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Experimental Study of the Intrinsic and Exxpetriminenstaicl StTudryaonf tshepInotrintsiPc arnodpExetrintsieic sTraonsfpoGrt rParopehrtietseofaGnradphiMte aundltMigurltiagrpaphenne SeamSpalesmples 1239 as shown by Arndt et al. (2009) and also by Dusari, Barzola-Quiquia, Esquinazi & García (2011). Furthermore, we speculate that the QHE behavior observed in bulk graphite samples (Kempa et al., 2006; Kopelevich et al., 2003) comes from internal interfaces. 3. Searching for the intrinsic transport properties of the graphene layers inside graphite 3.1 Background In this Section we will briefly discuss the background of the ballistic transport and its experimental observation in graphene layers inside the graphite structure. The wave nature of the electrons plays an important role when the sample dimensions are comparable with the wavelength of the electrons. This turns to be possible in graphite samples because the density of carriers is very small, increasing therefore the Fermi wavelength λF. On the other hand, as we will see below, a carrier within the graphene layers inside graphite can transit micrometers through the sample without collisions. Therefore the carriers in the graphene layers within an ideal graphite structure have the unusual property of having large λF as well as large mean free path l. The transport phenomenon in the ballistic regime is best described by the Landauer approach. Consider a narrow constriction connected through two wide contact leads across which a voltage is applied. Let the electrochemical potentials of two regions be μ1 and μ2. The net current flowing through the device can be taken as I = (2e2/h) ∑ Ti(μ1 − μ2) where Ti is the transmission probability of carriers and the factor 2 comes from the spin degeneracy in each sub-band (Büttiker, 1986; Landauer, 1957; Tsu & Esaki, 1973). The effective conductance through a narrow constriction is given by G = I/(μ1 − μ2) = (2e2/h) ∑ Ti. When the constriction dimensions are comparable to λF and much shorter than the mean free path l, one can see steps in the conductance when the constriction width is varied. These steps are nearly integer multiples of (2e2)/h. Conductance quantization can be also achieved by varying the potential energy. As the constriction width is reduced or the gate voltage is changed in a determined direction, the number of propagating modes at a given energy decreases, i.e. the sub-bands are cut off one by one, and therefore the conductance decreases. A new mode appears in the conductance when the constriction width increases by λF/2. Nowadays, it is feasible to fabricate devices that show ballistic transport. However, it is difficult and time consuming to fabricate these devices because of the required small dimensions when common metals or semiconductors are used. In the past there were some experiments reveling conductance quantization at low temperatures. The first experimental observations of conductance quantization in two dimensional electron gases (2DEG) were reported by van Wees et al. (1988) and Wharam et al. (1988). They studied the point contact conductance in GaAs-AlGaAs heterostructures as a function of a negative gate voltage at low temperatures. The conductance showed clear plateaus at integer multiples of 2e2/h as the width increases by an amount of λF/2. In both cases the authors could show that the transport is completely ballistic and the conductance is determined by the number of occupied sub-bands, independently of the channel length. 3.2 Ballistic transport in graphite For decades, the transport properties of bulk graphite were interpreted using Boltzmann-Drude approach assuming diffusive ohmic behavior for the conduction electrons (Kelly, 1981). Within this approach one has four temperature-dependent free parameters, namely two mobilities and two carrier densities. The determination of these parametersPDF Image | GRAPHENE SYNTHESIS CHARACTERIZATION PROPERTIES
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