Building a holographic superconductor with higher-derivative couplings

Abstract

We discuss the gravitational dual of a holographic superconductor consisting of a $U(1)$ gauge field, a complex scalar field coupled to a charged AdS black hole and a higher-derivative coupling between the $U(1)$ gauge field and the scalar with coupling constant $\ensuremath{\eta}$. In the presence of a magnetic field, the system possesses localized spatially dependent droplet solutions which, in the low temperature limit, have smaller critical temperature for $\ensuremath{\eta}>0$ than the droplet solutions without the interaction term ($\ensuremath{\eta}=0$). In the weak magnetic field limit, the opposite behavior is observed: the critical temperature increases as we increase $\ensuremath{\eta}$. We also calculate the energy gap in the probe limit and find that it is larger for $\ensuremath{\eta}<0$ than the energy gap in the conventional case ($\ensuremath{\eta}=0$).