  The nature of electronic eigenstates and quantum transport in a comb-shaped
Fibonacci nanostructure model is investigated within a tight-binding framework.
Periodic linear chains are side-attached to a Fibonacci chain, giving it the
shape of an aperiodic comb. The effect of the side-attachments on the usual
Cantor set energy spectrum of a Fibonacci chain is analyzed using the Greens
function technique. A special correlation between the coupling of the
side-attached chain with the Fibonacci chain and the inter-atomic coupling of
the Fibonacci chain results in a dramatic triggering of the fragmented Cantor
set energy spectrum into multiple sets of continuous sub-bands of extended
eigenstates. The result is valid even for a disordered comb and turns out to be
a rare exception of the conventional Anderson localization problem. The
electronic transport thus can be made selectively ballistic within desired
energy regimes. The number and the width of such continuous sub-bands can be
easily controlled by tuning the number of atomic sites in the side-coupled
periodic linear chains. This gives us a scope of proposing such aperiodic
nanostructures as potential candidates for prospective energy selective
nanoscale filtering devices.
