Anomalous Acoustic Plasmon Mode from Topologically Protected States

Plasmons, the collective excitations of electrons in the bulk or at the surface, play an important role in the properties of materials, and have generated the field of “plasmonics.” We report the observation of a highly unusual acoustic plasmon mode on the surface of a three-dimensional topological insulator (TI) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, using momentum resolved inelastic electron scattering. In sharp contrast to ordinary plasmon modes, this mode exhibits almost linear dispersion into the second Brillouin zone and remains prominent with remarkably weak damping not seen in any other systems. This behavior must be associated with the inherent robustness of the electrons in the TI surface state, so that not only the surface Dirac states but also their collective excitations are topologically protected. On the other hand, this mode has much smaller energy dispersion than expected from a continuous media excitation picture, which can be attributed to the strong coupling with surface phonons.

Figure 1

Experimental results of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (0001). (a) LEED pattern of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (0001) surface with incident energy of 80 eV at room temperature. The red dashed line is the first BZ of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (0001), and the red dots show the high-symmetry points. (b) The band structure along the $\overline{M}-\overline{\mathrm{\Gamma }}-\overline{M}$ direction measured by ARPES at 35 K, which shows the coexistence of the bulk conducting band and the $V$-shaped surface Dirac state. (c) 2D energy-momentum mapping of HREELS along the $\overline{\mathrm{\Gamma }}-\overline{K}$ direction with incident energy of 60 eV and (d) along the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction with incident energy of 110 eV. Four collective modes with energy loss features are labeled by $\alpha$, OP, $\gamma$, and $\zeta$, respectively. The gray dashed lines are provided to guide to eye. The corresponding negative energy loss features are antistocks peaks of $\alpha$, OP modes, respectively, which are labeled by ${\alpha }^{\prime }$, ${\mathrm{O}\mathrm{P}}^{\prime }$. (e) EDCs at $\overline{\mathrm{\Gamma }}$, $\overline{K}$, and $\overline{M}$ with the corresponding energy loss peaks labeled. (f) and (g) The second derivative image of (c) and (d), respectively, with elastic background removed.

Figure 2

Experimental results of Mn-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (0001). (a) 2D energy-momentum mapping of HREELS measurements along the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction with the incident energy of 110 eV at room temperature. Four collective modes with energy loss features are labeled by AP, OP, $\gamma$, and $\zeta$ mode, respectively. The gray dashed lines are provided to guide to eye. The corresponding negative energy loss features are antistocks peaks of AP, OP modes, respectively, which are labeled by ${\mathrm{A}\mathrm{P}}^{\prime }$, ${\mathrm{O}\mathrm{P}}^{\prime }$. The inset is the band structure along the $\overline{M}-\overline{\mathrm{\Gamma }}-\overline{M}$ direction measured by ARPES at 35 K, which shows that the $V$-shaped surface Dirac state disappears because of magnetic doping. (b) EDCs at $\overline{\mathrm{\Gamma }}$ and $\overline{M}$ with corresponding energy loss peaks labeled. (c) The second derivative image of (a).

Figure 3

Characteristics of the $\alpha$ plasmon mode. (a) The dispersions of the $\alpha$ mode, OP mode of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, and the AP mode of Mn-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. The dispersions of theoretically predicted Dirac plasmon and spin-plasmon are calculated by simply extrapolating the momentum range of the equations in Refs. [33] and [15], and plotted as black and green dashed lines, respectively. The shaded zones label the EHPC of massless Dirac electrons and normal bulk conducting electrons. (b) The enlarged EHPC of massless Dirac electrons in an extended energy range. (c) The normalized intensity and (d) FWHM of the $\alpha$ mode of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ with different incident energies. The shaded zones illustrate the EHPC of Dirac surface electrons and normal bulk conducting electrons, respectively. The normalized intensity and FWHM of the bulk plasmon ($\zeta$ mode) of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ are also plotted for comparison.