  In this note we adopt an approach by Grenier, Nguyen and Rodnianski in
\cite{GNR} for studying the nonlinear Landau damping of the two-species
Vlasov-Poisson system in the phase space $\mathbb{T}^d_x \times \mathbb{R}^d_v$
with the dimension $d\geq 1$. The main goal is twofold: one is to extend the
one-species case to the two-species case where the electron mass is finite and
the ion mass is sufficiently large, and the other is to modify the
$G$-functional such that it involves the norm in $L^{d+1}$ instead of $L^2$ as
well as derivatives up to only the first order.
