  In this paper, we investigate the holographic phase transition with dark
matter sector in the AdS black hole background away from the probe limit. We
disclose the properties of phases mostly from the holographic topological
entanglement entropy of the system. We find the entanglement entropy is a good
probe to the critical temperature and the order of the phase transition in the
general model. The behaviors of entanglement entropy at large strip size
suggest that the area law still holds with dark matter sector. We also conclude
that the holographic topological entanglement entropy is useful in detecting
the stability of the phase transitions. Furthermore, we derive the complete
diagram of the effects of coupled parameters on the critical temperature
through the entanglement entropy and analytical methods.
