Dynamics of Particle-Hole Pair Creation in Graphene

The process of coherent creation of particle-hole excitations by an electric field in graphene is quantitatively described. We calculate the evolution of the current density, number of pairs, and energy after switching on the electric field. In particular, it leads to a dynamical visualization of universal finite resistivity without dissipation in pure graphene. We show that the dc conductivity of pure graphene is π/2e²/h rather than the often cited value of 4/πe²/h. This value coincides with the ac conductivity calculated and measured recently at optical frequencies. The effect of temperature and random chemical potential (charge puddles) are considered and explain the recent experiment on suspended graphene. A possibility of Bloch oscillations is discussed within the tight binding model.