Transition from Ohmic to ballistic transport in oriented graphite: Measurements and numerical simulations

Abstract

In this work we show that the spreading Ohmic resistance of a quasi-two-dimensional system of size ⍀, thickness t, and with a constriction of size W connecting two half-parts of resistivity goes as ͑2 / t͒ln͑⍀ / W͒, diverging logarithmically with the size. Measurements in highly oriented pyrolytic graphite ͑HOPG͒ as well as numerical simulations confirm this relation. Furthermore, we present an experimental method that allows us to obtain the carriers' mean-free path ᐉ͑T͒, the Fermi wavelength ͑T͒, and the mobility ͑T͒ 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 m Շ ᐉ Շ 10 m, 0.1 m ՇՇ2 m, and a mobility 5 ϫ 10 4 cm 2 / V sՇ Շ 4 ϫ 10 7 cm 2 / 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.

Sample size effects on the transport characteristics of mesoscopic graphite samples

“…The advantage of using HOPG of good quality is that in these samples and due to the perfection of the graphene layers and low coupling between them, a low two-dimensional carrier density 2 × 10 8 cm −2 n 10 11 cm −2 in the temperature range 10 K T 300 K is obtained [9]. The carrier density values obtained in Ref.…”

“…There are at least three different reasons for the failing of the Kohler rule in graphite, namely: -One reason is related to the huge electron mean free path ℓ(T ) in graphite, which is much larger than the radius of curvature of an electron orbit under a magnetic field r c = m * v F /eB, with m * 0.01m the effective electron mass, v F ∼ 10 6 m/s the Fermi velocity and e the electron charge. For a field of 1 T, for example, we have r c ∼ 0.1 µm whereas ℓ > 0.1 µm for T < 200 K at zero field [9]. -Other reason is that the semiclassical picture of the MR breaks down when the Fermi wavelength λ F gets larger than r c , i.e.…”

“…Electron back scattering diffraction measurements done on similar HOPG samples indicate that the typical size of the single crystalline regions (on the (a,b) plane) ranges between 1 to ∼ 10 µm [9]. If the interface between the crystalline regions as well as the defects in the crystalline lattice have some influence on the transport properties we would expect to see a change in the behavior of the transport properties between samples of thickness of the order or less than the average thickness of the crystalline regions.…”

“…Therefore it should be possible to obtain their intrinsic transport properties without external influence other than those coming from the lattice defects. A direct proof of the perfection of the graphene layers in high quality graphite is given by the very low carrier density measured at low temperatures, which is nearly two orders of magnitude smaller than the minimum obtained for suspended graphene samples [9].…”

“…This effect was ascribed to the large carrier mean free path ℓ as well as the large Fermi (or de Broglie) wavelength λ F in graphite. Recently, García et al [9] reported the development of an experimental method and its theoretical basis to obtain without free parameters these two transport properties based on the measurement of the resistance through micro-constrictions on a ∼ 30 µm thick HOPG sample. In that work micrometer large values for ℓ and λ F at T ≤ 10 K were obtained in agreement with the expectations from the magnetoresistance results [8].…”