  We construct a holographic effective superconducting theory by considering a
special gauge-axion higher derivative term. The gauge-axion coupling results in
the transport behavior similar to the vortex response in the dual boundary
field theory leading to non-Drude behavior of alternating current (AC)
conductivity at the weak momentum dissipation. With the momentum dissipation
increasing, a dip exhibits in the AC conductivity at low frequency. It is
thought to be the result of a combination of the strong momentum dissipation
and the gauge-axion coupling. In the superconducting phase, this gauge-axion
coupling also plays a key role leading to a more evident gap at the low
frequency conductivity. In addition, we also study the combined effects of the
strength of momentum dissipation and various couplings among the gauge field,
axion fields and the complex scalar field.
