  In this paper, we analytically study the holographic superconductor models
with the high derivative (HD) coupling terms. Using the Sturm-Liouville (SL)
eigenvalue method, we perturbatively calculate the critical temperature. The
analytical results are in good agreement with the numerical results. It
confirms that the perturbative method in terms of the HD coupling parameters is
available. Along the same line, we analytically calculate the value of the
condensation near the critical temperature. We find that the phase transition
is second order with mean field behavior, which is independent of the HD
coupling parameters. Then in the low temperature limit, we also calculate the
conductivity, which is qualitatively consistent with the numerical one. We find
that the superconducting energy gap is proportional to the value of the
condensation. But we note that since the condensation changes with the HD
coupling parameters, as the function of the HD coupling parameters, the
superconducting energy gap follows the same change trend as that of the
condensation.
