Fig. 1: Concept of dynamic modulation of hybrid erbium–graphene system.

a Schematic illustration of the hybrid erbium–graphene system when the Fermi energy of graphene is tuned to  ~0.6 eV and the erbium–graphene interaction leads to intraband transitions, mainly associated with launching of propagating graphene plasmons (red waves). The system contains, from top to bottom, a monolayer of graphene, a thin film (~12 nm) of Y₂O₃ containing erbium ions (white spheres), a 285-nm-thick SiO₂ layer, and a p-doped silicon backgate. A backgate voltage, V_bg, is applied between the backgate and a gold electrode in contact with graphene for fast modulation. The SiO₂ layer serves as electrical isolation between graphene and the p-doped silicon. On top of graphene, there is a transparent topgate made of polymer electrolyte (not shown in the image). b Sinusoidal time evolution of the Fermi energy of graphene (dashed black line, left vertical axis) and the corresponding decay-enhancement factor F_P for an erbium emitter located at z = 5 nm from graphene (solid purple line, right vertical axis). The modulation of the Fermi energy, calculated following refs. ^28,29, leads to a modulation of F_P by more than one order of magnitude—from  <100 in the intraband regime to  >1000 in the interband regime. c Schematic illustration of the hybrid erbium–graphene system for E_F ~ 0.3 eV, which corresponds to interband transitions, mainly creating electron–hole pairs (red–blue spheres).