A note on Landau damping of two-species Vlasov-Poisson system

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.