Figure 1: Description of the material properties of a metallic dimer within the classical and quantum treatments.
From: Bridging quantum and classical plasmonics with a quantum-corrected model
Schematics of a metallic dimer composed of two spherical particles separated by a distance D with use of a (a) CEM, (b) QM and (c) QCM. The schematics show the variation of the dielectric properties of the materials at the boundaries of the dimers. The joint sketches show the corresponding absolute value of the conductivity σ (a,c) and electron density distribution |Ψ|2 (b). Within a classical framework (a), the conductivity is different from zero only inside the spheres and no electron transfer can occur between the particles (electron tunnelling probability T=0). In a fully quantum-mechanical treatment (b), the density of electrons in the gap is non-zero for small D and tunnelling is possible (T>0). In the QCM (c), the electron tunnelling is accounted for by describing the material in the junction with a fictitious dielectric medium (illustrated by a shaded red colour) characterized by a local dielectric permitivity 
(l(x, y), ω) that depends only on the local width l(x, y) of the junction and the nanoparticle material at both sides.
