Length dependence of the resistance in graphite: Influence of ballistic transport

Abstract

Using a linear array of voltage electrodes with a separation of several micrometers on a 20 nm thick and 30 µm long multigraphene sample we show that the measured resistance does not follow the usual length dependence according to Ohm's law. The deviations can be quantitatively explained taking into account Sharvin-Knudsen formula for ballistic transport. This allows us to obtain without free parameters the mean free path of the carriers in the sample at different temperatures. In agreement with recently reported values obtained with a different experimental method, we obtain that the carrier mean free path is of the order of ∼ 2 µm with a mobility µ ∼ 10 7 cm 2 V −1 s −1 . The results indicate that the usual Ohm's law is not adequate to calculate the absolute resistivity of mesoscopic graphite samples.

Evidence for semiconducting behavior with a narrow band gap of Bernal graphite

“…Following the characterization work of [27], the Raman spectra confirm similar stacking between the bulk and thin graphite samples. The micrometer large mean free path at 300 K and the low carrier density [28,29] are further proof of the high quality of the thin graphite flakes discussed in this work.…”

“…due to the large mean free path of the carriers in the graphene layers within the graphite structure, ballistic and not diffusive transport has to be taken into account [18,29]. To obtain the mean free path or the intrinsic carrier density of the graphene layers inside graphite, one cannot use straightforwardly the Boltzmann-Drude approach to interpret the longitudinal and transverse resistances.…”

“…Another experimental method is by the measurement of the length dependence of the resistance. If ballistic transport is important, then a finite resistance is extrapolated at zero sample length, a value that can be used to obtain directly the mean free path without free parameters or arbitrary assumptions [29]. Both independent methods provide similar large carrier mean free paths as well as a much lower carrier density than those found in the literature for bulk graphite samples.…”

Effect of ambient air on femtosecond laser ablation of highly oriented pyrolytic graphite

“…And the cross-plane size is estimated to be ∼40 nm by the reciprocal of the graphite's optical absorption coefficient of 800 nm wavelength according to Beer-Lambert law. Therefore, both the in-plane and cross-plane characteristic sizes of the heated region are relatively small compared with the phonons' MFPs even accounting for the MFPs' decrease with the increase of the target temperature [14]. So the classical size effect leading to a slower heat conduction rate than that predicted by Fourier law [15] must be considered in the heat conduction process.…”

Evidence for room temperature superconductivity at graphite interfaces

“…Several electrical resistance measurements of graphite samples of different thickness published in the last years suggest that graphite samples are not homogeneous and that the temperature as well as the absolute value of the electrical resistivity and Hall effect are not unique but thickness- [18,[20][21][22] and sample-length dependent [23,24]. Whereas the last dependence is due to the increasing contribution of ballistic transport to the total resistance the smaller the sample length, the thickness dependence observed in the transport properties is mainly due to the existence of interfaces between the two stacking orders, hexagonal or Bernal (2H) and rhombohedral (3R), see Fig.…”