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We provide an analytical as well as a numerical study of the holographic$s$-wave superconductors in Gauss-Bonnet gravity with Power-Maxwellelectrodynamics. We limit our study to the case where scalar and gauge fieldsdo not have an effect on the background metric. We use a variational method,based on Sturm-Liouville eigenvalue problem for our analytical study, as wellas a numerical shooting method in order to compare with our analytical results.Interestingly enough, we observe that unlike Born-Infeld-like nonlinearelectrodynamics which decrease the critical temperature compared to the linearMaxwell field, the Power-Maxwell electrodynamics is able to increase thecritical temperature of the holographic superconductors in the sublinearregime. We find that requiring the finite value for the gauge field on theasymptotic boundary $r\rightarrow \infty$, restricts the power parameter, $q$,of the Power-Maxwell field to be in the range $1/2<q<{(d-1)}/{2}$. Our studyindicates that it is quite possible to make condensation \emph{easier} as $q$\emph{decreases} in its allowed range. We also find that for all values of $q$,the condensation can be affected by the Gauss-Bonnet coefficient $\alpha$.However, the presence of the Gauss-Bonnet term makes the transition slightlyharder. Finally, we obtain an analytic expression for the order parameter andthus obtain the associated critical exponent near the phase transition. We findthat the critical exponent has its universal value of $\beta=1/2$ regardless ofthe parameters $q$, $\alpha$ as well as dimension $d$, consistent withmean-field values obtained in previous studies.

Analytical and Numerical Study of Gauss-Bonnet Holographic Superconductors with Power-Maxwell Field