Electron effective mass in graphene

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.