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 Lippmann-Schwinger 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 ͑for a model impurity potential very similar to the Gaussian͒ 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 ͑which is due to the rearrangement of the transverse energy levels͒ and influences the character of conductance quantization.

Conductance signatures of electron confinement induced by strained nanobubbles in graphene

“…This resonant behavior is a multimode effect previously observed in quasi-one dimensional systems with impurities 55,56 , finite-range local potential scattering 57,58 , and short-range impurity potentials 53,54,59-61 . It can be understood by recalling that in quantum wires electric current is carried by independent transverse modes.…”

Disorder suppression and precise conductance quantization in constrictions of PbTe quantum wells

“…One can recall here a number of theoretical models describing the conductance of 1D constrictions containing short-range scattering centers, approximated by Dirac δ-function. 36,37,38,39 The common result of these models is the strong dependence of the conductance quantization steps on the sign of the scattering potentials. In particular, for repulsive centers, the steps are altered rather weakly.…”

“…This remains valid even when extending the theory to scattering centers of small, but non-zero, range. 39 Because we do not have any independent information on the sign of the short-range part of impurity potentials in PbTe, the problem of their possible residual influence on conductance quantization remains open.…”

Fano effect in quasi‐one‐dimensional wires with short‐ or finite‐range impurities

“…where we denoted by χ + k (x) and χ − k (x) the scattering states for which the incident wave comes comes from −∞ and +∞ respectively [6]. These states describe the background (nonresonant) scattering, which is the scattering in a hypothetical system in which there is no coupling to a bound state [4].…”

“…The Fano function [2] has been shown to arise as the most general resonance line shape in these systems, provided that two scattering channels -a resonant and a nonresonant one, interfere. Resonances of the Fano type have been treated theoretically in various condensed matter systems including transport through quantum wires with attractive impurities (or embedded quantum dots) [3][4][5][6]. In these systems, the coupling between a bound state of the impurity and the continuum results in a quasibound (resonant) state.…”