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

A gap plasmon is an electromagnetic wave propagating in a gap between two noble metal surfaces. Such gap plasmons have previously been studied using only a classical description of the noble metals, but this model fails and shows unphysical behavior for sub-nanometer gaps. To overcome this problem quantum spill-out is included in this paper by applying Density-Functional Theory (DFT), such that the electron density is smooth across the interfaces between metal and air. The mode index of a gap plasmon propagating in the gap between the two metal surfaces is calculated from the smooth electron density, and in the limit of vanishing gap width the mode index is found to converge properly to the refractive index of bulk metal. When neglecting quantum spill out in this limit the mode index shows unphysical behavior and diverges instead. The mode index is applied to calculate the reflectance of an ultrasharp groove array in silver, as gaps of a few nm are found in the bottom of such grooves. At these positions the gap plasmon field is highly delocalized implying that it mostly exists in the bulk silver region where absorption takes place. Surprisingly, when the bottom width is a few nm and the effect of spill out at a first glance seems to be negligible, strong absorption is found to take place 1-2 Å from the groove walls as a consequence of the dielectric function being almost zero at these positions. Hence quantum spill out is found to significantly lower the reflectance of such groove arrays in silver.