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In this work, we investigate an extended model of holographic superconductorby a non-linear electrodynamic interaction coupled to a complex scalar field.This non-linear interaction term can make a quantum phase transition at zerotemperature with finite charge carrier density. By solving full equations ofmotion, we can construct various shapes of the superconducting phase in thephase diagram. With a specific choice of interaction coefficients, we canconstruct a phase diagram with a superconducting dome. Also, we find a newgeometric solution inside the superconducting dome, which turns out to be aLifshitz-type geometry. This geometry is characterized by a dynamical criticalexponent, which plays a crucial role near the quantum critical point. We referto this region in the phase diagram as a `quantum critical region.'

Construction of Superconducting Dome and Emergence of Quantum Critical Region in Holography