| Summary: | We study the ground state and excited states of holographic superconducting phase transition in a gravity model with scalar field coupled to Gauss-Bonnet invariance. We investigate the effect of the coupling on the condensate properties for the first three states of holographic superconductor. We find that the holographic superconducting phase transition only occurs when the coupling parameter is smaller than a critical value, which is reasonable because the strong coupling would force the scalar field to fall into the black hole. Our investigation shows that the coupling has interesting prints on the critical temperature, condensation strength and optical conductivity for the ground state, first and second excited states of the holographic superconductor.
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