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 pole-zero structures in the Fano resonance are discussed with the help of these formulae.Comment: 8 pages, 5 eps figure

Controlled delocalization of electronic states in a multi-strand quasiperiodic lattice

Finite strips, composed of a periodic stacking of infinite quasiperiodic Fibonacci chains, have been investigated in terms of their electronic properties. The system is described by a tight binding Hamiltonian. The eigenvalue spectrum of such a multi-strand quasiperiodic network is found to be sensitive on the mutual values of the intra-strand and inter-strand tunnel hoppings, whose distribution displays a unique three-subband self-similar pattern in a parameter subspace. In addition, it is observed that special numerical correlations between the nearest and the next-nearest neighbor hopping integrals can render a substantial part of the energy spectrum absolutely continuous. Extended, Bloch like functions populate the above continuous zones, signalling a complete delocalization of single particle states even in such a non-translationally invariant system, and more importantly, a phenomenon that can be engineered by tuning the relative strengths of the hopping parameters. A commutation relation between the potential and the hopping matrices enables us to work out the precise correlation which helps to engineer the extended eigenfunctions and determine the band positions at will.Comment: 8 pages, 6 figure