  Electrically charged black holes with flat event horizon in anti-de Sitter
space have received much attention due to various applications in Anti-de
Sitter/Conformal Field Theory (AdS/CFT) correspondence, from modeling the
behavior of quark-gluon plasma to superconductor. Crucial to the physics on the
dual field theory is the fact that when embedded in string theory, black holes
in the bulk may become vulnerable to instability caused by brane
pair-production. Since dilaton arises naturally in the context of string
theory, we study the effect of coupling dilaton to Maxwell field on the
stability of flat charged AdS black holes. In particular, we study the
stability of Gao-Zhang black holes, which are locally asymptotically anti-de
Sitter. We find that for dilaton coupling parameter $\alpha$ > 1, flat black
holes are stable against brane pair production, however for 0 < $\alpha$ < 1,
the black holes eventually become unstable as the amount of electrical charges
is increased. Such instability however, behaves somewhat differently from that
of flat Reissner-Nordstr\"om black holes. In addition, we prove that the
Seiberg-Witten action of charged dilaton AdS black hole of Gao-Zhang type with
flat event horizon (at least in 5-dimension) is always logarithmically
divergent at infinity for finite values of $\alpha$, and is finite and positive
in the case $\alpha$ tends to infinity . We also comment on the robustness of
our result for other charged dilaton black holes that are not of Gao-Zhang
type.
