N García, P. Esquinazi, J. Barzola-Quiquia, B. Ming, and D. Spoddig

In this work we show that the spreading Ohmic resistance of a quasi-two-dimensional system of size Ω, thickness t, and with a constriction of size W connecting two half-parts of resistivity ρ goes as (2ρ/πt)ln(Ω/W), diverging logarithmically with the size. Measurements in highly oriented pyrolytic graphite (HOPG) as well as numerical simulations confirm this relation. Furthermore, we present an experimental method that allows us to obtain the carriers’ mean-free path ℓ(T), the Fermi wavelength λ(T), and the mobility μ(T) directly from experiments without adjustable parameters. Measuring the electrical resistance through microfabricated constrictions in HOPG and observing the transition from Ohmic to ballistic regime, we obtain that 0.2 μm≲ℓ≲10 μm, 0.1 μm≲λ≲2 μm, and a mobility 5×10⁴ cm²/V s≲μ≲4×10⁷ cm²/V s when the temperature T decreases from 270 to 3 K. A comparison of these results with those from literature indicates that conventional, multiband Boltzmann-Drude approaches are inadequate for oriented graphite. The upper value obtained for the mobility is much larger than that for the mobility in graphene samples of micrometer size can have.