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We study radial symmetric point defects with degree $\frac {k}{2}$ in 2D diskor $\mathbb{R}^2$ in $Q$-tensor framework with singular bulk energy, which isdefined by Bingham closure. First, we obtain the existence of solutions for theprofiles of radial symmetric point defects with degree $\frac k2$ in 2D disk or$\mathbb{R}^2$. Then we prove that the solution is stable for $|k|=1$ andunstable for $|k|>1$. Some identities are derived and used throughout the proofof existence and stability/instability.

Point defects in 2-D liquid crystals with singular potential: profiles and stability