Zitterbewegung, chirality, and minimal conductivity in graphene

It has been recently demonstrated experimentally that graphene, or single-layer carbon, is a gapless semiconductor with massless Dirac energy spectrum. A finite conductivity per channel of order of $e^{2}/h$ in the limit of zero temperature and zero charge carrier density is one of the striking features of this system. Here we analyze this peculiarity basing on the Kubo and Landauer formulas. Appearance of final conductivity without scattering is shown to be a characteristic property of Dirac chiral fermions in two dimensions.