  Angular correlations between vector boson and heavy flavors~(HF) are
potentially new effective tools to gain insight into the partonic interactions
in the quark-gluon plasma (QGP). In this paper, we present the theoretical
study of the azimuthal angular de-correlations of $\gamma+$HF in
nucleus-nucleus collisions as a new probe of the in-medium $P_T$-broadening
effect. The initial production of $\gamma+$HF in p+p is generated by SHERPA
which matches the next-to-leading hard processes with parton shower. The
in-medium heavy quark evolution is implemented by a Monte Carlo Langevin
simulation, which takes into account the collisional and radiative energy loss.
We observe considerable suppression at $\Delta\phi_{\gamma D}\sim\pi$ and
enhancement at $\Delta\phi_{\gamma D}<2.8$ in $\gamma+$D azimuthal angular
distribution in $0-10\%$ Pb+Pb collisions at $\sqrt{s_{NN}}=$5.02 TeV compared
to the p+p baseline, which indicates evident in-medium $P_T$-broadening of
charm quarks. We also find that the overall modification patterns of $\gamma+$D
angular distribution are sensitive to the selection cut of D meson $p_T$.
Furthermore, by constructing the 2D ($x_{J}^{\gamma D}, \Delta\phi_{\gamma D}$)
correlation diagram, it's possible to display the respective impacts of the two
aspects of jet quenching, energy loss and $P_T$-broadening, on the final-state
$\gamma+$D observable simultaneously. Additionally, we find weaker angular
de-correlations of $\gamma+$B compared to $\gamma+$D which may be helpful to
understand the mass hierarchy in heavy-ion collisions. Finally, the nuclear
modification of $\Delta \phi_{\gamma D}$ distributions in central $0-10\%$
Au+Au collisions at RHIC energy is provided for completeness.
