Minimum conductivity and maximum Fano factor in mesoscopic graphene

We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip of graphene (with no impurities or defects), to obtain the conductance and shot noise as a function of Fermi energy. We find that the minimum conductivity of order e2/h at the Dirac point (when the electron and hole excitations are degenerate) is associated with a maximum of the Fano factor (the ratio of noise power and mean current). For short and wide graphene strips the Fano factor at the Dirac point equals 1/3, three times smaller than for a Poisson process. The minimum conductivity of order e2/h and the Fano factor of 1/3 are two remarkable results which indicate that ballistic transport of relativistic electrons at the Dirac point is pseudo-diffusive. This is due to the fact that transport occurs via evanescent modes.