Quantum spill out in few-nanometer metal gaps: Effect on gap plasmons and reflectance from ultrasharp groove arrays

Plasmons in ultranarrow metal gaps are highly sensitive to the electron density profile at the metal surfaces. Using a fully quantum mechanical approach, we study the effects of electron spill-out on gap plasmons and reflectance from ultrasharp metal grooves. We demonstrate that the mode index of ultranarrow gap plasmons converges to the bulk refractive index in the limit of vanishing gap and, thereby, rectify the unphysical divergence found in classical models. Surprisingly, spill-out also significantly increases the plasmonic absorption for few-nanometer gaps and lowers the reflectance from arrays of ultrasharp metal grooves. These findings are explained in terms of enhanced gap plasmon absorption taking place inside the gap 1-2 {\AA} from the walls and delocalization near the groove bottom. Reflectance calculations taking spill-out into account are shown to be in much better agreement with measurements compared with classical models.