Excited states of holographic superconductors with backreaction

In this paper we investigate the model of the anti-de Sitter gravity coupled to a Maxwell field and a free, complex scalar field, and construct a fully back-reacted holographic model of superconductor with excited states. With the fixed charge $q$, there exist a series of excited states of holographic superconductor with the corresponding critical chemical potentials. The condensates as functions of the temperature for the two operators $\mathcal{O}_1$ and $\mathcal{O}_2$ of excited states are also studied. For the optical conductivity in the excited states, we find that there exist the additional peaks in the imaginary and real parts of the conductivity. Moreover, the number of peaks corresponding to $n$-th excited state is equal to $n$.