Electrical resistance of ballistic-electron transport through a finite disordered Fibonacci chain

Abstract

The average resistances of both a finite fully-random chain and a finite disordered Fibonacci chain are calculated as a function of the chain length. From these calculated average resistances, the localization lengths are computed and analyzed. The more the randomness of the system, the stronger the localization behavior will exhibit. The stronger the localization behavior, the smaller the localization length will be. A complete localization behavior for the fully-random chain with a small localization length is reproduced from our study as expected. However, only incomplete localization behavior is found for all the disordered Fibonacci chains with p 0.5. Moreover, the values of localization lengths of all the disordered Fibonacci chains approach one larger common value due to suppression of the weak randomness by the strong self-similarity of the disordered Fibonacci chains. It turns out that the so-called disordered Fibonacci chain does not contain any more randomness than the pure Fibonacci chain. Our result agrees with the fact that the same Lyapunov exponent was found for both a pure Fibonacci chain and a disordered Fibonacci chain with random tiling that introduces phason flips at certain sites on the chain [see Phys.

Statistics of Lyapunov exponent in random Fibonacci multilayer

“…The random tiling introduced by phason flips at certain sites on the chain does not exhibit a change in LE compared to the pure Fibonacci chain, indicating that this type of disorder is irrelevant for both electron and phonon excitations. This result was confirmed by Huang et al [23] by calculating the average resistances of both a finite fully-random chain and a finite disordered Fibonacci chain as a function of the chain length.…”

The Fibonacci quasicrystal: case study of hidden dimensions and multifractality

“…A weak form of structural disorder was considered in (Velhinho and Pimentel, 2000), by allowing randomness in the substitution rules for building chains. The conclusion reached in this and a later study (Huang and Huang, 2004) is that this type of disorder is irrelevant, in that the Lyapunov exponents of states were not changed. To modify the critical states of the pure system, the disorder must break some symmetries of the Fibonacci Hamiltonian as in the models we discuss in the following section.…”

The transmission properties of nonlinear superlattice in the presence of a weak electric field

“…Employing the boundary conditions at n x x = , continuity of the wave function and discontinuity of its derivative, the second-order differential equation (1) can be mapped by means the Poincare map to the following recursive equation [11] ( ) ( ) …”

“…On the other hand, there has been a continuous interest in the study of electrical field-induced effects in crystals or other periodic and random structures [10][11][12][13][14][15][16][17]. The external electrical field-induced transport phenomena of ballistic electrons in a superlattice were studied [1,18,19].…”