Spontaneous scalarization of Bardeen black holes

We study the spontaneous scalarization of Bardeen black holes, whose tachyonic instability triggers the formation of scalarized charged black holes (SCBHs). In this case, we find infinite ($n=0,1,2,\cdots$) branches of SCBHs with magnetic charge $g$. The $n=0$ branch of SCBHs can be found for the coupling parameter $\alpha \ge {\alpha }_{n=0}(g)$ with both quadratic (1-$\alpha {\phi }^2$) and exponential ($e^{-\alpha {\phi }^2}$) couplings, where ${\alpha }_{n=0}(g)$ represents the threshold of tachyonic instability for the Bardeen black holes. Furthermore, it is shown that the $n=0$ branch for both couplings is stable against radial perturbations. This stability shows that this branch can be used for further observational implications.