An insight into the electronic structure of graphene: from monolayer to multi-layer

TL;DR

This paper analytically explores the electronic structure of Bernal-stacked graphene from monolayer to multi-layer, deriving Green's functions and proposing a non-destructive method for layer identification using STM measurements.

Contribution

It provides an analytical expression for the Green's function of multi-layer graphene and introduces a high-throughput STM-based method for layer identification.

Findings

Green's function derived for multi-layer graphene

Spatial anisotropy with three-fold symmetry observed

STM method effectively identifies graphene layers

Abstract

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.