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

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 ¼ 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. electronic structures | infrared spectroscopy | zone-folding method T he unique electronic properties of graphene, a single-monolayer of sp 2 -hybridized carbon, have attracted much attention (1). Graphene's few-layer counterparts have also recently been the subject of much interest, since this broader class of materials offers the potential for further control of electronic states by interlayer interactions (2-6). Indeed, theoretical investigations have predicted dramatic changes in the electronic properties in few-layer graphene (FLG) compared with single-layer graphene (SLG) (7-17): When two or more layers of graphene are present in ordered FLG, the characteristic linearly dispersing bands of the single layer are either replaced or augmented by pairs of split hyperbolic bands. These new bands correspond to fermions of finite mass, unlike the electrons present in SLG that behave as massless fermions. Further, the characteristics of the electrons in FLG are expected to change sensitively with increasing layer number N, before ultimately approaching the bulk limit of graphite. Despite these fascinating predictions, experimental investigations have been limited to SLG and a few studies of the electronic properties of bilayer graphene (18-24). We examine these predictions experimentally by probing the electronic structure of FLG graphene samples for layer thickness up to N ¼ 8 using infrared conductivity spectroscopy. For each thickness, we find well-defined and distinct peaks arising from the critical points for transitions between valence and conduction bands of the relevant FLG material. The position and shape of these features in the experimental spectra, recorded over a photonenergy range of 0.2-0.9 eV, provide direct information about key features of the band structure of FLG materials.We are able to compare the posi...

Relaxation Dynamics in Graphene

“…6. This low-intensity peak overlaps the featureless frequency-independent absorption region and has already been experimentally observed [63]. In the ultra-violet region of the spectrum, two pronounced absorption peaks appear resulting from the transitions v 1 → c 1 and v 2 → c 2 , respectively.…”

Configuration-enriched magneto-electronic spectra of AAB-stacked trilayer graphene

“…The essential electronic properties can be drastically changed by the layer number [35][36][37], stacking configuration [37][38][39][40][41][42], magnetic field [43,44], electric field [45][46][47], dopping [48,49], mechanical strain [50][51][52], and temperature variation [53,54]. Few-and multi-layer graphenes have been successfully produced by experimental methods such as exfoliation of highly orientated pyrolytic graphite [55][56][57][58], metalorganic chemical vapour deposition (MOCVD) [61][62][63][64][65][66], chemical and electrochemical reduction of graphene oxide [67][68][69], and arc discharge [70,71]. There exist important stacking configurations, including AAB [57,58,69], ABC [59,60,[66][67][68][69], AAA …”

“…Few-and multi-layer graphenes have been successfully produced by experimental methods such as exfoliation of highly orientated pyrolytic graphite [55][56][57][58], metalorganic chemical vapour deposition (MOCVD) [61][62][63][64][65][66], chemical and electrochemical reduction of graphene oxide [67][68][69], and arc discharge [70,71]. There exist important stacking configurations, including AAB [57,58,69], ABC [59,60,[66][67][68][69], AAA [62,63], ABA [60,61,66,69], and twisted [62,69] and turbostratic ones [64]. The interlayer atomic interactions and stacking configurations induce the rich electronic properties of graphene.…”

Infrared and Terahertz Spectroscopy of Strongly Correlated Electron Systems under Extreme Conditions

“…The IR spectra of these systems have revealed much information about, for example, their fundamental electronic structures and band gap, the dynamics and density of mobile carriers, and phonon and molecular vibrations. A small sample of graphene was either mounted alone on a substrate, 154,159) or attached to metal electrodes and/or gates that were lithographically patterned on a substrate. [155][156][157][158] The SWCNT work was also performed with electrodes attached to the sample.…”