Fano resonances in quantum wires with impurities and a transverse electric field

Abstract

Electronic transport through a quantum wire with an attractive impurity is investigated via the Feshbach coupled-channel approach (in the three-channel approximation). The impurity is modeled by a $\ensuremath{\delta}$-function potential along the propagation direction while it is Gaussian in the transverse direction. For such an impurity, it is well known that the transmission probability may exhibit a single Fano resonance (due to a zero-pole pair) in each energy subband. It is shown here that varying the parameters of the impurity (such as its strength, position, and lateral extent) may produce substantially different effects on the Fano resonance, depending on the subband it occurs. In particular, the resonance widths and the asymmetry parameters of Fano line shapes that occur in the first and second subbands are investigated and compared to each other. The temperature dependence of the Fano resonances is also demonstrated. Furthermore, the effect of a transverse electric field on the resonances is examined. It is shown that increasing the field strength from zero causes either the collapse of the Fano profile in the first subband or the collapse of the Fano profile in the second subband, depending on whether the electric field points in the negative or positive direction. Comparison of the three-with the two-channel model is made.