Electron transport in a quantum wire with realistic Coulomb interaction

TL;DR

This paper provides an exact analytical study of electron transport in a quantum wire considering realistic Coulomb interactions, revealing significant effects on charge distribution, impedance, and wave velocity.

Contribution

It introduces an exact analytical solution incorporating both direct and image charge Coulomb interactions in a quantum wire, extending beyond the short-range interaction models.

Findings

Coulomb interaction significantly alters electron density distribution.

Charge density increases near contacts due to Coulomb effects.

Quantum wire impedance oscillates with frequency due to charge wave resonances.

Abstract

Electron transport in a quantum wire with leads is investigated with actual Coulomb interaction taken into account. The latter includes both the direct interaction of electrons with each other and their interaction via the image charges induced in the leads. Exact analytical solution of the problem is found with the use of the bosonization technique for one-dimensional electrons and three-dimensional Poisson equation for the electric field. The Coulomb interaction is shown to change significantly the electron density distribution along the wire as compared with the Luttinger liquid model with short-range interactions. In DC and low frequency regimes, the Coulomb interaction causes the charge density to increase strongly in the vicinity of the contacts with the leads. The quantum wire impedance shows an oscillating behavior versus the frequency caused by the resonances of the charge waves. The Coulomb interaction produces a frequency dependent renormalization of the charge wave velocity.