  The static dielectric function in AA-stacked bilayer graphene (BLG),
subjected to an electric field applied perpendicular to layers, is calculated
analytically within the random phase approximation (RPA). This result is used
to calculate the screened Coulomb interaction and the electrical conductivity.
The screened Coulomb interaction, which here can be tuned by the perpendicular
electric field, shows a power-law decay as $1/(\gamma^{2}+V^2)$ at
long-distance limit where $V$ and $\gamma$ are the electrical potential and the
inter-layer hopping energy respectively, indicating that the Coulomb
interaction is suppressed at high perpendicular electric fields. Furthermore,
Our results for the effect of the short-range and the long-range (Coulomb)
scattering on the electrical conductivity show that the shot-range scattering
yields a constant electrical conductivity which is not affected by the
perpendicular electric filed. While the electrical conductivity limited by the
Coulomb scattering is enhanced by the perpendicular electric field and
increases linearly in $V^2$ at small $V$ with a finite value at $V=0$,
indicating that we can tune the electrical conductivity in AA-stacked BLG by
applying a perpendicular electric field.
