Spatially resolved quantum plasmon modes in metallic nano-films from first-principles

Abstract

Electron energy loss spectroscopy (EELS) can be used to probe plasmon excitations in nanostructured materials with atomic-scale spatial resolution. For structures smaller than a few nanometers, quantum effects are expected to be important, limiting the validity of widely used semiclassical response models. Here we present a method to identify and compute spatially resolved plasmon modes from first-principles based on a spectral analysis of the dynamical dielectric function. As an example we calculate the plasmon modes of 0.5 to 4 nm thick Na films and find that they can be classified as (conventional) surface modes, subsurface modes, and a discrete set of bulk modes resembling standing waves across the film. We find clear effects of both quantum confinement and nonlocal response. The quantum plasmon modes provide an intuitive picture of collective excitations of confined electron systems and offer a clear interpretation of spatially resolved EELS spectra.

Visualizing hybridized quantum plasmons in coupled nanowires: From classical to tunneling regime

“…39 However, S 1 and S 2 , are seen to be redshifted with respect to the classical value in the limit q → 0, and for S 1 the redshift increases further with decreasing R. A redshift is expected for decreasing size of simple metal nanostructures due to electron spill-out; as the surface to bulk ratio increases, the spill-out will lead to a decrease in the mean electron density, which results in a lower plasmon frequency. This redshift was also observed for the plasmon eigenmodes of thin slabs of sodium, 31 and for quantum calculation on small Na clusters. 40 This is opposed to the behavior of silver nanostructures, where coupling to single-particle transitions originating from the 3d states leads to blue shift with decreasing size.…”

“…Thus, for this mode, the impact of spill-out exceeds the size quantization effects, which leads to an overall redshift in energy. 41 For calculations on thin Na slabs, 31 a redshift of the dipole plasmon mode was observed at 5-nm film thickness, and since spill-out will have a larger impact on 1D structures this indicates that the redshift should be observable for much thicker wires. The magnitude of the q dispersion is expected to be independent on R for large q, and interestingly, we find an apparent linear dispersion of the surface modes with q in this range.…”

“…This allows us to study simple metals such as Na, where local field effects have been found to be negligible. 31 We note that for the study of noble metals such as Ag and Au this jellium approach will not be justified since the 3d and 4d bands of these metals play a large role in screening the plasmon excitations and therefore must be included. The local density approximation (LDA) was used for exchange correlation.…”

“…The right-hand-side eigenfunctions, φ n (r ,ω n ), define the induced potential of the eigenmodes, and the corresponding induced density ρ n (r ,ω n ) can be obtained as the left-hand-side (dual) eigenfunctions of the dielectric function. 31 In the case of larger and frequency-dependent damping, a more accurate approach is to use the eigenvalues of (r,r ,ω), denoted n (ω), and use the criterion…”

Plasmons in metallic monolayer and bilayer transition metal dichalcogenides

“…27. In the present work, the method has been used to analyze the plasmon excitations of the bilayer structure.…”