Abstract
In this paper, based on analytic technique, several properties of holographic $ s $-wave superconductors have been investigated in the presence of various higher derivative (\textit{non linear}) corrections to the usual Maxwell action. Explicit expressions for the critical temperature and the condensation values have been obtained in the probe limit. Finally, the nature of condensate solutions have been investigated by immersing the superconductor in an external magnetic field. It is found that below certain critical magnetic field strength ($ B_c $) there exists a superconducting phase. Most importantly it has been observed that the value of this critical field strength ($ B_c $) indeed gets affected due to the presence of higher derivative corrections to the usual Maxwell action.
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