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Building a Holographic Superconductor with Higher-derivative Couplings

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 η. 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 η>0 than the droplet solutions without the interaction term (η=0). In the weak magnetic field limit, the opposite behavior is observed: the critical temperature increases as we increase η. We also calculate the energy gap in the probe limit and find that it is larger for η<0 than the energy gap in the conventional case (η=0).