  In this work, we have analytically analyzed the insulator/superconductor
phase transition in the presence of a 5-dimensional $AdS$ soliton background
using matching method and thermodynamic geometry approach. We have first
employed the matching method to obtain the critical chemical potential. We then
move on to investigate the free energy and thermodynamic geometry of this model
in 3+1 dimensions. This investigation of the thermodynamic geometry leads to
the critical chemical potential of the system from the condition of the
divergence of the scalar curvature. We have then compared the value of the
critical chemical potential $\mu_{c}$ in dimension $d=5$ obtained from these
two different methods, namely, the matching method and the thermodynamic
geometry procedure. We have also obtained an expression for the condensation
operator using the matching method. Our findings agree very well with the
numerical findings in the literature.
