In this paper, we analytically investigate the electronic structure of Bernal stacking (AB stacking) graphene evolving from monolayer (a zero-gap semiconductor with a linear Dirac-like spectrum around the Fermi energy) to multi-layer (semi-metal bulk graphite). We firstly derive a real space analytical expression for the free Green's function (propagator) of multi-layer graphene based on the effective-mass approximation. The simulation results exhibit highly spatial anisotropy with three-fold rotational symmetry. By combining with the STM measurement of d2I/dV2 (the second derivative of current), we also provide a clear high-throughput and non-destructive method to identify graphene layers. Such a method is lacking in the emerging graphene research.
@article{arxiv.cond-mat/0703422,
title = {An insight into the electronic structure of graphene: from monolayer to multi-layer},
author = {Z. F. Wang and Huaixiu Zheng and Q. W. Shi and Jie Chen and Jinlong Yang and J. G. Hou},
journal= {arXiv preprint arXiv:cond-mat/0703422},
year = {2007}
}