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We analytically study the phase transitions between s-wave holographicinsulator/superconductor and metal/superconductor. The problem is solved by thevariational method for the Sturm-Liouville eigenvalue problem in the theorywith dark matter sector of U(1)-gauge field coupled to the Maxwell field.Additionally in the probe limit we investigate the marginally stable modes ofscalar perturbations in the AdS solitonic background, connected with magneticfield in the dark matter sector. We have found that even with dark mattersector the superconducting transition temperature $T_c$ is proportional tocharge density $\rho$ in power 1/3. This value seem to be strong couplingmodification of the exponent 2/3 known from the Bose - Einstein condensation ofcharged local pair bosons in narrow band superconductors. The holographicdroplet solution is affected by the coupling to the dark matter. Interestinglyin the probe limit the critical chemical potential increases with thedecreasing coupling to dark matter making the condensation transition harder toappear.

Analytic investigation of holographic phase transitions influenced by dark matter sector