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Electronic transport in monolayer and bilayer graphene: physics of zero mass versus non-zero mass electrons

Electronic transport in monolayer and bilayer graphene: physics of zero mass versus non-zero mass electrons

Graphene is a single, one atom thick layer of carbon atoms, extracted from graphite. It constitutes a rare realization of a two dimensional conductor. The electrons move in the potential landscape defined by the carbon atoms, which are arranged in a hexagonal (honeycomb-like) lattice. This particular atomic arrangement confers to the electrons of the graphene monolayer a striking property: they behave as though they were massless particles. Add a second layer of these carbon atoms to the first, to form the so-called bilayer, and the electrons recover a mass, as happens in most other conductors.

In order to understand the electrical resistance of both monolayer and bilayer, one needs to determine the kind of impurities and defects that scatter electrons. To this end we compared monolayer and bilayer samples fabricated in similar conditions and that had identical conductivities: we identified the nature of the dominant scatterers and analyzed their effect on the motion of massless versus massive particles.

This was achieved by comparing two collision times, τtr and τe, which have different dependences on the size of the scatterers. The collision times were extracted from the magnetic field variations of the sample resistances (see figure). As we changed the electrons’ energy (via a gate electrode) we followed the variations of these collision times, as well as the ratio of these two times, which remained practically constant and equal to two. This suggests that long ranged charged impurities are not the dominant scatterers, as was previously believed. Rather, electrons seem to collide mostly with short range scatterers, that behave as neutral hard spheres, the size of a few carbon-carbon interatomic distances.

Interestingly, we find the same dominants scatterers for both monolayer and bilayer, even though the scattering times themselves differ in the two materials.



The difference between massive and massless particles has a different signature at very low temperature. In such a “mesoscopic” transport regime, the wavelike nature of electrons causes reproducible variations of the sample conductance as a parameter such as magnetic field or electron density is varied. These variations, called fluctuations, are a direct consequence of the interfering electron waves, whose quantum phase is changed by magnetic field or electron density. We showed that the carrier’s mass determines the characteristic fields and energies of these fluctuations, which are related to the quantum coherence lengths in the samples.

Thus the comparison of the monolayer and bilayer, chemically so close but electronically so different, is a promising avenue for the exploration of the physics of massless particles in condensed matter physics.



Transport and Elastic Scattering Times as Probes of the Nature of Impurity Scattering in Single-Layer and Bilayer Graphene - M. Monteverde, C. Ojeda-Aristizabal, R. Weil, K. Bennaceur, M. Ferrier, S. Guéron, C. Glattli, H. Bouchiat, J. N. Fuchs, and D. L. Maslov, Phys. Rev. Lett. 104, 126801 (2010)

Conductance Fluctuations and Field Asymmetry of Rectification in Graphene - C. Ojeda-Aristizabal, M. Monteverde, R. Weil, M. Ferrier, S. Guéron, and H. Bouchiat, Phys. Rev. Lett. 104, 186802 (2010)