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Some interpretations of $R_{D^{(*)}}$ anomaly in $B$ meson decay usingleptoquark (LQ) models can also generate top quark decays through FlavorChanging Neutral Current (FCNC). In this work we focus on two LQs, i.e. scalar$S_1$ and vector $U_1$ which are both singlet under the $SU(2)_L$ gauge groupin the Standard Model (SM). We investigate their implications on the 3-body topFCNC decays $t\to c \ell_i \ell_j$ at tree level and the 2-body $t\to c V$ atone-loop level, with $\ell$ being the SM leptons and $V=\gamma, Z, g$ being theSM gauge bosons. We utilize the $2\sigma$ parameter fitting ranges of the LQmodels and find that $Br(t\to c \ell_i \ell_j)$ at tree level can reach$\mathcal{O}(10^{-6})$ and $Br(t\to c V)$ at one-loop level can reach$\mathcal{O}(10^{-10})$. Some quick collider search prospects are alsoanalyzed.

Correlation between $R_{D^{(*)}}$ and top quark FCNC decays in leptoquark models