Surface states in one-dimensional graphene-dielectric photonic crystal

In this work, we theoretically investigate the propagation and localization of electromagnetic waves in both infinite and semi-infinite superlattice (SL) composed of graphene/dielectric bilayers. Our aim is to demonstrate the existence of band gaps in an infinite SL despite the thinness of the graphene layer. Additionally, we explore the existence of surface modes in a semi-infinite SL terminated by a thin cap layer, which can be either dielectric or graphene in analogy with surface modes observed in one-dimensional superconducting photonic crystals. These surface modes fall below the light line of vacuum and within the SL band gaps. By analyzing the electric and magnetic fields of these modes, we study their spatial localization within the system.