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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 describes
the correlation $\Gamma$ 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.
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