  In this paper, we study the nonlocal Choquard equation $$ -\varepsilon^2
\Delta u_\varepsilon + V u_\varepsilon= (I_\alpha *
|u_\varepsilon|^p)|u_\varepsilon|^{p-2}u_\varepsilon $$ where $N\geq 1$,
$I_\alpha$ is the Riesz potential of order $\alpha \in (0, N)$ and
$\varepsilon>0$ is a parameter. When the nonnegative potential $V\in C
(\mathbb{R}^N)$ achieves $0$ with a homogeneous behaviour or on the closure of
an open set but remains bounded away from $0$ at infinity, we show the
existence of groundstate solutions for small $\varepsilon>0$ and exhibit the
concentration behaviour as $\varepsilon\to 0$.
