Holographic entanglement entropy in general holographic superconductor models with logarithmic nonlinear electrodynamics

We explore the behaviors of the holographic entanglement entropy (HEE) in holographic superconductor models with logarithmic nonlinear electrodynamics (LNE) both in AdS soliton and in AdS black hole backgrounds. We observe that the slope of the HEE at the phase transition point behaves discontinuously for different LNE parameters b and geometry parameters l, which may be a quite general feature for the second order phase transition. Moreover, at the critical point, the stronger nonlinearity of the LNE gives rise to the smaller HEE in metal/superconductor while leaves the HEE in insulator/superconductor model as is. Interestingly, the behavior of the HEE also implies a "confinement/deconfinement" phase transition in the insulator/superconductor model, and the critical width of the phase transition depends on the chemical potential and the strength of the LNE.