  We calculated the minimal longitudinal conductivity in prefect single and
bilayer graphene by extending the two methods developed for Dirac fermion gas
by A. W. W. Ludwig et al. in Phys. Rev. B {\bf 50}, 7526 (1994). Using the Kubo
formula which was originally applied for spintronic systems we obtain
$\sigma^{\text min}_{xx}= (J \pi /2) e^2/h$ while from the other formula used
in the above mentioned work we find $\bar{\sigma}^{\text min}_{xx}= (4J/\pi)
e^2/h$, where J=1 for single layer and J=2 for bilayer graphene. The two
universal values are different although they are numerically close to each
other. Our two results are in the same order of magnitude as that of
experiments and for single layer case one of our result agrees many earlier
theoretical predictions. However, for bilayer graphene only two studies are
known with predictions for the minimal conductivity different from our
calculated values. Similarly to the single layer case, the physical origin of
the minimal conductivity in bilayer graphene is also rooted back to the
intrinsic disorder induced by the Zitterbewegung which is related to the
trembling motion of the electron.
