Many body renormalization of the minimal conductivity in graphene

The conductance of ballistic graphene at the neutrality point is due to coherent electron tunneling between the leads, the so called pseudodiffusive regime. The conductance scales as function of the sample dimensions in the same way as in a diffusive metal, despite the difference in the physical mechanisms involved. The electron-electron interaction modifies this regime, and plays a role similar to that of the environment in macroscopic quantum phenomena. We show that interactions, and the presence of external gates, change substantially the transport properties, and can lead to a diverging resistivity at the neutrality point.