Quantized Evolution of the Plasmonic Response in a Stretched Nanorod

Quantum aspects, such as electron tunneling between closely separated metallic nanoparticles, are crucial for understanding the plasmonic response of nanoscale systems. We explore quantum effects on the response of the conductively coupled metallic nanoparticle dimer. This is realized by stretching a nanorod, which leads to the formation of a narrowing atomic contact between the two nanorod ends. Based on first-principles time-dependent density-functional-theory calculations, we find a discontinuous evolution of the plasmonic response as the nanorod is stretched. This is especially pronounced for the intensity of the main charge-transfer plasmon mode. We show the correlation between the observed discontinuities and the discrete nature of the conduction channels supported by the formed atomic-sized junction.

Figure 1

Evolution of the plasmonic response of a sodium nanorod under stretching. (a) Selected snapshots of the simulated stretching process of the nanorod. Elongation distances $d$ from $A$ to $H$: 0, 6, 10, 14, 20, 22, 26, and 28 Å. (b) Longitudinal photoabsorption spectra of the stretched nanorod as a function of energy $\hslash \omega$. Solid lines following the plasmon modes (see main text for the label definitions) are drawn to guide the eye. (c) IID maps [see Eq. (2)] as a function of energy and $z$ coordinate along the main axis of the nanorod. The maps have been smoothed along $z$ to emphasize the gross features of the induced density [27]. Insets show the corresponding geometries (right) and spectra (top). Note that in panels $E$, $F$, and $G$, the low-energy part of the IID map and spectrum have been scaled by the indicated factor.

Figure 2

Detailed analysis of the plasmon modes during the nanorod stretching. (a) Peak energy and (b) integrated intensity (the area under the peak) of the plasmon modes as a function of the nanorod elongation $d$ [52]. The intensities are normalized so that the full spectrum integrates to the number of valence electrons (261). The line labels correspond to the labeling used in Fig. 1 and labels $A$–$H$ to the geometries shown in Fig. 1. (c) Zero-bias conductance of the junction formed during the stretching. Horizontal lines mark values of $1G_0$, $3G_0$, and $6G_0$. Vertical lines mark the discontinuities found in the evolution of the plasmon modes.