Quantum transport in graphene: Impurity scattering as a probe of the dirac spectrum

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 particular Dirac spectrum 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 show 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. It is found 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 transport of Andreev pairs in the presence of superconducting electrodes. We will also discuss the modification of electronic properties of graphene in the presence of adsorbed atoms and molecules and in particular focus on spin dependent scattering on adsorbates leading to a spin orbit interaction. There is indeed a big interest in controlling and inducing spin orbit interactions in graphene. One can hope to induce and detect a spin Hall effect with a great potential impact in graphene based spintronic devices and ultimately reach a regime of quantum spin Hall physics. In contrast with these very short range scatterers, we discuss the possibility to engineer networks of larger range strained regions in which electronic properties are locally modified by transferring graphene on arrays of silicon oxyde nanopillars.