We present conductance measurements of a ballistic circular stadium influenced by a scanning gate. When the tip depletes the electron gas below, we observe very pronounced and regular fringes covering the entire stadium. The fringes correspond to tra
nsmitted modes in constrictions formed between the tip-induced potential and the boundaries of the stadium. Moving the tip and counting the fringes gives us exquisite control over the transmission of these constrictions. We use this control to form a quantum ring with a specific number of modes in each arm showing the Aharonov-Bohm effect in low-field magnetoconductance measurements.
We measure the dependence of the conductivity of graphene as a function of magnetic field, temperature and carrier density and discover a saturation of the dephasing length at low temperatures that we ascribe to spin memory effects. Values of the spi
n coherence length up to eight microns are found to scale with the mean free path. We consider different origins of this effect and suggest that it is controlled by resonant states that act as magnetic-like defects. By varying the level of disorder, we demonstrate that the spin coherence length can be tuned over an order of magnitude.
The effect of electron-electron interaction on the low-temperature conductivity of graphene is investigated experimentally. Unlike in other two-dimensional systems, the electron-electron interaction correction in graphene is sensitive to the details
of disorder. A new temperature regime of the interaction correction is observed where quantum interference is suppressed by intra-valley scattering. We determine the value of the interaction parameter, F_0 ~ -0.1, and show that its small value is due to the chiral nature of interacting electrons.
