Time-crystalline phase in a single-band holographic superconductor

We investigate the emergence of a time-crystalline phase in a single-band holographic superconductor, extending the the Anti-de Sitter/Conformal Field Theory (AdS/CFT) framework. By incorporating a nonlinear gauge-scalar coupling and external driving, we derive coupled equations of motion for the plasma and Higgs modes, analogous to those in high- T c superconductors. Multi-scale analysis reveals a sum resonance with subharmonic growth indicating broken time-translation symmetry. We perform numerical computation of quasinormal mode and demonstrate the transition to the time-crystalline phase. The holographic model may serve as a robust tool for studying strongly coupled time crystals.