Interpretation of STM images of graphite with an atomic vacancy via density-functional calculations of electronic structure

This paper is devoted to the interpretation of scanning tunneling microscopy (STM) images of a single atomic vacancy on single and double graphene sheets as a model for the (0001) surface of graphite. We first selected a one-layer model which would allow us to run periodic density-functional theory calculations without destroying the charge density waves that form in the vicinity of the vacancy. We assigned the main features of STM images [bright spots in the vicinity of the defect, ((root 3x root 3)R30 degrees)R30 degrees modulation of the local electronic density near the Fermi level, third-order symmetry structure] to the electronic band structure of the defective graphite surface. We further analyzed a more extended crystal working cell model to ensure convergence toward the isolated atomic vacancy. The interlayer interaction plays a crucial role in the interpretation of STM images. A double-layer model was subsequently considered and the impact of the interlayer interaction analyzed. We produce the local density of state for the alpha and beta vacancies which may be differentiated. Our calculations reproduce the main features of STM images and the results we get are in good agreement with experimental observations.