Quantum effects in tunnelling plasmonics

The optical response of metallic nanoparticles shows antenna resonance effects at optical frequencies derived from the collective excitation of the conduction electrons at the boundaries of the particles, so called surface plasmons. This response is commonly described in the framework of classical electrodynamics by means of a linear polarizability obtained within a local or nonlocal approach of the excitations. Alternatively, quantum mechanics within time-dependent density functional theory (TDDFT) offers an appropriate framework to fully address the complex exchange and correlations of the electron gas in the metal together with an accurate description of the geometrical boundaries of the particles through the corresponding potential barriers. In Fig. 1 we show the differences between a classical and a quantum treatment of the optical response for the two lowest bonding plasmon modes in a Na nanodimer. Quantum effects derived from the spill out of the electrons at the boundaries and from the electron tunnelling between particles are properly addressed within the TDDFT showing clear differences with respect to a classical treatment. However the number of electrons that can be considered in the quantum calculation is typically limited to a few thousands of electrons, therefore far from realistic plasmonic systems that usually involve millions or billions of electrons. Here we introduce a quantum-corrected model (QCM) that integrates the quantum response of a metallic cavity with the macroscopic response of the rest of the plasmonic system [1]. This hybrid response accounts properly for quantum effects derived from the coherent tunnelling across the cavity while tracing the macroscopic plasmonic modes.