  We study the dynamical stability of holographic superconductors. We first
classify perturbations around black hole background solutions into vector and
scalar sectors by means of a 2-dimensional rotational symmetry. We prove the
stability of the vector sector by explicitly constructing the positive definite
Hamiltonian. To reveal a mechanism for the stabilization of a superconducting
phase, we construct a quadratic action for the scalar sector. From the action,
we see the stability of black holes near a critical point is determined by the
equation of motion for a charged scalar field. We show the effective mass of
the charged scalar field in hairy black holes is always above the
Breitenlohner-Freedman bound near the critical point due to the backreaction of
a gauge field. It implies the stability of the superconducting phase. We also
argue that the stability continues away from the critical point.
