  Recent experiments on two-dimensional (2D) electron systems have found a
sharp increase in the effective mass of electrons with decreasing electron
density. In an effort to understand this behavior we employ the many-body
theory to calculate the quasiparticle effective mass in 2D electron systems.
Because the low density regime is explored in the experiments we use the
$GW\Gamma$ approximation where the vertex correction $\Gamma$ describes the
correlation effects to calculate the self-energy from which the effective mass
is obtained. We find that the quasiparticle effective mass shows a sharp
increase with decreasing electron density. Disorder effects due to charged
impurity scattering plays a crucial role in density dependence of effective
mass.
