Figure 1: The impact of quantum mechanical effects on plasmonic resonances.
From: Quantum mechanical effects in plasmonic structures with subnanometre gaps
Sketch of the different regimes for the plasmon resonances of a sphere-dimer in vacuum identified as a function of the gap distance d. These regimes are illustrated by the energies of the plasmonic modes predicted by the classical (red dashed line) and quantum calculations (solid lines). For large gap distances, the system is in the classical regime and its response can be described using Maxwell’s equations with empirical or model local dielectric constants of the metal ɛM. In the nonlocal regime (d<dNL), the actual position of the screening charges with respect to the geometrical boundaries given by δF leads to an effective correction of the ‘physical’ gap distance compared with the geometrical gap distance d. The nonlocal screening leads to deviations between the classical (dashed line) and quantum descriptions (solid line). In the tunnelling regime, the ac tunnelling current Jω across the junction strongly changes the optical response, when the conductivity of the junction becomes larger than σth (which sets the corresponding threshold gap distance dth). The plasmon modes of the separated dimer are progressively extinguished, and the CTP modes emerge before their direct geometrical overlap. We denote the distance range where the electric tunnelling and/or the nonlocal screening are important as the ‘quantum regime’. The plasmonic resonance in this regime can be addressed using ab-initio approaches or model descriptions. The transition between the different regimes is smooth and the boundaries shown in the figure are only indicative.
