Analytic investigation of holographic phase transitions influenced by dark matter sector

We analytically study the phase transitions between s-wave holographic insulator/superconductor and metal/superconductor. The problem is solved by the variational method for the Sturm-Liouville eigenvalue problem in the theory with the dark matter sector of a U(1)-gauge field coupled to the Maxwell field. Additionally in the probe limit we investigate the marginally stable modes of scalar perturbations in the AdS solitonic background, connected with a magnetic field in the dark matter sector. We have found that even with the dark matter sector the superconducting transition temperature T-c is proportional to charge density rho in power 1/3. This value seems to be the strong coupling modification of the exponent 2/3 known from the Bose-Einstein condensation of charged local pair bosons in narrow band superconductors. The holographic droplet solution is affected by the coupling to the dark matter. Interestingly in the probe limit the critical chemical potential increases with the decreasing coupling to dark matter, making it more difficult for the condensation transition to appear.