Electron Effective Mass in Graphene

TL;DR

This paper proposes a simple, consistent theoretical definition of effective mass applicable to graphene and similar non-parabolic materials, aligning with experimental measurements and resolving previous divergences.

Contribution

It introduces a new theoretical expression for effective mass that works for both parabolic and non-parabolic isotropic materials, including graphene.

Findings

Effective mass in graphene shows linear dependence on momentum.

The new definition aligns with cyclotron resonance measurements.

Applicable to non-parabolic materials like graphene.

Abstract

The particle effective mass in graphene is a challenging concept because the commonly used theoretical expression is mathematically divergent. In this paper, we use basic principles to present a simple theoretical expression for the effective mass that is suitable for both parabolic and non-parabolic isotropic materials. We demonstrate that this definition is consistent with the definition of the cyclotron effective mass, which is one of the common methods for effective mass measurement in solid state materials. We apply the proposed theoretical definition to graphene and demonstrate linear dependence of the effective mass on momentum, as confirmed by experimental cyclotron resonance measurements. Therefore, the proposed definition of the effective mass can be used for non-parabolic materials such as graphene.