Study of the single neutral top-pion production process at $\gamma \gamma$ collider

$\gamma \gamma \to {\mathrm{\Pi }}_t^0$ is the major production mechanism of neutral top-pion at the linear colliders. In this paper, we calculate the cross section of the process $\gamma \gamma \to {\mathrm{\Pi }}_t^0$ and discuss the potential to observe the neutral top-pion via its various decay modes at the planned ILC. The study show that, among the various neutral top-pion production processes at the linear colliders, the cross section of $\gamma \gamma \to {\mathrm{\Pi }}_t^0$ is the largest one which can reach the level of ${10}^1-{10}^2$ fb. Due to the existence of the tree-level flavor-changing coupling ${\mathrm{\Pi }}_t^{0}t\bar{c}$, $\gamma\gamma\to \Pi_t^0 \to t\bar{c}$ can provide enough number of typical signals to identify the neutral top-pion with the clean SM background. Therefore, the process $\gamma \gamma \to {\mathrm{\Pi }}_t^0$ play an important role in searching for the neutral top-pion and test the TC2 model.