Transport properties of a quantum wire: the role of extended time-dependent impurities

TL;DR

This paper investigates how extended, time-dependent impurities affect electron transport in a quantum wire modeled by the Tomonaga-Luttinger framework, revealing conditions under which conductance exceeds quantized values.

Contribution

It provides an exact solution for backscattering current with extended impurities and demonstrates conductance enhancement beyond quantization for a range of interactions.

Findings

Backscattering current can be expressed via static barrier current.

Conductance exceeds quantized value for 0<g<1 with extended impurities.

Results differ from point-like impurity cases, especially for 0<g<1/2.

Abstract

We study the transport properties of a quantum wire, described by the Tomonaga-Luttinger model, in the presence of a backscattering potential provided by several extended time-dependent impurities (barriers). Employing the B\" uttiker-Landauer approach, we first consider the scattering of noninteracting electrons ($g=1$) by a rectangular-like barrier and find an exact solution for the backscattering current, as well as a perturbative solution for a weak static potential with an arbitrary shape. We then include electron-electron interactions and use the Keldysh formalism combined with the bosonization technique to study oscillating extended barriers. We show that the backscattering current off time-dependent impurities can be expressed in terms of the current for the corresponding static barrier. Then we determine the backscattering current for a static extended potential, which, in the limit of noninteracting electrons ($g=1$), coincides with the result obtained using the B\" uttiker-Landauer formalism. In particular, we find that the conductance can be increased beyond its quantized value in the whole range of repulsive interactions $0<g<1$ already in the case of a single oscillating extended impurity, in contrast %contrary to the case of a point-like impurity, where this phenomenon occurs only for $0<g<1/2$.