Based on the time dependence of the mean square displacement, it is found that a diffusive property is observed in our systems without any stochastically fluctuating time-varying perturbation. The diffusion constant is investigated as a function of the strength and the frequency of the coherently time-varying perturbation.

A Study of the Power Law Resistance in a Fibonacci Lattice

The power law with respect to length n is studied numerically in detail mainly for the resistance r ( n , E ) ( E : energy) averaged over subsystems (denoted by ( ω ) of size n of a Fibonacci lattice, ω ∝ n β + ( E , n ) exp { B ( E ) n }. The Lyapunov exponent B ( E ) and the mean value ( l ) of the exponent of power β + ( E , l ) have a fractal structure with respect to energy which corresponds to that of the energy spectrum. Both are energy sensitive. The possibility of finding a power law in conductivity with respect to temperature (at low temperatures) is discussed in view of a stability of both the mean value of the exponent of power l and the exponent of power β + ( E , n ,ω) for each sample ω over an energy interval k B T .

Flat-Band Localization in Weakly Disordered System

We present a detailed analysis of the insulator–metal–insulator transition of a disordered system, starting from a characteristic three-dimensional system possessing highly degenerated localized ei...

Three-dimensional Flat-Band Models

Typical three-dimensional flat-band models of tight-binding electronic systems on cubic and diamond lattices are presented to demonstrate the wide applicability of the method proposed by Nishino et...

Statistical Properties of Self-Diffusion in AgI in a Classically Mesoscopic Regime.

The distribution p ( x , t ) of time-developing Cartesian component of particle displacement, x = x ( t )- x (0), starting from δ-function is studied extensively in a superionic conductor AgI in a classically mesoscopic regime using the method of molecular dynamics calculation. The distribution law is modified from that of the Gaussian process, and is found to have the form p ( x , t )∝exp {- a x β / t α }, ( a >0, 0 ≤α≤1, 0 ( t )∝ t 2α/β seems to be t -linear, i.e., 2α/β≃1, in the molten and/or α phase. At the melting point or the superionic transition point, two different distributions of this type seem to compete with each other.

A new class of disordered systems a modified Bernoulli system with long range structural correlation

Spectral property and Lyapunov exponent of electronic wave function ( L -exponent) in a modified Bernoulli system with inverse-power-law structural correlation, is studied in detail numerically and theoretically. By changing the value of the bifurcation parameter B specifying a strength of the correlation in the interval (1, ∞), two transitions (a transition around B =3/2 and another one at B =2) appear. For the case 3/2≤ B 2), L -exponent in infinite system vanishes with probability 1.

Numerical Study of a Universal Distribution and Non-Universal Distributions of Resistance and Transmission Coefficient in 1-D Disordered Systems

A universal probability distribution of resistance and transmission coefficient in a one dimensional disordered system proposed by Mello from a macroscopic point of view is examined numerically from a microscopic point of view for some tightly binding disordered systems. Some universal relations between the cumulants are well observed at the band center energy E =0 in a weakly disordered system, while these are modified at the other energies E ≠0. They are modified even at E =0 in the strongly disordered system. It is further found that the universal relations are broken in a modified Bernoulli system with an inverse-power law structural correlation.

Response Function and Conductance of a Fibonacci Lattice

A power law with respect to length n is numerically observed in the off-diagonal term of the one-particle Greens function g l , l ± n ( E ) ( E : energy, l : lattice site) and in the resistance r ( n , E ) and conductance g ( n , E ) of a Fibonacci lattice. The exponent is insensitive to energy, and the power law crosses over an exponential law at a length n * ( E )=1/ A ( E ), where A ( E ) is a Lyapunov exponent which is strongly energy-sensitive. As a result, power law conductivity and resistivity with respect to temperature T are expected to be observed over a suitable range of temperatures.