Quantum dots in aperiodic order

We study numerically with a Green-function technique one-dimensional arrays of quantum dots with two different models. The arrays are ordered according to the Fibonacci, the Thue–Morse, and the Rudin–Shapiro sequences. As a comparison, results from a periodically ordered chain and also from a random chain are included. The focus is on how the conductance (calculated within the Landauer–Büttiker formalism) depends on the Fermi level. In the first model, we find that in some cases rather small systems (≈60 dots) behave in the same manner as very large systems (>16,000 dots) and this makes it possible in these cases to interpret our results for the small systems in terms of the spectral properties of the infinite systems. In particular, we find that it is possible to see some consequences of the singular continuous spectra that some of the systems possess, at least for temperatures up to 100 mK. In the second model, we study the phenomenon ohmic addition, i.e. when the resistances of the constrictions add up to the total resistance. It results that of the systems studied, it is only the Rudin–Shapiro system that has this behaviour for large structures, while the resistances of the Fibonacci and the Thue–Morse systems might reach a limiting value (as a periodic system does).