Two distinct ballistic processes in graphene at the Dirac point

The dynamical approach is applied to ballistic transport in mesoscopic graphene samples of length L and contact potential U. At times shorter than both relevant time scales, the flight time t_L=L/v_g (v _g is Fermi velocity) and t_U=/U, the major effect of the electric field is to create electron-hole pairs, i.e., causing interband transitions. In linear response, this leads (for width WL) to conductivity σ₂=π/2 e2/h. On the other hand, at times lager than the two scales, the mechanism and value are different. It is shown that the conductivity approaches its intraband value, equal to the one obtained within the Landauer-Bütticker approach resulting from evanescent waves. It is equal to σ₁=4/π e2/h for WL and t_Ut_L. The interband transitions, within linear response, are unimportant in this limit. Between these extremes there is a crossover behavior dependent on the ratio between the two time scales t_L/t_U. At strong electric fields (beyond linear response) the interband process dominates. The electron-hole mechanism is universal, namely, does not depend on geometry (aspect ratio, topology of boundary conditions, properties of leads), while the evanescent modes mechanism depends on all of them. On basis of the results we determine that while in absorption measurements and in dc transport in suspended graphene σ₂ was measured, σ₁ would appear in experiments on small ballistic graphene flakes on substrate.