Mathematical aspects and simulation of electron-electron scattering in graphene

TL;DR

This paper analyzes the mathematical properties and simulation of electron-electron scattering in graphene, emphasizing its significant role in accurately determining electrical currents and characteristic curves.

Contribution

It provides a detailed mathematical analysis and Monte Carlo simulation of electron-electron collisions in graphene, highlighting their importance in electronic property evaluations.

Findings

Electron-electron scattering significantly affects current calculations.

Monte Carlo simulations reveal the non-negligible role of electron-electron interactions.

Mathematical analysis clarifies properties of the collision operator in graphene.

Abstract

Some properties of the electron-electron collision operator in graphene are analyzed along with the evaluation of collision rate. Monte Carlo simulations complete the study and highlight the non-negligible role of the electron-electron scattering for an accurate evaluation of the currents and, as a consequence, of the characteristic curves.