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 $Ad{S}_4$. 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.