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 sigma of each excited state has an additional pole in Im[sigma] and a delta function in Re[sigma] arising at the low temperature inside the gap, which is just the evidence of the existence of excited states.