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

TL;DR

This study investigates how ballistic transport affects the resistance of multigraphene, revealing deviations from Ohm's law and enabling precise measurement of carrier mean free paths at different temperatures.

Contribution

It demonstrates the significance of ballistic transport in mesoscopic graphite, providing a parameter-free method to determine carrier mean free paths and challenging traditional resistivity calculations.

Findings

Resistance deviates from Ohm's law due to ballistic effects.

Carrier mean free path is approximately 2 micrometers.

Usual Ohm's law is inadequate for mesoscopic graphite resistivity.

Abstract

Using a linear array of voltage electrodes with a separation of several micrometers on a $20 $nm thick and 30 $\mu$m 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 $\sim 2 \mu$m with a mobility $\mu \sim 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.