  We revisit the Cauchy problem of nonlinear massive Dirac equation with Yukawa
type potentials $\mathcal F^{-1}\left[(b^2 + |\xi|^2)^{-1}\right]$ in 2
dimensions. The authors of \cite{tes2d, geosha} obtained small data scattering
and large data global well-posedness in $H^s$ for $s > 0$, respectively. In
this paper we show that the small data scattering occurs in $L_x^2(\mathbb
R^2)$. This can be done by combining bilinear estimates and modulation
estimates of \cite{yang, tes2d}.
