Abstract
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.
Highlights
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
Importantly, one does not need to make a perfect superlattice in order to observe these modulations of optical responses which are dominated by inter-band transitions in a series of isolated slabs
The penetration depth converges with b once it is longer than 3 Å and it depends very sensitively on a even if a is longer than 100 nm; the penetration depth for terahertz waves of a metal with sub-nm gaps (a = 100 nm) is about one order of magnitude longer than that of a bulk metal, even if the volumetric fraction of the gaps is only 0.3%
Summary
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. We calculate the optical responses of a metal with sub-nm gaps using the eigenstates obtained from an effective-mass quantum theory. The dielectric responses can be significantly modified by tuning the inter-gap distances. The key question is how this theory is modified if there are sub-nm gaps in a metal. We perform quantum-mechanical calculations, at the level of an effective-mass theory, on the eigenvalues and wavefunctions of electrons in a metal with sub-nm gaps (Fig. 1), from which we evaluate the complex dielectric functions and penetration depths
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