Electron mobility in graphene without invoking the Dirac equation

Chaitanya K. Ullal, Jian Shi, Ravishankar Sundararaman

Published 2018-06-25Version 1

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.