The evolution of electronic structure in few-layer graphene revealed by optical spectroscopy

Kin Fai Mak, Matthew Y. Sfeir, James A. Misewich, Tony F. Heinza

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Abstract

The massless Dirac spectrum of electrons in single-layer graphene has been thoroughly studied both theoretically and experimentally. Although a subject of considerable theoretical interest, experimental investigations of the richer electronic structure of few-layer graphene (FLG) have been limited. Here we examine FLG graphene crystals with Bernal stacking of layer thicknesses N = 1,2,3,...8 prepared using the mechanical exfoliation technique. For each layer thickness N, infrared conductivity measurements over the spectral range of 0.2-1.0 eV have been performed and reveal a distinctive band structure, with different conductivity peaks present below 0.5 eV and a relatively flat spectrum at higher photon energies. The principal transitions exhibit a systematic energy-scaling behavior with N. These observations are explained within a unified zone-folding scheme that generates the electronic states for all FLG materials from that of the bulk 3D graphite crystal through imposition of appropriate boundary conditions. Using the Kubo formula, we find that the complete infrared conductivity spectra for the different FLG crystals can be reproduced reasonably well within the framework a tight-binding model.

Original languageEnglish (US)
Pages (from-to)14999-15004
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume107
Issue number34
DOIs
StatePublished - Aug 24 2010

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