Full Counting Statistics of Charge Transport in Graphene

Recently experimental realization of graphene, a mono-layer of carbon atoms with hexagonal lattice structure, has introduced new type of two dimensional materials with unique properties [1]. Due to a gapless semiconducting electronic band structure with a linear dispersion relation at low energies the electrons in graphene behave identical to two dimensional massless Dirac fermions. Such a peculiar quasiparticle spectrum is fundamentally different from that of a normal metal or a semiconductor and has led to anomalous behavior in several transport phenomena including the integer quantum Hall effect, the conductance quantization and Josephson effect [2, 3, 4].The relativistic-like nature of the quasiparticles is expected to have anomalous effects on the low temperature fluctuations of the current through a graphene sample. Tworzydlo et.al. [5] studied the second-order correlation of the current fluctuations, the so called shot noise, of a ballistic graphene strip. They found that at low concentration of the charge carriers (Dirac point) the shot noise can be drastically different from an ordinary ballistic contact depending on the type of the graphene edges and the width to length ratio W/L. Interestingly for wide graphene strip the shot noise of a ballistic graphene tends to have the value of the corresponding diffusive structure. Shot noise measurement provides additional information about the transport process which is not extractable from the average current. However, the complete statistics of the charge transport is given by the so called full counting statistics (FCS) which is generally given by the probability P(n) that the total number n of the charge carriers to be transferred within a certain period of time. By P(n) one can access all orders of the current correlations (cumulants)