Plasmons on the edge of ${\mathrm{MoS}}_2$ nanostructures

Using ab initio calculations we predict the existence of one-dimensional (1D), atomically confined plasmons at the edges of a zigzag ${\mathrm{MoS}}_2$ nanoribbon. The strongest plasmon originates from a metallic edge state localized on the sulfur dimers decorating the Mo edge of the ribbon. A detailed analysis of the dielectric function reveals that the observed deviations from the ideal 1D plasmon behavior result from single-particle transitions between the metallic edge state and the valence and conduction bands of the ${\mathrm{MoS}}_2$ sheet. The Mo and S edges of the ribbon are clearly distinguishable in calculated spatially resolved electron energy loss spectrum owing to the different plasmonic properties of the two edges. The edge plasmons could potentially be utilized for tuning the photocatalytic activity of ${\mathrm{MoS}}_2$ nanoparticles.

Figure 1

Induced electric potential of the three plasmon eigenmodes at $q=0.2{\AA }^{-1}$, calculated as the eigenvectors of ${\epsilon }_q(\mathbf{r},{\mathbf{r}}^{\prime },\omega )$. The structure of the ribbon is shown in front view, with the ribbon running into the plane of the page. The Mo and S edge, covered by sulfur dimers, is found to the right and left of the ribbon, respectively.

Figure 2

(a) Electronic band structure revealing three metallic edge states (I–III). (b) The three eigenvalues for the dielectric matrix fulfilling $\mathrm{Re}{\epsilon }_n(q,\omega )=0$ plotted for $q=0.06{\AA }^{-1}$. The color (red, blue, green) illustrates the one-to-one connection between the electronic bands and the plasmon eigenmodes.

Figure 3

(a) Energy dispersion of the three edge plasmons, showing plasmon energy (dots) as well as intraband transitions (dashed lines). The dot size indicates the plasmon weight, defined as the integral over the loss peak. The gray contours map the regions of single-particle transitions, which contribute to the damping of the plasmons. (b) Comparison of the dispersion of the S-dimer plasmon to the undamped intraband mode obtained by only including the metallic state (III) in the response calculation. The inset shows the evolution of plasmon weight with $q$ for the undamped and the full calculation. A 1D RPA model valid at low $q$, identical to the Tamonaga-Luttinger result, has been fitted to the intraband results.

Figure 4

Spatially resolved electron energy loss spectrum calculated for two different values of momentum transfer, $q_x$. We observe a strong signal associated with the S-dimer plasmon at the Mo edge, while the two other plasmon modes give a weaker response. At low momentum transfers, the signal is less localized due to the long range of the Coulomb potential.