Electron-Electron scattering and resistivity of ballistic multimode channels

TL;DR

This paper demonstrates that electron-electron scattering significantly increases resistivity in ballistic multimode wires, with observable effects at low temperatures and distinct temperature dependencies in 2D and 3D channels.

Contribution

It reveals a non-exponentially small, temperature-dependent resistivity contribution from electron-electron scattering in ballistic multimode channels, which was previously not well understood.

Findings

Resistivity increases due to electron-electron scattering in ballistic wires.

The effect scales as T^2 in 3D channels.

The effect scales as T^{5/2} in 2D channels.

Abstract

We show that electron--electron scattering gives a positive contribution to the resistivity of ballistic multimode wires whose width is much smaller than their length. This contribution is not exponentially small at low temperatures and therefore may be experimentally observable. It scales with temperature as $T^2$ for three-dimensional channels and as $T^{5/2}$ for two-dimensional ones.