  We investigate the contribution of charge puddles to the non-vanishing
conductivity minimum in disordered graphene flakes at the charge neutrality
point. For that purpose, we study systems with a geometry that suppresses the
transmission due to evanescent modes allowing to single out the effect of
charge fluctuations in the transport properties. We use the recursive Green's
functions technique to obtain local and total transmissions through systems
that mimic vanishing density of states at the charge neutrality point in the
presence of a local disordered local potential to model the charge puddles. Our
microscopic model includes electron-electron interactions via a spin resolved
Hubbard mean field term. We establish the relation between the charge puddle
disorder potential and the electronic transmission at the charge neutrality
point. We discuss the implications of our findings to high mobility graphene
samples deposited on different substrates and provide a qualitative
interpretation of recent experimental results.
