Theory and computation of Hall scattering factor in graphene

TL;DR

This paper combines analytical and ab initio methods to accurately determine the Hall scattering factor in graphene, revealing its strong temperature dependence at low doping and providing a simple model for calculations.

Contribution

It introduces a new analytical model for the Hall scattering factor in graphene, accounting for temperature and doping effects based on first-principles calculations.

Findings

At high carrier densities, r ≈ 1 across temperatures.

At low doping, r varies strongly with temperature, reaching values up to 4 below 300 K.

The model accurately predicts r over a wide range of conditions.

Abstract

The Hall scattering factor, $r$, is a key quantity for establishing carrier concentration and drift mobility from Hall measurements; in experiments it is usually assumed to be 1. In this paper we use a combination of analytical and \textit{ab initio} modelling to determine $r$ in graphene. While at high carrier densities $r \approx 1$ in a wide temperature range, at low doping the temperature dependence of $r$ is very strong with values as high as 4 below 300~K. These high values are due to the linear bands around the Dirac cone and the carrier scattering rates due to acoustic phonons. At higher temperatures $r$ can instead become as low as $0.5$ due to the contribution of both holes and electrons and the role of optical phonons. Finally, we provide a simple analytical model to compute accurately $r$ in graphene in a wide range of temperatures and carrier densities.