  We study the effect of the quadratic field strength correction to the usual
Maxwell field on the holographic dual models in the backgrounds of AdS black
hole and AdS soliton. We find that in the black hole background, the higher
correction to the Maxwell field makes the condensation harder to form and
changes the expected relation in the gap frequency. This effect is similar to
that caused by the curvature correction. However, in the soliton background we
find that different from the curvature effect, the correction to the Maxwell
field does not influence the holographic superconductor and insulator phase
transition.
