Electron-electron scattering and conductivity of long multimode channels

TL;DR

This paper investigates how electron-electron scattering affects the resistance of long, multi-mode channels, revealing saturation behavior and differences between 2D and 3D systems related to temperature dependence and electron distribution.

Contribution

It provides a theoretical analysis of resistance saturation due to electron-electron scattering in long channels, highlighting dimensional differences and temperature effects.

Findings

Resistance increases due to electron-electron scattering saturates in infinitely long channels.

In 3D channels, the resistance correction is temperature-independent.

In 2D channels, the resistance correction is proportional to temperature.

Abstract

The electron-electron scattering increases the resistance of ballistic many-mode channels whose width is smaller than their length. We show that this increase saturates in the limit of infinitely long channels. Because the mechanisms of angular relaxation of electrons in three and two dimensions are different, the saturation value of the correction to the resistance is temperature-independent in the case of three-dimensional channels and is proportional to the temperature for two-dimensional ones. The spatial behavior of electron distribution in the latter case is described by an unusual characteristic length.