Since the very first investigations of the electronic properties of graphene the nature of the scattering disorder potential has been shown to play an essential role in determining the carrier density dependence of the conductance. Impurity scattering is characterized by two different times the transport and elastic scattering times which are sensitive to the linear energy dispersion of graphene. The analysis of the ratio between these two times gives insight on the nature (neutral or charged) and range of the scatterers. We discuss how to extract these two times from magneto-transport measurements and analyze their differences in monolayer and bilayer Graphene in relation with the different symmetry properties of their band structure and wave functions. We show that whereas short range impurity scattering is the dominant mechanism limiting the classical transport, phase coherent mesoscopic transport is very sensitive to long range disorder. In particular, the formation of electron/hole puddles in the vicinity of the charge neutrality point strongly affects the amplitude of the conductance fluctuations and the induced supercurrent in the presence of superconducting electrodes.
Seminar on Disorder and strong electron correlations: " What are the relevant disorder scales for quantum transport in graphene? "
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