Fano resonance in discrete lattice models: Controlling lineshapes with impurities

The possibility of controlling Fano lineshapes in the electronic transmission is addressed in terms of a simple discrete model within a tight binding framework, in which a finite sized ordered chain is coupled from one side to an infinite linear chain (the ‘backbone’) at one lattice point. It is found that, the profile of Fano resonance is strongly influenced by the presence of impurity atoms in the backbone. We specifically discuss the case with just two substitutional impurities sitting in the otherwise ordered backbone. Precise analytical formulae relating the locations of these impurities to the size of the side coupled chain have been presented. The nature of the transmission spectrum and the reversal of the peak-dip structures in the Fano resonance are discussed with the help of these formulae.