Electronic transmission in quasiperiodic serial stub structures

We present exact results on the electronic transmission through quantum stub waveguides arranged in a Fibonacci quasiperiodic pattern. Discretizing the Schrodinger equation, we map the problem into an equivalent tight binding form and study the transmission spectrum using the transfer matrix method. We emphasize the effect of local positional correlations in a Fibonacci quantum stub array that may lead to resonant eigenstates. Using the real space renormalization group ideas we unravel various local clusters of stubs responsible for resonance. Extended eigenstates have been shown to exist and we find that, under some special circumstances, the electronic charge density exhibits a totally periodic character in such a non-periodic sequence. Our method is completely general and can be applied to any arbitrary sequence of stubs: periodic, quasiperiodic or random. This may lead to a possible experimental verification of the role of positional correlations in the transport behaviour of a class of mesoscopic devices.