Instability of AdS black holes with lattices

Anti-de Sitter(AdS)black holes with lattices are essential for optical conductivity studies in the holographic approach.We investigate the instability of these black holes that can result in the holographic description of charge density waves.In the presence of homogeneous axion fields,we show that the instability of AdS-Reissner-Nordström(AdS-RN)black holes 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 the metal/insulator phase transition.This novel phenomenon is reminiscent of the behavior of the holographic entanglement entropy during quantum phase transitions.