  We investigate the analytical properties of the s-wave and p-wave holographic
insulator/superconductor phase transitions at zero temperature. In the probe
limit, we analytically calculate the critical chemical potentials at which the
insulator/superconductor phase transition occurs. Those resulting analytical
values perfectly match the previous numerical values. We also study the
relations between the condensation values and the chemical potentials near the
critical point. We find that the critical exponent for condensation operator is
1/2 for both models. The linear relations between the charge density and the
chemical potential near the critical point are also deduced in this paper,
which are qualitatively consistent with the previous numerical results.
