A Fibonacci atomic chain with side coupled quantum dots: crossover from a singular continuous to a continuous spectrum and related issues

Abstract

Interaction of bound states with a singular continuous spectrum is studied using a one dimensional Fibonacci quasicrystal as a prototype example. Single level quantum dots are attached from a side to a subset of atomic sites of the quasiperiodic chain. The proximity of the dots to the chain is modeled by introducing a tunnel hopping between a dot and the backbone. It is shown that, depending upon the proximity of the side coupled dot, the spectrum of an infinite quasiperiodic chain can display radical changes from its purely one dimensional characteristics. Absolutely continuous parts in the spectrum can be generated as well as isolated resonant eigenstates whose positions in the spectrum are sensitive to the proximity of the quantum dots. The cycles of the matrix map and the two terminal transport are discussed in details.