Electronic properties of a quasi-periodic array of tight binding rings immersed in a magnetic field

Abstract

Electronic properties of model mesoscopic rings of two different sizes placed in contact with each other in a quasi-periodic Fibonacci sequence have been examined within the tight binding framework. The array of the rings is immersed in a constant magnetic field. The resonant one electron transport is analysed for selected sizes of the rings. It is found that the resonance is a result of a subtle positional correlation, sometimes revealed only when the field assumes special values. The energy eigenvalues at resonance all correspond to a six-cycle of the full matrix map of the Fibonacci array of rings. Interestingly, we find that for a certain combination of the rings, the charge density at the band centre displays a cross-over, going from a perfectly extended (even periodic) character to a fractal behavior as a function of the external field.