A 3Nrule for the electronic properties of doped graphene

Doping a graphene sheet with different atoms is a promising method for tuning its electronic properties. We report a first-principle investigation on the electronic properties of N, B, S, Al, Si or P doped graphene. It is revealed that the doped graphene can show an interesting physical regularity, which can be described by a simple 3N rule: a doped graphene has a zero gap or a neglectable gap at the Dirac point when its primitive cell is 3N × 3N (N is an integer), otherwise there is a gap tunable by the dopant concentration. This unique 3N rule provides a useful guideline for the design of doped graphene for electronic applications.