Ballistic transportin graphene: A window into relativistic physics of masslessfermions

Excitations near Dirac points in graphene are 2 + 1 dimensional massless (pseudo) relativistic fermions with Fermi velocity v_g = 10⁶m/s playing a role of velocity of light. Electron-hole pairs are copuously created by an DC or AC applied electric field, a process well described using a dynamic first quantized & approach. Evolution of current density, number of pairs and energy in ballistic regime exhibits host of novel relativistic phenomena. We show how the physics far from the two Dirac points enters various physical quantities in linear response via the chiral anomaly. The series in electric field strength E up to third order indicate that at certain time scale t_nl α E-₁/₂ the physical behaviour dramatically changes and the perturbation theory breaks down. Beyond the linear response physics is explored using an exact solution of the first quantized equations. While for small electric fields the I-V curve is linear characterized by the universal minimal conductivity σ = π/2(e²/h), att > t_nl the current grows lin-early with time due to copious Schwinger's pair creation (with rate E³/²). Eventually it leads to creation of the electron-hole plasma, a process terminated by a relaxational recombination. Since there is no energy gap, the radiation due to the pairs annihilation is enhanced. The spectrum of radiation exhibits a maximum at ω = _̃/eEv_g/_Ť̃ and has a distinctive angular and polarization dependence.