Effects of the finite band width in a two-dimensional electron gas: The renormalization constant and the effective mass

We have studied effects of a finite band width on the renormalization constant (Formula presented) and the effective mass (Formula presented) in a two-dimensional interacting electron gas. We first determine the polarization function (Lindhard function), taking into account a finite band width. Using the modified polarization function, we have evaluated (Formula presented) and (Formula presented) with respect to the fraction of the occupied band in the GW random phase approximation. The effect of the finite band width is found to be larger than or comparable to that of the local field correction. In particular, the finite band effects are much pronounced in the low-density regime. Further, it is found that, in an almost filled band system, (Formula presented) can be smaller than the bare electron mass due to the pure many-body interaction effects. It is also shown that results of (Formula presented) considering the finite band width describe well the experimental results in the high-density regime ((Formula presented)=0.5-2.0).