Formation, structure, and bonding of boron-vacancy pairs in graphene: A first-principles study

Abstract

Using density-functional theory calculations, we examine how a mobile single vacancy $(V)$ interacts with substitutional boron (B) in graphene and the effect of boron-vacancy $(\text{B}V)$ pairing on the electronic structure of graphene. We find that B in a $\text{B}V$ pair energetically favors fourfold coordination, rather than remaining twofold coordinated, by forming a distorted tetrahedral structure with neighboring C lattice atoms. In the fourfold state, the binding energy of a $\text{B}V$ pair is predicted to be 2.54 eV with respect to B and $V$. Our calculations also suggest magnetic-moment oscillations by interconversion between the twofold $(1\text{ }{\ensuremath{\mu}}_{\text{B}})$ and fourfold $(0\text{ }{\ensuremath{\mu}}_{\text{B}})$ states, as their energy difference is rather moderate $(\ensuremath{\approx}0.3\text{ }\text{eV})$. We also discuss the bonding mechanisms of a $\text{B}V$ pair in the twofold and fourfold states and modifications in the electronic structure of graphene by $\text{B}V$ pairing as compared to isolated B and $V$ cases. Finally, the pathways and energetics of $V$ migration in the vicinity of B are calculated; the results suggest that B is likely to trap mobile single vacancies within a certain radius and can possibly serve as an anchor for vacancy clusters.