  Using the Kubo formula we develop a general and simple expression for the
minimal conductivity in systems described by a two by two Hamiltonian. As an
application we derive an analytical expression for the minimal conductivity
tensor of bilayer graphene as a function of a complex parameter $w$ related to
recently proposed symmetry breaking mechanisms resulting from electron-electron
interaction or strain applied to the sample. The number of Dirac points changes
with varying parameter w, this directly affect the minimal conductivity. Our
analytic expression is confirmed using an independent calculation based on
Landauer approach and we find remarkably good agreement between the two
methods. We demonstrate that the minimal conductivity is very sensitive to the
change of the parameter $w$ and the orientation of the electrodes with respect
to the sample. Our results show that the minimal conductivity is closely
related to the topology of the low energy band structure.
