Coherent electronic transport in a multimode quantum channel with Gaussian-type scatterers

Abstract

Coherent electron transport through a quantum channel in the presence of a general extended scattering potential is investigated using a T-matrix Lippmann-Schwinger approach. The formalism is applied to a quantum wire with Gaussian type scattering potentials, which can be used to model a single impurity, a quantum dot or more complicated structures in the wire. The well known dips in the conductance in the presence of attractive impurities are reproduced. A resonant transmission peak in the conductance is seen as the energy of the incident electron coincides with an energy level in the quantum dot. The conductance through a quantum wire in the presence of an asymmetric potential is also shown. In the case of a narrow potential parallel to the wire we find that two dips appear in the same subband which we ascribe to two quasi bound states originating from the next evanescent mode.

Evidence for the formation of quasibound states in an asymmetrical quantum point contact

“…Importantly, the dot potential contained a repulsive boundary region. One possible cause of the suppression may be that the effective potential seen in the first channel possesses a sufficiently high barrier, arising from this repulsive boundary region, which even at the center of the first channel, is able to partially block the transmission 12 .…”

“…Alternatively, numerical simulations have shown such features to be possible when considering a quantum dot embedded in the 1D channel, when the dot potential is attractive and gives rise to a quasi-bound state 12,13 . Importantly, the dot potential contained a repulsive boundary region.…”

“…Second and surprisingly, in some geometries, a complete destruction of the first quantized plateau at 2e 2 /h is observed. Such a behavior was completely unexpected, and from a theoretical perspective has only been seen in numerical simulations when a quasi-bound state is introduced 12,13 . Other features bear similarity to symmetric QPCs: Nonlinear characterizations reveal features reminiscent of the 0.7 structure, such as the 0.25 plateau at high DC bias, and point to the possibility of ferromagnetic properties.…”

Ground state structure and conductivity of quantum wires of infinite length and finite width

“…14 We note that a scattering matrix approach has been recently employed to calculate the conductance through a semiextended barrier or well in the wire. 34 In this case, G can be expressed in terms of the incident electron energy E in the form G = ͑2e 2 / h͚͒ n T n ͑E͒, where T n ͑E͒ is the current transmission coefficient for an electron incident in the nth subband. In our approach, G is calculated in an alternative way in which the conductance is the linear current response of the system to an external static electric field and hence is an intrinsic property of the strip, as, for example, its dielectric constant.…”

Transient magnetotransport through a quantum wire

“…When solving the Lippmann-Schwinger equation (11) we use the methods described earlier 19,20 in order to obtain analytically the contribution of the poles of the Green function and perform the remaining principal part integration by removing the singularity by a subtraction of a zero. 21,22 The main difference from the solution of the corresponding equation in the static case is that here in the dynamic case the evanescent states are explicitly present in the time-dependent Green function (8), but in the static case they had to be included by remembering that the q 2 terms there can have either sign depending on whether they refer to a propagating state with a real wave vector or an evanescent state with an imaginary one.…”