  We present spontaneous scalarization of charged black holes (BHs) which is
induced by the coupling of the scalar field to the electromagnetic field
strength and the double-dual Riemann tensor
$L^{\mu\nu\alpha\beta}F_{\mu\nu}F_{\alpha\beta}$ in a scalar-vector-tensor
theory. In our model, the scalarization can be realized under the curved
background with a non-trivial electromagnetic field, such as
Reissner-Nordstr$\ddot{\rm o}$m Black Holes (RN BHs). Firstly, we investigate
the stability of the constant scalar field around RN BHs in the model, and show
that the scalar field can suffer a tachyonic instability. Secondly, the bound
state solution of the test scalar field around a RN BH and its stability are
discussed. Finally, we construct scalarized BH solutions, and investigate their
stability.
