  The Anti-de Sitter (AdS) black hole with lattice structure plays an essential
role in the study of the optical conductivity in holographic approach. We
investigate the instability of this sort of black holes which may lead to the
holographic description of charge density waves. In the presence of homogeneous
axion fields, we show that the instability of AdS-Reissner-Nordstr\"om(AdS-RN)
black hole is always suppressed. However, in the presence of Q-lattices, we
find that the unstable region becomes the smallest in the vicinity of the
critical region for metal/insulator phase transition. This novel phenomenon is
reminiscent of the behavior of the holographic entanglement entropy during
quantum phase transition.
