Excited states of holographic superconductors

In this paper we re-investigate the model of the anti-de Sitter gravity coupled to Maxwell and charged scalar fields, which has been studied as the gravitational dual to a superconductor for a long time since the famous work [Phys. Rev. Lett.101 (2008) 031601]. By numerical method, we present a novel family of solutions of holographical superconductor with excited states, and find there exists a lower critical temperature in the corresponding excited state. Moreover, we study the condensate and conductivity in the excited states. It is very interesting that the conductivity σ of each excited state has an additional pole in Im[σ] and a delta function in Re[σ] arising at the low temperature inside the gap, which is just the evidence of the existence of excited states.