Fano Resonances in Stubbed Quantum Waveguides with Impurities

TL;DR

This paper investigates Fano resonances in T-shaped two-dimensional quantum waveguides with impurities, analyzing how defect strength and geometry influence conductance resonances using S-matrix pole analysis.

Contribution

It introduces a numerically stable method to determine resonance parameters in complex quantum waveguides with impurities using S-matrix pole analysis and the *-product composition rule.

Findings

Resonance behavior depends on impurity strength and device geometry.

Resonance parameters are accurately determined via S-matrix pole analysis.

The method provides stable numerical evaluation of scattering matrices.

Abstract

We consider T--shaped, two--dimensional quantum waveguides containing attractive or repulsive impurities with a smooth, realistic shape, and study how the resonance behavior of the total conductance depends upon the strength of the defect potential and the geometry of the device. The resonance parameters are determined locating the relevant S-matrix poles in the Riemann energy surface. The total scattering operator is obtained from the S-matrices of the various constituent segments of the device through the *-product composition rule. This allows for a numerically stable evaluation of the scattering matrix and of the resonance parameters.