Holographic superconductors in the AdS black hole with a magnetic charge
  In this work we study the analytical properties of a 2+1 dimensional magnetically charged holographic superconductor in $AdS_4$. We obtain the critical chemical potential $\mu_c$ analytically, using the Sturm-Liouville variational approach. Also, the obtained analytic result can be used to back up the numerical computations in the holographic superconductor in the probe limit. 
M. R. Setare, D. Momeni, R. Myrzakulov, Muhammad Raza
physics.gen-ph hep-th