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We discuss spontaneous scalarization of the Reissner-Nordstr\"om black holein the presence of higher derivative gauge field corrections that arise in thecontext of string, as well as higher-dimensional more fundamental gravitytheories. Our theory admits the Reissner-Nordstr\"om solution at the scalarvacuum of the theory ($\phi=0$) and we find that the higher order derivativegauge field correction term results in the tachyonic instability of our systemonce the coupling function satisfies the condition that its second derivativeis positive at the scalar vacuum in the appropriate parameter space. We findthat the branches do not end with an extremal black hole, rather with asingularity as indicated by the divergence of the Kretschmann scalar. The blackholes can be overcharged in the sense that they may carry larger electriccharge in comparison to their mass. Finally, these solutions possess largerentropy at the event horizon radius when compared to the Reissner-Nordstr\"omblack hole, as well as to scalarized black holes without the higher orderderivative gauge field terms, indicating in this way the thermodynamicprefer-ability of our system, when compared to existing literature, while theyrespect the energy conditions.

Scalarization of the Reissner-Nordstr\"om black hole with higher derivative gauge field corrections