Scattering of electron from a disk in 2D electron gas: full cross section, transport cross section, and the interaction correction

TL;DR

This paper investigates how a finite-sized disk impurity affects electron scattering in a 2D electron gas, analyzing cross sections and interaction corrections influenced by Friedel oscillations near the Fermi level.

Contribution

It provides a detailed analysis of full and transport cross sections for a disk impurity, revealing their asymptotic behaviors and the impact of electron interactions, extending previous point-like impurity models.

Findings

Transport cross section saturates faster than full cross section.

Interaction correction vanishes for full cross section.

Interaction correction is enhanced for the transport cross section.

Abstract

It is known that the presence of the Fermi sea modifies the scattering of an electron from a point-like impurity. This is due to the Friedel oscillations of the electron density around the impurity. These oscillations create an additional scattering potential for incident electrons. The closer the energy of the incident electron to the Fermi level, the stronger the additional scattering. We study this effect for the case when the impurity is not point-like but rather a hard disk, with a radius much bigger than the de Broglie wavelength. We start with a careful examination of the full and transport cross sections from an extended target. Both cross sections approach their limiting values upon increasing the wave vector of the incident electron. We establish that the transport cross section saturates much faster than the full cross section. With regard to the interaction correction, we establish that it vanishes for the full cross section, while for the transport cross section, it is enhanced compared to the case of a point-like scatterer.