Electron mobility in graphene without invoking the Dirac equation

TL;DR

This paper explains graphene's high electron mobility using basic semiconductor concepts and linear band structure, avoiding complex relativistic physics, making it accessible for students and researchers from diverse backgrounds.

Contribution

It introduces an intuitive approach to understanding graphene's effective mass and mobility without relying on the Dirac equation, bridging a gap in educational explanations.

Findings

Transverse effective mass approaches zero in undoped graphene at low temperature.

Graphene's high mobility is due to its near-zero transverse effective mass.

The approach compares graphene's properties with metals and semiconductors.

Abstract

The Dirac point and linear band structure in Graphene bestow it with remarkable electronic and optical properties, a subject of intense ongoing research. Explanations of high electronic mobility in graphene, often invoke the masslessness of electrons based on the effective relativistic Dirac-equation behavior, which are inaccessible to most undergraduate students and are not intuitive for non-physics researchers unfamiliar with relativity. Here, we show how to use only basic concepts from semiconductor theory and the linear band structure of graphene to explain its unusual effective mass and mobility, and compare them with conventional metals and semiconductors. We discuss the more intuitive concept of transverse effective mass that emerges naturally from these basic derivations, which approaches zero in the limit of undoped graphene at low temperature and is responsible for its extremely high mobility.