Fractal Property of Band Branching in Fibonacci Mesoscopic Rings

Abstract

We present the branching rules of the energy spectrum for a one-dimensional Fibonacci array of AB rings with an arbitrary generation based on the band map diagram. A band edge equation with the recursive scheme is used in calculating the band map to avoid numerical instability. We find that the energy spectrum for the Fibonacci AB rings with an arbitrary generation can be divided to several regions, each of which has a similar pattern. As the generation order is greater than two, the characteristics of the subbands branching in each region, including the zero transmission lines, the enveloped group bands, the major subgaps, convergence of the group bands and major subgaps for a higher generation, and number of splitting subbands in each group band for an arbitrary generation, have been proposed in the study. Moreover, electron localization in the major subgaps of the Fibonacci rings is demonstrated by the transmission spectra.