  We investigate the effect of the mass anisotropy on Friedel Oscillations,
Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, screening properties, and
Boltzmann transport in two dimensional (2D) metallic and doped semiconductor
systems. We calculate the static polarizability and the dielectric function
within the random phase approximation with the mass anisotropy fully taken into
account without making any effective isotropic approximation in the theory. We
find that carrier screening exhibits an isotropic behavior for small momenta
despite the anisotropy of the system, and becomes strongly anisotropic above a
certain threshold momentum. Such an anisotropy of screening leads to
anisotropic Friedel oscillations, and an anisotropic RKKY interaction
characterized by a periodicity dependent on the direction between the localized
magnetic moments. We also explore the disorder limited dc transport properties
in the presence of mass anisotropy based on the Boltzmann transport theory.
Interestingly, we find that the anisotropy ratio of the short range disorder
limited resistivity along the heavy- and light-mass directions is always the
same as the mass anisotropy ratio whereas for the long range disorder limited
resistivity the anisotropy ratio is the same as the mass ratio only in the low
density limit, and saturates to the square root of the mass ratio in the high
density limit. Our theoretical work should apply to many existing and
to-be-discovered anisotropic 2D systems.
