Optical responses of a metal with sub-nm gaps

If the size of a metallic structure is reduced to be comparable to or even smaller than the typical quantum-mechanical lengths such as the Fermi wavelength or Thomas-Fermi wavelength, the electronic structure and optical responses are modulated by quantum effects. Here, we calculate the optical responses of a metal with sub-nm gaps using the eigenstates obtained from an effective-mass quantum theory. According to our simulation, the dielectric responses can be significantly modified by tuning the inter-gap distances. Remarkably, sub-nm gaps occupying a 0.3% volumetric fraction can elongate the penetration depth by an order of magnitude in the terahertz regime. We find that the detailed dependences of electron-photon interaction matrix elements on the involved electronic wavefunctions play an important role in the optical responses. The results draw our attention to these recently fabricated systems.