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

TL;DR

This paper investigates how attaching quantum dots to a Fibonacci quasicrystal alters its spectral properties, revealing transitions from singular continuous to continuous spectra and affecting transport characteristics.

Contribution

It demonstrates that side-coupled quantum dots can induce significant spectral changes in a Fibonacci chain, including the emergence of continuous spectra and resonant states.

Findings

Spectral transitions depend on the proximity of quantum dots.

Continuous spectra can be engineered in quasiperiodic systems.

Transport properties are significantly affected by side coupling.

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.