Interplay of Surface and Dirac Plasmons in Topological Insulators: The Case of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

We have investigated plasmonic excitations at the surface of ${\mathrm{Bi}}_2{\mathrm{Se}}_3(0001)$ via high-resolution electron energy loss spectroscopy. For low parallel momentum transfer $q_{\parallel }$, the loss spectrum shows a distinctive feature peaked at 104 meV. This mode varies weakly with $q_{\parallel }$. The behavior of its intensity as a function of primary energy and scattering angle indicates that it is a surface plasmon. At larger momenta ($q_{\parallel }\sim 0.04{\AA }^{-1}$), an additional peak, attributed to the Dirac plasmon, becomes clearly defined in the loss spectrum. Momentum-resolved loss spectra provide evidence of the mutual interaction between the surface plasmon and the Dirac plasmon of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. The proposed theoretical model accounting for the coexistence of three-dimensional doping electrons and two-dimensional Dirac fermions accurately represents the experimental observations. The results reveal novel routes for engineering plasmonic devices based on topological insulators.

Figure 1

(a) HREELS spectra measured for ${\mathrm{Bi}}_2{\mathrm{Se}}_3(0001)$ at various primary electron beam energies. The spectra were measured in specular geometry, with an incident angle of 55° with respect to the sample normal. (b) HREELS spectra measured for various scattering geometries, for specular conditions (angles are measured with respect to the normal to the surface). The primary electron beam energy is 25 eV.

Figure 2

(a) Momentum-resolved HREELS spectra. (b) After background subtraction, the raw HREELS spectrum recorded for $q_{\parallel }=0.09{\AA }^{-1}$ (top spectrum) has been fitted with two Gaussian line shapes (bottom spectrum). The primary electron beam energy is 25 eV.

Figure 3

(a) Coupled surface and Dirac plasmon dispersion relation measured on a ${\mathrm{Bi}}_2{\mathrm{Se}}_3(0001)$ surface. Green diamonds indicate peak positions when a two-peak fit is applied to the experimental spectrum. The intensity plot exhibits the surface-loss function calculated for the two-component system (jellium and Dirac fermions). (b) Surface plasmon dispersion obtained for a single-component jellium model. (c) Dirac plasmon dispersion in a separate 2D Dirac electron system formed by surface-state electrons. Inset: Sketch of the modeled surface electronic structure of bismuth selenide.