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Updated: May 11, 2026

Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding
Published on: September 23, 2018
A 3N rule for the electronic properties of doped graphene
Ye-Cheng Zhou1, Hao-Li Zhang, Wei-Qiao Deng
1State Key Laboratory of Applied Organic Chemistry (SKLAOC), College of Chemistry and Chemical Engineering, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China.
Abstract:
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.
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