Conductance of a quantum wire with a Gaussian impurity potential and variable cross-sectional shape

Abstract

We calculate the conductance through a Gaussian impurity potential in a quantum wire using the LippmannSchwinger equation. The impurity has a decay length d along the propagation direction while it is localized along the transverse direction. In the case of a repulsive Gaussian impurity it is shown that the conductance quantization is strongly affected by the decay length. In particular, increasing d causes gradual suppression of backscattering and smaller contribution of evanescent modes, leading to progressively sharper conductance steps. The dependence of the conductance on the impurity position is also examined. In the case of an attractive Gaussian impurity it is shown that multiple quasibound states are formed due to the finite size of the impurity. By varying the size of the impurity these quasibound states may evolve into highly localized states with greatly enhanced lifetime. It is also shown sfor a model impurity potential very similar to the Gaussiand that the transmission exhibits asymmetric Fano line shape. Under certain circumstances the Fano line shape may appear “inverted” or evolve into a Breit-Wigner dip. We consider also the effects of the cross-sectional shape of the wire on the quantum transmission. It is shown that varying the cross-sectional shape causes shifting of the positions of the conductance steps swhich is due to the rearrangement of the transverse energy levelsd and influences the character of conductance quantization.