Abstract: Interlayer interaction and electronic screening in multilayer graphene Taisuke Ohta, 1, 2 Aaron Bostwick, 1 J. L. McChesney, 1, 3 Thomas Seyller, 4 Karsten Horn, 2 and Eli Rotenberg 1 Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California, USA Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany Montana State University, Bozeman, Montana, USA Institut f¨ r Physik der Kondensierten Materie, Universit¨ t Erlangen-N¨ rnberg, Erlangen, Germany u a u (Dated: March 30, 2007) The unusual transport properties of graphene are the direct consequence of a peculiar bandstruc- ture near the Dirac point. We determine the shape of the π bands and their characteristic splitting, and find the transition from two-dimensional to bulk character for 1 to 4 layers of graphene by angle-resolved photoemission. By detailed measurements of the π bands we derive the stacking order, layer-dependent electron potential, screening length and strength of interlayer interaction by comparison with tight binding calculations, yielding a comprehensive description of multilayer graphene’s electronic structure. PACS numbers: Much recent attention has been given to the electronic structure of multilayer films of graphene, the honeycomb carbon sheet which is the building block of graphite, car- bon nanotubes, C 60 , and other mesoscopic forms of car- bon [1]. Recent progress in synthesizing or isolating mul- tilayer graphene films [2–4] has provided access to their physical properties, and revealed many interesting trans- port phenomena, including an anomalous quantum Hall effect [5, 6], ballistic electron transport at room temper- ature [7], micron-scale coherence length [7, 8] and novel many-body couplings [9]. These effects originate from the effectively massless Dirac Fermion character of the carri- ers derived from graphene’s valence bands, which exhibit a linear dispersion degenerate near the so-called Dirac point energy, E D [10]. These unconventional properties of graphene offer a new route to room temperature, molecular-scale electron- ics capable of quantum computing [6, 7]. For example, a possible switching function in bilayer graphene has been suggested by reversibly lifting the band degeneracy at the Fermi level (E F ) upon application of an electric field [11, 12]. This effect is due to a unique sensitivity of the bandstructure to the charge distribution brought about by the interplay between strong interlayer hopping and weak interlayer screening, neither of which are currently well-understood [13, 14]. In order to evaluate the interlayer screening, stack- ing order and interlayer coupling, we have systemati- cally studied the evolution of the bandstructure of one to four layers of graphene using angle-resolved photoemis- sion spectroscopy (ARPES). We demonstrate experimen- tally that the interaction between layers and the stacking sequence affect the topology of the π bands, the former inducing an electronic transition from two-dimensional (2D) to 3D (bulk) character when going from one layer to multilayer graphene. The interlayer hopping integral and screening length are determined as a function of the num- ber of graphene layers by exploiting the sensitivity of π FIG. 1: (color online) Photoemission images revealing the bandstructure of (a) single and (b) bilayer graphene along high symmetry directions, Γ-K-M-Γ. The blue dashed lines are scaled DFT bandstructure of free standing films [16]. Inset in (a) shows the 2D Brillouin zone of graphene. states to the Coulomb potential, and the layer-dependent carrier concentration is estimated. The films were synthesized on n-type (nitrogen, 1 × 10 18 cm −3 ) 6H-SiC(0001) substrates (SiCrystal AG) that were etched in hydrogen at 1550 C. Annealing in a vac- uum first removes the resulting silicate adlayer and then causes the growth of the graphene layers between 1250 to 1400 C [15]. Beyond the first layer, the samples have a ± 0.5 monolayer thickness variation; the bandstructures of different thicknesses were extracted using the method of Ref. [11]. ARPES measurements were conducted at the Electronic Structure Factory endstation at beamline 7.01 of the Advanced Light Source, equipped with a Sci- enta R4000 electron energy analyzer. The samples were cooled to ∼ 30K by liquid He. The photon energy was 94 eV with the overall energy resolution of ∼30 meV for Fig. 1 and Fig. 2(a-d). The bandstructures of a single (Fig. 1 (a)) and a bi-