Fano resonance in discrete lattice models: controlling lineshapes with impurities

TL;DR

This paper investigates how impurities in a discrete lattice model can be used to control Fano resonance lineshapes in electronic transmission, providing analytical insights into impurity effects on resonance profiles.

Contribution

It introduces a simple discrete model demonstrating how impurity atoms influence Fano resonance profiles and provides analytical formulas relating impurity positions to system parameters.

Findings

Impurities significantly alter Fano lineshapes in the transmission spectrum.

Analytical formulas link impurity locations to the size of the coupled chain.

Reversal of pole-zero structures in Fano resonance is explained.

Abstract

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.