Building a Holographic Superconductor with a Scalar Field Coupled Kinematically to Einstein Tensor

We study the holographic dual description of a superconductor in which the gravity sector consists of a Maxwell field and a charged scalar field which except its minimal coupling to gravity it is also coupled kinematically to Einstein tensor. As the strength of the new coupling is increased, the critical temperature below which the scalar field condenses is lowering, the condensation gap decreases faster than the temperature, the width of the condensation gap is not proportional to the size of the condensate and at low temperatures the condensation gap tends to zero for the strong coupling. These effects which are the result of the presence of the coupling of the scalar field to the Einstein tensor in the gravity bulk, provide a dual description of impurities concentration in a superconducting state on the boundary.