Holographic model of a three-dimensional current carrying superconductor or superfluid with dark matter sector described by the additional U(1)-gauge field coupled to the ordinary Maxwell one, has been studied in the probe limit. We investigated analytically by the Sturm-Liouville variational method, the holographic s-wave and p-wave models in the background of the AdS soliton as well as five-dimensional AdS black hole spacetimes. The two models of p-wave superfluids were considered, the so

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... ed SU(2) and the Maxwell-vector. Special attention has been paid to the dependence of the critical chemical potential and critical transition temperature on the velocity of the condensate and dark matter parameters. The current J in holographic three-dimensional superconductor studied here, shows the linear dependence on T_c-T for both s and p-wave symmetry. This is in a significant contrast with the previously obtained results for two-dimensional superconductors, which reveal the (T-T_c)^3/2 temperature dependence. The coupling constant α, as well as, chemical potential μ_D and the velocity S_D of the dark matter, affect the critical chemical potential of the p-wave holographic SU(2) system. On the other hand, α, dark matter velocity S_D and density ρ_D determine the actual value of the transition temperature of the same superconductor/superfluid set up. However, the dark matter does not affect the value of the current.