Two distinct ballistic processes in graphene at the Dirac point

Abstract

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) = (h) over bar /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 W >> L) to conductivity sigma(2) = pi/2 e(2)/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-Butticker approach resulting from evanescent waves. It is equal to sigma(1) = 4/pi e(2)/h for W >> L and t(U) << t(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 sigma(2) was measured, sigma(1) would appear in experiments on small ballistic graphene flakes on substrate.