  We study hairy black hole solutions in
Einstein(--Maxwell)--scalar--Gauss--Bonnet theory. The scalar coupling function
includes quadratic and quartic terms, so the gravitational action has a U(1)
symmetry. We argued that when the effective mass of the scalar field is at the
critical value, the non-hairy black holes transform into hairy black holes in a
symmetry-broken vacuum via spontaneous symmetry breaking. These hairy black
holes are stable under scalar perturbations, and the Goldstone bosons are
trivial. Moreover, we found that the spontaneous symmetry breaking associated
with local U(1) is unlikely to occur in this theory.
