Bulk Excitations in single crystal Bi$_{2}$Se$_{3}$: Electron Energy Loss Spectroscopy Study

Bi$_{2}$Se$_{3}$ with larger figure of merit has been used in room-temperature thermoelectric applications. Furthermore, it is also one of a handful known topological insulators. Most of recent studies were focused on the topological surface states of Bi$_{2}$Se$_{3}$ while few of them studied the electronic excitations of bulk Bi$_{2}$Se$_{3}$. Here, we report studies of electronic excitations of single-crystal Bi$_{2}$Se$_{3}$ by electron energy-loss spectroscopy (EELS). EELS spectrum in bulk Bi$_{2}$Se$_{3}$ reveals several spectral features at $\sim $7, $\sim $16.8, $\sim $26.4 and $\sim $28.4 eV. The peaks at $\sim $26.4 and $\sim $28.4 eV are due to excitations from Bi 5$d$ electrons. The $\sim $7 and $\sim $16.8 eV peaks are easily identified as bulk-plasmon excitations according to the frequency-dependent complex dielectric function derived from experimental spectrum with Kramers-Kr\"onig analysis. Furthermore, momentum ($q)$-dependent EELS spectra along [110], [300] and [001] directions were also performed in this study. When momentum transfer $q$ is parallel [110] and [300] directions, the 16.8 eV-peak (bulk plasmon) significantly shift to higher energy (up to 23 eV) with increasing $q$ values, while this peak shifts less than 1 eV when momentum transfer $q$ is parallel to [001] direction, revealing the distinct anisotropy of bulk plasmon dispersions. Detailed characteristics of this anisotropic behavior will also be discussed.