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We show that a discrete tight-binding model representing either a random or aquasiperiodic array of bonds, can have the entire energy spectrum or asubstantial part of it absolutely continuous, populated by extendedeigenfunctions only, when atomic sites are coupled to the lattice locally, ornon-locally from one side. The event can be fine-tuned by controlling only thehost-adatom coupling in one case, while in two other cases cited here anadditional external magnetic field is necessary. The delocalization ofelectronic states for the group of systems presented here is sensitive to asubtle correlation between the numerical values of the Hamiltonian parameters -a fact that is not common in the conventional cases of Anderson localization.Our results are analytically exact, and supported by numerical evaluation ofthe density of states and electronic transmission coefficient.

Engineering bands of extended electronic states in a class of topologically disordered and quasiperiodic lattices