The quantum localization in the quantum Hall regime is revisited using Graphene monolayers with accurate measurements of the longitudinal resistivity as a function of temperature and current. We experimentally show for the first time a cross-over fro
m Efros-Shklovskii Variable Range Hopping (VRH) conduction regime with Coulomb interactions to a Mott VRH regime without interaction. This occurs at Hall plateau transitions for localization lengths larger than the interaction screening length set by the nearby gate. Measurements of the scaling exponents of the conductance peak widths with both temperature and current give the first validation of the Polyakov-Shklovskii scenario that VRH alone is sufficient to describe conductance in the Quantum Hall regime and that the usual assumption of a metallic conduction regime on conductance peaks is unnecessary.
We report on direct measurements of the electronic shot noise of a quantum point contact at frequencies nu in the range 4-8 GHz. The very small energy scale used ensures energy independent transmissions of the few transmitted electronic modes and the
ir accurate knowledge. Both the thermal energy and the quantum point contact drain-source voltage Vds are comparable to the photon energy hnu leading to observation of the shot noise suppression when $V_{ds}<h u/e$. Our measurements provide the first complete test of the finite frequency shot noise scattering theory without adjustable parameters.
